Theory in Ocean Dynamics

Peter B. Rhines

University of Washington

INTRODUCTION

This is a brief review of theory in oceanography, where:

* theory is constantly changing in character and subject, yet effectively canonizes the principles of our subject, and provides for their teaching and transmission into the future;
* it is characterized by surprise and simplicity: the discovery of surprising relationships among known physical quantities of interest, or the definition of new quantities never anticipated, and new relationships that in some way are simple and economical. A key role of theory is in defining new descriptive field variables that are measurable, and in discovering idealized yet complex events like baroclinic instability, that then can be used as a 'meta-language'.
* the balance of abstract 'discovery-driven' science and pressing applications is changing, and should change;
* ocean theory (practiced by 'full-time' theoreticians) has lost its 'voice' in the larger oceanographic community, and despite its high quality fails as yet to unify itself with atmospheric sciences, its most natural ally.
* yet, it is alive and well as 'part-time' theory in combination with numerical modelling and analysis of observations. It is also particularly vital in new interdisciplinary work, in climate research, but also in planetary physics and the wider branches of physics. Physical theory of the 1970s and 1980s is now settling into the minds of the ocean community;
* global computer linkages are altering every aspect of science, including theory;
* there is an unspoken relationship of successful science with power, influence and money in society, which affects the long-term success of a scientific subject or technique.
* theory is part of the venture capital of oceanography, just as the core program at NSF is a form of venture capital.

When still photography was invented (by Joseph-Nicephore Nie'pce, a collaborator with Daguerre, in 1826) it soon became so popular that it was expected to mark the end of drawing and painting. Instead, photography made artists honest, requiring more of them than mere representation. Somewhat the same relationship holds between computer modelling and theory. While vastly more resources are poured into computer simulation than into theory, we see that mathematical analysis is alive and well. Indeed, it forms the basis of our teaching programs, and the mode of transmission to our students of the principles of oceans and atmospheres. Simplicity is (or should be) the object of scientific work; for the results of an NSF grant to be effective they must be both simple, powerful, and communicable. Theory, and its applications in observational work and numerical modelling, provide us with hope for simplicity. Without it, at least as an organizing principle if not as detailed 'prediction', we are left with a hopeless morass of detail, and become idiot savants reeling off accurate but unorganized masses of factual detail.
The time required for theoretical work to be distilled into its ultimate form can be long, however. The chaos revolution spurred by Lorentz's equations, essentially a product of geophysical fluid dynamics (GFD), is still working its way through science and society (if one doubts its impact, a trip to see the play Arcadia, by Tom Stoppard, is recommended).

DETAILED PROBLEM AREAS

The daunting task of summarizing all this in a brief paper leads me to pick out a few topics from both lists, at the expense of the majority.

OCEAN MIXED LAYER

The double turbulent boundary layers through which the ocean and atmosphere communicate. Classical models begin with the Ekman layer, still a viable object because of its robust (integral) independence from the detailed turbulent stress. The Krauss-Turner process of 'solving' the energy equation with assumed dependence of energy dissipation and mixing on the surface stress led to the most widely used models, particularly after later inclusion of bulk momentum dynamics. More detai led attempts at modelling effects of fully developed turbulence have led to more complex mixed-layer models, and a generation of 'large-eddy-simulation' models. Here and in the atmospheric boundary layer community the power of theory seems not up to the task of relating fluxes of heat, momentum, tracers to their mean gradients, given the variety of environments in which boundary layers occur. Important observations of mixed-layer structure made in the 1980s began to 'test' or 'calibrate' the models, and emphasized the importance of time-dependence, including diurnal heating effects on stability. The difficulties of turbulence have been soothed, at least, by direct turbulence measurement. But of greater importance was the discovery or rediscovery of dis tinct events in the mixed layer, particularly Langmuir roll vortices aligned with the wind. Innovative observations of bubble clouds with acoustic imaging, and 3-dimensional Lagrangian particle histories with floats, in company with a series of theories involving surface-wave/mean flow interaction and with laboratory experiments in wave flumes, have led to significant advances. Key elements of the Craik-Leibovitch theory of their generation appear to be present, yet with important contributions from wave -breaking.
Theory has moved on, in other directions, by taking more seriously the large-scale environment in which the boundary layers are embedded. Stable density stratification and convection, and time-dependent forcing produce a new set of constraints. We see 'Ekman demon' interaction of downward pumping by wind-stress and seasonal mixing and a family of calculations trying to relate water-mass creation to surface boundary conditions ('warm', subtropical- and 'cold', subpolar subduction). A group of 'geostrophic adjustment' theories, developed after the pattern of Rossby's original calculations, add vital time-dependence. The study of sharp density fronts begun in atmospheric sciences is found to have many applications in the oceanic mixed layer: determining for example whether lateral wind-driven Ekman transport remains at the surface or is channeled to the interior when it encounters a front. These are familiar lessons of oceanographic theory: we cannot and should not wait for a 'theory of turbulence' before working on the many aspects of theory of the communication of the mixed layer and the geostrophic interior. Often, by proceeding with a GFD problem with new physical effects added, one can circumscribe and perhaps avoid the missing elements of turbulence.
The original goal of mixed layer research was to take known wind-stress, air-sea heat flux and precipitation-evaporation, and cast them as boundary conditions for some sort of simplified interior circulation (while also producing a prediction of mixed- layer depth and properties over time). Observationally we now see how ignorant we are of the fresh-water cycle, globally and locally, even though its buoyancy is comparable with (sometimes far exceeding) that due to heat; and, lacking the atmospheric feed back of thermal buoyancy, fresh-water anomalies are advected much greater distances round the circulation. We see more clearly the diversity of upper-oceanography, and theory has been important in making this transition. The 'known' atmosphere is of course being abandoned in favor of some level of interactive ocean/atmosphere. Most ENSO models use a bare minimum of ocean, often just the mixed layer, and yet these have already produced tentative theory for a coupled-oscillator ENSO which combines significant long-wave propagation with mixed-layer dynamics. Conversely, high-latitude ocean response to the North Atlantic Oscillation is being modelled using a minimalist's model of the atmospheric boundary layer.
The process of buoyant convection has long been a dominant sub-field in atmospheric sciences, but is only recently emerging in oceanography. While it has long been known to occur as part of the mixed layer, 'convective adjustment' models, slab response obeying bulk thermodynamics, were thought a sufficient description. The dynamics of convection explored at some of the more dramatic sites (Mediterranean, Greenland Sea, Labrador Sea) has however improved our appreciation of the process. The very high Rayleigh numbers put us well beyond marginal stability, so that the oceanic case has relied more on numerical and laboratory modelling, plus dimensional analysis. Yet one feels that early theoretical description of the effects of rotation, and its strange constraints on cyclonic and anticyclonic components, were a useful guide to large-amplitude yet small diameter (100 to 1000m) plumes. The full force of the nonlinear equation of state, through cabbelling and thermobaric instability, is found to be essential at higher latitudes. An essential part of the evolution is the rapid generation of mesoscale (10 to 100 km-scale) energy, seemingly an elaboration of the rapid increase in lateral scale in geostrophic turbulence (which was essentially a theoretical prediction).

INTERNAL WAVES, INSTABILITY, OCEAN MIXING

Internal wave research reached a feverish pitch in the 1970s as an appreciation for the spectrum of observed waves was gained, and weak interaction theory produced useful results about the production of turbulent mixing, and induction of mean currents. The theory of critical-layer absorption and reflection (where the mean flow speed U equals the phase speed, c, of the wave in the direction of mean flow) showed us how such interactions can also be 'strong', and localized in space. Generally, the power of geometrical optics (ray theory) was demonstrated in wholly new classes of problems. Attention then drifted toward nonlinear waves that are outside of the random-phase approximation of triad interaction theory: solitary waves and undular bores for example. Inverse-scattering theory allowed one to trace uniquely the distribution of solitons emerging from complex initial conditions. This gives one of many examples where a significant GFD discovery ( here traceable back to Scott-Russell riding along canals in Victorian England on horseback ) radiated outward into many areas of physics and engineering. (The discovery that solitons in fiber-optics cables travel farther than small-amplitude signals may lead to $G savings in communications.)
One was impressed how here and in atmospheric sciences very basic discoveries were being made even at the level of nearly linear wave propagation: conservation of wave action; variational principles and Hamiltonian structure of waves and mean flows; critical layers; advanced calculations of a spectrum of triads of interacting waves, formulation of wave/mean-flow interaction resulting in clear appreciation for both the driving force and the role of Coriolis effects in limiting and altering the response (i.e., the forcing of the mean circulation). Immediate, powerful results include the understanding of rectified flows round seamounts and banks, and the quasi-biennial oscillation of the equatorial stratosphere. Simplicity: conservation of the quantity E/c where E is wave energy and c the wave's phase speed relative to the (possibly sheared) mean flow. This expresses the basic momentum transport in waves, and their driving of the time-averaged Eulerian mean flow. E/c is known as 'pseudo-momentum', or wave-action times wavenumber in the direction of the mean flow, or wave enstrophy/mean potential vorticity gradient in the case of large-scale quasi-geostrophic flow. Here GFD becomes a little like particle physics.
Internal waves seem to play very different roles in ocean and atmosphere: transporting momentum in the latter, and mixing T and S in the former. Mountain-wave drag is now routinely parameterized in atmospheric gcm's, the pressure force on the mountain slopes producing a zonal acceleration high in the atmosphere where wave breaking or critical layers occur.
On the way to ocean mixing we encounter flow instability, a vast theoretical subject in itself. The oceans and atmosphere are nearly everywhere turbulent. We can view this turbulence as continuing bouts of flow instability. In GFD the effects of stratification, rotation and beta enrich the subject, and several alternative definitions of instability arise (making it less than an 'obvious' concept): normal Fourier modes whose growth is exponential in time; a Lagrangian definition by G.I.Taylor, expressing instability as a growth of rms particle displacements; alternate non-normal modes known as 'shear transients' which do not grow exponentially, but grow algebraically before decaying. These lead to a definition of 'optimal' modes of instability, initial conditions back-tilted relative to the mean shear that give the biggest bang over short or moderate times, and can be viewed as E/c conserving modes moving away from their critical lines; finally, generalizations to non-parallel flows and finite amplitude disturbances (particularly by V.I. Arnold). Instability criteria appear as statements of global momentum conservation, relating to translational symmetries in the Hamiltonian description of small disturbances.
Ocean mixing has implicitly used theory to relate observable small-scale velocity gradients with, first, turbulent energy dissipation and, second, turbulent mixing coefficients for temperature/salinity. But at a higher level, weak wave interaction theory has also been developed to connect the level of 10m vertical shear of horizontal velocity (often inertial/tidal oscillations) to the turbulent mixing rates, and to predict topographic generation patterns. This exemplifies theory as an interpolator: bridging between observable waves and unobservable rates of mixing and mixing-induced mean diapycnal velocity. And there are surprises: theory predicts that a linear density stratification will break into a staircase of well-mixed layers separated by concen trated interfaces, either due to double diffusion or to small-scale turbulence, and it does so.
The problem of mixing near ocean boundaries has received attention ever since Walter Munk presented us with the paradox of mixing rates seemingly required to allow the general circulation to upwell abyssal water through the thermocline (at a rate which balanced the known sinking regions). Boundary mixing has generated interesting theory of many kinds, in which a schematic model of turbulence is used to infer secondary and tertiary flows that develop in response, including the successful quenching of the Ekman flux over a sloping bottom boundary. Of course a paradox ('the truth standing on its head') is often resolved by destroying its initial assumptions, and this begins to appear with the increasing signs of oceanic circulation rising as well as sinking at high latitude, where the potential energy barrier is weakest. But, finally, successful deep measurements of turbulent dissipation have appeared which now associate strong dissipation regions with the rough flanks of ocean ridges, and give us a new geography for our abyssal recipes. Theory needs sustenance, in the form of well paced observations, otherwise it runs eventually runs down.

TURBULENCE, VORTICITY, POTENTIAL VORTICITY

Geostrophic turbulence studies in the late 1960s combined similarity arguments, integral constraints (enstrophy- and energy conservation) and direct numerical simulation. This is a good example of adaptation of theory to use new tools, with numerical models providing more direct 'measurements' than laboratory simulation has been capable of. The dominant energy-containing eddies in ocean and atmosphere evolve according to cycles of potential-energy release (the large-amplitude, perhaps turbulent, version of baroclinic instability), expansion of lateral scale, and cascade into the barotropic mode. This sequence, derived from theory and since christened the 'life cycle of baroclinic instability' by meteorologists, is at work widely in oceans and atmosphere. Solitary eddies may arise spontaneously. In the geophysical setting with beta-effect, topography, and mean circulation we see the entstrophy/energy cascade driving zonal jets (as on Jupiter). Thus, rather as a small-scale stratified fluid 'breaks' into layers when stirred homogeneously, so does a beta-plane fluid break into zonal jets often with step-like potential vorticity.
Inviscid 'form-'drag transmits horizontal momentum laterally and also vertically, giving almost instaneous communication of momentum vertically across wavy isopycnal surfaces. Bottom topography tends to exert westward forces on the fluid in this way. Baroclinic instability is an example of such a process of 'spinning up' the deep ocean.
These ideas describe the 'fabric' of large-scale rotating, stratified fluids. Theory's ability to simplify, summarize and transmit ideas is crucial. The vorticity equation (for constant-density, incompressible fluid), is

D(omega sub a)/Dt = (omega sub a dot grad)u + nu Lapl(omega sub a) = chsi sub ij omega sub a,j) + nu Lapl(omega sub a)

where omega sub a is the absolute vorticity, 2 cap omega + 2 omega, omega = curl(u)is the vorticity, cap omega the Earth's rotation vector, and chsi sub ij is the rate-of-strain tensor and D/Dt is time-rate of change following the fluid. It leads directly to the idea of vortex lines which are also ma terial lines (like 'dye' lines marked in the fluid) whose strength ((a times area of a marked fluid disk normal (a) is conserved as they are advected, tipped, and stretched by the flow. Together with the identity that kinetic energy in an unbounded fluid dissipates at a rate

nu int int int |omega|^2 dV.

This property shows how energy dissipation can occur so rapidly in a turbulent fluid, and its connection with the increase in length of marked fluid lines.
With density stratification, the component of vortex tube strength normal to the potential-density (sigma-) surfaces remains conserved, since buoyancy twisting cannot act in that plane. This gives us the conservation of potential vorticity,

Dq/Dt = 0 + external mechanical forcing/unresolved mixing + external buoyancy forcing/mixing - dissipation where q = ro^-1 omega sub a dot grad sigma or, identically ro q = del dot (omega sub a sigma),

the latter expression emphasizing the possibility for robust conservation of the volume integrated potential vorticity ('pv' or 'povorty', perhaps would be a catchy new name, suggesting our funding situation).
The remarkable thing about Ertel's and Rossby's pv is that it is both conserved following the motion of an idealized (non-diffusive, unforced) fluid parcel, and it can be inverted to describe much of the velocity and perturbation density fields of the fluid (remembering that important zero-pv objects like equatorial Kelvin waves are invisible to that analysis). Unfortunately this does not solve the age-old 'reference level' problem for converting hydrography into velocity, since the boundary conditions for the pv inversion are not known in that case.
Closure parameterizations and 'large-eddy simulations' attempt to provide theories of the energy containing eddies (their spectra and turbulent fluxes). The work is technically challenging, and has tended to develop on its own, without great interactio n with the rest of the field. A surprise: pv changes only due to the divergence of a vector flux, even in the presence of mixing and external mechanical stress, and pv fluxed in this way cannot cross isopycnal surfaces.

ROSSBY WAVES, WIND-DRIVEN CIRCULATION, BOUNDARY CURRENTS

As with internal waves, theory of large-scale waves and ocean circulation saw spurts of activity in the 1950s/60s and again in the early 1980s. The Sverdrup vorticity balance, beta v = f delta w/delta z, itself is remarkable in its generality and simplicity. It tells us that stiffness imparted to a large-scale fluid by planetary rotation leads to conservation of the separation of marked fluid surfaces measured parallel with the rotation vector, cap omega; again, in spite of small-scale mixing, buoyancy twisting and mesoscale eddies of observed intensity.
Perhaps the biggest paradigm shift was from the steady theories of Sverdrup/Stommel interior and boundary currents to the case of evolving or continually time-dependent oceans. Spin-up of the circulation from rest occurs with a whole ensemble of waves carrying information of the forcing, through the fluid interior. Even if one's interest is in the end-product, a steady circulation, spin-up establishes cause-and-effect relations. The large-scale structure of pv imparted by Earth's sphericity and topography provides the elastic restoring effect for Rossby waves (though in the important class of long baroclinic waves the fluid avoids conflict with this stiffness, by vertical stretching). Rossby waves, both barotropic and baroclinic, were first conclusively observed in the 1973 MODE experiment in the western Sargasso Sea, and the satellite altimeter measurements now give us a dramatic view of the gravest baroclinic mode (which tends to dominate the sea-surface elevation). The Rossby wave becomes the model for wave motions in many kinds of flows with vorticity gradients. Baroclinic instability is a delicately orchestrated interaction between two Rossby waves, separated by the steering level where U=c, which become locked together and feed back positively. Theory can be carried to the weakly nonlinear stage in which zonal flow and waves execute an intricate, slow set of interactions. Ideas like these, Rossby waves and baroclinic instability, become a form of 'meta-language', to use Joe Pedlosky's term. They are rather complex events, yet once appreciated they become objects in our mental landscape, which combine into a view of the complete ocean system.
The presence of the large-scale pv gradient (due to beta, topography, mean currents) allows theory to describe much more about the downward transmission of horizontal momentum by eddies (through inviscid pressure drag), than was the case in geostrophically turbulent fields of eddies. Vertical flux of horizontal momentum now appears as a direct consequence of the lateral stirring of the moderate- or large-scale field of pv. This mechanism for spinning up the deep ocean (and correspondingly, the lower atmosphere) has been supported by direct mooring observations of pv fluxes in the deep inertial recirculations of the North Atlantic.
Ocean circulation theory advanced when it was realized that the modification of the contours of constant potential vorticity (away from simple latitude circles) by the circulation was the central effect: pv is a tracer that distorts itself. The development of baroclinic wind-driven circulation theory was spurred by what could be called the 'Anderson-Gill catastrophe'. When a wind stress is switched on over a resting ocean, barotropic Rossby waves quickly (days to weeks) set up the deep-reaching baro tropic mode, and its attendant western boundary currents. Then, gradually, successive baroclinic modes work westward, instilling the conditions from the eastern boundary. Each successive mode arrival concentrates the horizontal velocity more sharply in th e upper ocean, until under linear theory, U(z) is a delta function just beneath the mixed layer. It was this unhappy result of trying to generalize Anderson and Gill's 2-layer model to many layers, that led the search for more realistic solutions, incorporating the nonlinear shaping of the pv field by the circulation itself. The solutions involve both direct ventilation, in which pv values established by mixed layer dynamics are advected downward into the geostrophic interior, and stronger eddy stirring of pv. The development of general circulation is a competition between 'warm' and 'cold' subduction of high- and low-pv at the surface, injection of predominantly high pv from the sea-floor, and internal pv mixing and widespread homogenization by mesoscale eddies.
A long historical memory within the theoretical community helps us with ocean dynamics calculations: vorticity is produced near boundaries in a classical non-rotating flow past a cylinder, and it can fill a huge volume of what would otherwise be irrotational flow. Now we begin to see potential vorticity being stripped from 'reservoirs' at boundaries (wherever potential density surfaces intersect the boundary because one or the other is sloped relative to the horizon). Boundary sources can color the pv of the entire interior of model-, and perhaps real, oceans. There is a continuum of problems, from the classical flows round bluff bodies, to non-rotating, stratified flow over and around hills, to the rotating f- and beta-plane cases at large scale. Dis covering the modes of vorticity and pv production represents an important and very broad challenge to gfd.
The role of the major oceanic boundary currents is as yet unresolved; there are many theoretical models, beginning with Stommel's classic solutions. It is a problem awaiting a decisive set of observations, which will determine how pv, salinity, potential temperature and other tracers survive the journey through these 'pipes'. Neutrally buoyant floats with hydrography have already shown the dual role of the Gulf Stream as 'barrier' (near the surface) and 'blender' (at depth).
At this point we have to point out an indirect product of theory, in defining new quantities that are measurable, mappable, and interesting. Regardless of the correctness of specific theoretical models, they awakened us to the pivotal role of pv in dyna mics, and led to mapping of observed pv on isopycnal surfaces. The richness of these maps of dynamically active tracer is independent support for its importance. Stratospheric pv is mostly relative vorticity, even though baroclinic Rossby waves tickle it from below. Large-scale (>50 km) oceanic pv is mostly 'stretching', or isopycnal layer thickness, measured parallel to the Earth's rotation vector. Both are readily observed with modern measurements. Other examples of 'new, measurable, interesting fields' like helicity and knottedness of vortex lines await. There is more to theory than mere prediction!

DECADAL CLIMATE

Even greater attention to time-dependent circulation has been stimulated by observations of climate variability. Over decades to centuries the shifts involve propagation of Rossby waves (fast barotropic, slower baroclinic, and 'generalized' Rossby waves in shear), together with topographic waves and Kelvin waves, and more advective changes in general circulation. Communication with the tropics along meridional boundaries suggests that the usual zeroing of the circulation at eastern boundaries should be abandoned, for purposes of calculating the developing extratropical circulation. Indeed, there are already signs that 'distant el Nino signals' may reach the extratropics through the ocean waveguide. Theory of Rossby waves in realistic m ean circulations is incomplete as yet, though this wave/mean flow interaction is a key to the idealized theories indicated above.
Impacts on observational work of Rossby-wave theory have been great, though more to date in atmospheric sciences than oceanography. In fact, in the atmosphere we have seen wave/mean flow interaction theory explain two of the most dramatic transient e vents: the Quasi-biennial (~26-month) Oscillation (QBO) of the zonal wind in the equatorial stratosphere and the Stratospheric Sudden Warming, in which the cyclonic wintertime polar vortex is suddenly braked by upward propagating Rossby waves. It might be said that the atmospheric community did not take wave/mean flow theory of the QBO at all seriously until it was demonstrated in the simple laboratory experiment of Plumb and McEwan. Generalized Rossby wave theory is the key to understanding baroclinic and barotropic instability, and their application to the atmospheric general circulation. Note that in this example the intrinsic wave period is much shorter than the time-scale of the circulation change, whose change is a cumulative effect of wave pv-flux. (This warns against the facile argument that the ocean must be important to decadal climate, because the atmosphere has no long-period memory.)
With our local Ford dealer offering el Nino specials this week, among deluges of rain that would normally hit Seattle, being diverted to Southern California, we bring up the area of ENSO (el Nino/Southern Oscillation) research, and more widely, the importance of global decadal climate change in the interacting oceans and atmosphere. We have seen Atlantic hurricanes change in frequency and intensity, plentiful in the 1930s-50s, scarce in late 50s-80s, and once again plentiful and intense in the 1990s. Given that a direct hit of a major hurricane on Miami might cost us G$100, this is clearly an area of importance to oceanography. Even more terrible, storm surges on the low-lying lands of Bangaladesh have cost hundreds of thousands of lives in recent years, and these events are sensitive both to climate trends of storm intensity, and to the gradual, global-warming induced rise of sea-level. ENSO represents an area where fairly simple theoretical models, built into minimal numerical models, have produced credible prediction over periods of 6 months or so. Whether the delayed-oscillator theory has validity in the presence of porous western boundary is less certain. Large international institutes have been built, and generally the world is anxious over something that, when it occurred in 1956, interested only a few Scripps oceanographers (judging from Henry Stommel's notes from a meeting held at the Inn at Rancho Santa Fe). Currently we are experiencing the strongest el Nino on record, and its di stant signals are eagerly awaited.
This is a remarkable example of the role of sheer power in our research: power to describe the state of our environment, or to predict into the future. It has happened as a focus of three elements: the largest in situ ocean observation network ever created (the TOGA-TAU array), the timely occurrence of repeated, intense el Ninos since 1976, and a 'locally' successful delayed oscillator theory of ENSO. Clearly, the high wave-speeds of equatorial Kelvin- and Rossby waves, plus the relative success of simple feedback parameteriz ations, has led to a some success of theory, with direct practical application to the environment. God is subtle, however, and we have not seen the last word of this theory. The possibility that greenhouse warming is being 'expressed' through ENSO and the North Atlantic Oscillation, is exciting.
Indeed, the wild behavior of the Southern Oscillation Index and the North Atlantic Oscillation index during the past 25 years suggests more than a local tropical interaction. One is reminded of Simmons and Branstator demonstration that weak barotropic instability of the northern hemisphere westerly winds tends to favor certain sites for strong PNA response to the el Nino sea-surface temperature pattern. These instabilities are difficult to see because of all the synoptic-scale baroclinic instability going on, but the standing-wave pattern of the hemisphere gives strong geographical preference to the (generalized, unstable) Rossby-wave response of the atmosphere.

MERIDIONAL OVERTURNING, DEEP CIRCULATION

It would be exaggeration to say that pv rules everything. Excessive concentration on physical dynamics tends to make us ignore thermodynamics, heat-salt-ice dynamics, and particularly the nature of the fresh-water cycle. The up-down/north-south movement of ocean water involves new and difficult effects of mixing and even exotica like the geothermal seafloor heat source. Theories of the deep, overturning circulation evolved in the 1950s, in a sort of natural progression that many of us have followed, from wind-driven, super-thermocline- to thermohaline, deep circulation. At first the Stommel-Arons work centered on the broad, slow upwelling required by one-dimensional heat balance models with surface downward heat flux. Sinking regions were placed judiciously, with a sense that their locations were incidental. One of the strongest theoretical ideas was simply that the nature of forcing by buoyancy flux at the surface favors very small sinking regions, with upwel ling almost everywhere. Similarity theory of the thermocline provided guidance and predictions of the buoyancy field while pv constraints filled in the lateral circulation. Unfortunately these 'theories of everything' could not readily cope with the co mplex of dynamical regimes that probably exist in the deep circulation.
The late Pierre Welander published (in Tellus, 1959) alongside a Stommel-Robinson paper on the diffusive thermocline, a radical proposal that the thermocline is instead advective, and that a vertical advective/diffusive buoyancy balance is not required . Deep water need not rise through the tropical/subtropical thermocline, with diffusive and vertically advective heat-flux divergence in balance (note that one-dimensional thermocline does not say that vertical advection of heat balances vertical diffusi on of heat, as one often reads! It is a continuing nuisance that one cannot define an 'absolute', vector, advective + diffusive heat flux field uniquely, owing to the non-unique reference value for temperature). Science is not a democratic process in which victory is decided at each step by majority vote, and despite persistent energy applied in advocacy of the diffusive thermocline, it now appears that Welander's imagination may have been correct: the small diapycnal diffusivity in mid-ocean (excepting rough topographies) seems to favor a deep circulation that glides upward without crossing potential density surfaces, in search of (perhaps high-latitude, 'low-energy-penalty') sites at which to return to the surface.
Once it was thought that mixing, circulation and baroclinic Rossby wave speeds in the deep mid-ocean regions were all so slow that the spin-up of the ocean under a changing atmospheric climate would take thousands of years. However the topographic wav eguides at the ocean margins provide fast pathways for response to climate change, and the chilling down of the subpolar Atlantic during the past 25 years has sent both information and tracer-marked waters to the Equator, with lag times of only a few years. The meridional, thermohaline circulation has seen great activity from a community of numerical modellers, generally running coarse-resolution Cox-Bryan models. Much of this activity stems from Stommel's 1961 box model, and Claes Rooth's development of it: theory of the simplest kind which plays off the competing buoyancy sources of heat-flux and fresh-water/salt/ice. I find it worrisome that so little attention is given by the T/S oscillator community to issues of fluid dynamics. At low resolution, key features of sinking regions, deep convection, western boundary currents and fronts are difficult to relate to real fluid behavior. The kind of numerical catastrophe represented by the Veronis effect (the artificial diapycnal diffusion that occurs with Cartesian diffusion in the presence of steeply sloping buoyancy field) produced misleading circulations that were masked by zonal averaging of the overturning circulation (for the 25 years since its presentation at the Durham, N.H. ocean meeting in 1972, coincidentally the year of the return of strong wintertime forcing to the subpolar Atlantic). The splitting off of the numerical and theoretical community is largely to blame for this.
Fortunately, there is great activity, a kind of new-age theoretical work, aimed at improving the ragged corners of numerical circulation models, for example incorporating the 'bolus flux' of baroclinic eddy fields as a mixing tool, and building isopycnal eddy-incorporating analysis into calculations of meridional circulation from model fields. Research into ocean mixing, boundary layers great and small (benthic, surface, western), deep convection, high-latitude heat/salt/ice interactions all serve this end, and yet are respectable science in their own right.
Deep ocean convection, also on this fix-it list, is currently under active study in the Labrador Sea. Here the activity is dominated by observations, lab- and numerical models and scale-analysis. The classical theory of convection and convection with ro tation is occasionally alluded to but one feels here a disjointness and loss of solid results obtained by Fultz, Hide, Nakagawa, Frenzen, Kuo, Veronis, T.Rossby and others in the 1950s/60s. We are sometimes lazy about assimilating older works, which accu rately portrayed the smallness of rotating convection cells, and some aspects of their large-scale dynamics through baroclinic instability.

INVERSE CALCULATIONS

As a part of theory's growth and sophistication we find a large array of sophisticated data-analysis schemes, with a rigorous base of matrix algebra. If we had the synoptic data enjoyed by the atmospheric scientists, we would be deep in empirical orthogonal functions, cluster analysis, SVD analysis of pairs of fields, and indeed these techniques are in use on those fields that permit them. With a few global data sets, notably satellite altimetry, infrared SST, and scatterometer wind fields, we do have the opportunity to exercise the theory of spatial patterns. But below the top mm of the ocean, we are faced with very sparse observations which are fitted into typically under-constrained problems for mapping the observations themselves, or for converting one field (say density) into another (say velocity). Assimilation of observations into numerical models is a sophisticated approach to mapping and interpolation, used routinely by the weather community with atmospheric gcm's. The hybrid model/data product is a new field of play for theoreticians, and is very different from the usual forward, prognostic process of solving equations with natural, well-posed boundary conditions.

A BRIEF SURVEY OF THEORETICAL ACTIVITY

I note that the Journal of Physical Oceanography in 1979 averaged 33% theoretical articles, and 10% numerical modelling, and in 1996 about 25% theory and 30% numerical modelling. I had intended to write that theory was deeply on the wane, or had moved elsewhere, but this does not seem to be true. Yet in October 1996 JPO, of the 23 articles fully 19 use (or misuse, in the final entry) theory while 6 are full-fledged theory. Perhaps all the Woce people were out at sea the year before.
The primary measure of the effectiveness of theory is the extent to which it makes powerful discoveries, leads to useful activity by others in oceanography, and produces important applications that save lives or money, or at least inspire. I would stress, however that another important measure of the effectiveness of theory is the extent to which it radiates out into other fields. I have given some examples of this, and it is quite remarkable how many major fields of 'classical physics' arose in ocean/atmosphere theoretical dynamics. It has been enjoyable during the past year to go to meetings on plasma- and two-dimensional turbulence, complexity in the earth sciences, planetary atmospheric circulations, and geostrophic turbulence and find work that began in oceanography playing important roles.

LOSS OF VOICE

All the same, despite the successes of 'full-time' theory and its outward radiation into other fields, within physical oceanography it seems that the theoretical community is not now very visible. This is not in any way a criticism of the work: if anything the opposite. Either it has lost its 'voice' or the observationalists and circulation modellers have lost their 'hearing'. I am saying that much of the great activity in numerical general circulation modelling and the dramatically successful observa tional work, ignores true theory. In omitting theoretical understanding, some workers in these fields diminish their work just as surely as some theoreticians in the past diminished their work by ignoring observations. Institutionalizing this omission, large programs like Woce have widened the gap between theory and observation. Of course exceptions to this argument abound. There are growing theoretical branches of model/observation assimilation and dynamical parameterization, active ENSO theory/model/o bservation interplay, and such work gives us hope that the three communities may converge. We take heart also in the beginnings of 'straight physics' interactive modelling and theory, and note that this has been occurring in atmospheric sciences for some time.
Let me repeat: It is not ill will but the remarkable success of new-age observations and global gcms, taken separately, that has caused a wide gap.
A group of us at Woods Hole were long ago discussing why physical oceanographers seem to be such a friendly community, unlike a group of chemical oceanographers we had just seen trying to tear each other apart (verbally). It was suggested that that we physical oceanographers (unlike the 'chemists' we would never call ourselves 'physicists') agree on the basic principles of our subject, whereas all that 'chemists' agree upon is that the world is made of atoms.
Within our friendly community, however, there has always been a state of tension between theoreticians and everyone else. When I first arrived at Woods Hole in 1972 (for my 3d job in the field) I was branded a "d-v d-x'er", in jest of course. I realized I was nearly alone as a theoretician (there were few if any 'modellers' then) entering into a complicated environment where I might not survive. Some of the 'water-catchers' went out of their way to interact however, and I remember Bill Schmitz making a real effort to build a bridge between his current meter data and prevailing theories of eddies and circulation. But often it was a question of 'here's some real data, kid: explain it if you can'.
We were no less guilty however. A prominent theoretician speaking on nonlinear dynamics introduced his talk with an aged transparency showing the atmospheric circulation at some unspecified height; asked later in the talk if he had any examples from observations he replied, 'I showed a data slide, and if you've seen one, you've seen them all.'
There is a social hierarchy in science, where the engineer, naturalist, taxonomist is slighted by the theoretician, the theoretician is slighted by the applied mathematician, and the applied mathematician by the pure mathematician (one of whom, a Scottish house-mate of mine, once said that all the rest of us in the house were simply failed mathematicians). Henry Stommel once remarked on this arrogance, saying that many oceanographers, especially students, hold in awe those with more ability (or, often, experience mistaken for ability) at formal mathematics. It is easy for such theoreticians to slight a student's work, sometimes with only a simple remark, and in doing so they can do untold damage. To some extent, the growth of new forms of theory and the rise of numerical modelling has eclipsed this 'debate'. But it is worth keeping in mind as we ask how theory can recover its lost 'voice'.
The isolation of theoreticians from the rest of oceanography is more than anecdotal. They are small in number, and the hoped-for alliance of theory and numerical models has not occurred widely, as numerical modelers historically have had their own blinders on. If, indeed, physical oceanographers 'agree on basic principles' are these principles not basically statements of theory? Observationalists comment that oceanography is a 'data-driven' science where essentially all major discoveries are observational (this again is nearly a direct quote). I would favor a more balanced view in which theoretical ideas, observations, and simulations play a sort of game of leap-frog, advancing together. In what other field could you hope to teach a class on the theory of rotating thermal convection, then sit at a DECstation watching an animated numerical simulation of convection in a basin of fluid, then walk across the street to a GFD lab and see the same kind of convection marked by fluorescent dyes and tracked with a laser velocimeter, and the next day fly to Halifax to join a ship bound for the Labrador Sea in winter, to see with a remarkable set of new instruments wintertime convection reaching 2000m (on the airplane journey of course one has reviewed the hydrographic datasets on a laptop computer)? This is the joy of being a modern oceanographer: it is possible to lead several complementary lives, where others are confined to just one.

PREDICTIONS OF FUTURE THEORETICAL DISCOVERIES

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HOW OUR ACTIVITY WILL CHANGE IN THE NEXT 25 YEARS

Our environment has suddenly developed global computer interconnection. One negative effect of Internet communication I see is loss of diversity. Theory thrives on some degree of isolation in which ideas can develop before being made public. It is still a process of individual creativity. It leads to many strains of theory that can compete, rather than one 'Microsoft' decree. One reason I moved away from Woods Hole was that there was a tendency for so many bright minds all to cluster round the same qu estion. Theory also requires a kind of dedicated concentration that is sometimes difficult to maintain in the cacophony of computer technology. The commercialization of the technology of computing and communication seems aimed at infinite distraction thro ugh entertainment (see Daedalus quote, below). The discipline required to harness computing for good science can be found, though many have fooled themselves about the productivity gains from this machinery.
On the positive side, the Internet gives us the possibility of finding our soul-mates across the world, for we are a small, almost sub-critical activity. Perhaps we can then find our lost 'voice', which the cacophony of exciting computing and grand n ew ocean observations seems to have drowned out.
There are other, clear changes in our field that are coming or already are upon us. We see in the book-shops many 'popular' hard-cover products of science...the high science of evolution, molecular biology, cosmology. Oceanography has had its Cousteau and Ballard excitements, all to the good I would say. But now we are embarking on a more serious voyage of publicity, involving global climate change, and its impacts on life on Earth.
Some of the dominant themes currently are:
plus, the more immediate questions:
High-science activities are developing in the context of major changes in life on Earth, in brief, the 'end of Nature' the 'population explosion', and attendant global plagues. We live at a time when a deadly virus unknown in 1980 now infects 30 M people, with 6 M new HIV cases per year, and its emergence from the African jungles can be viewed as a consequence of a scarred environment (The Hot Zone, Richard Preston).
This month, 1500 delegates are meeting in Kyoto to try to make the next step in the policy of carbon emission (or remission) reductions, to moderate global warming. Theory is suddenly catapulted into public view. A terrifying Pandora's is opened. Emotionally charged popular books appear: The Heat is On (R. Gelpspan, Addison Wesley 1997), Hot Talk, Cold Science: Global Warming's Unfinished Debate (S.F.Singer, The Independence Inst. 1997). Below I include a page-2 newspaper article from the week of 1 Dec . 1997, Associated Press, describing Wally Broecker's campaign publicizing a potential global thermohaline catastrophe, and its possible association with global greenhouse emissions. This follows Broecker's Scientific American (1995) article and Stefan Rahmstorf's (Nature,378, 145-149 1995) coarse-resolution model study in which the meridional overturning under current conditions is found close to a bifurcation in which either collapse or intensification could occur.
It is remarkable to see public fascination over the meridional overturning circulation, essentially a downstream product of Stommel and Rooth's (theoretical) box models and Frank Bryan's numerical circulation modelling. It seems to me that in view of the extreme stability of interglacial climate, both over the past 10,000 years following the Younger-Dryas event, and during the previous interglacial period, these are fighting words. [The frenzy of publicity over climate oscillations during the Eemian ( previous interglacial) seen near the base of the Greenland ice cores has largely been discredited, see Adkins, Boyle, Keigwin & Cortijo, Nature,13 Nov. 97.]
Surely, the decrease in salinity of all the major water masses in the subpolar Atlantic during the past 25 years is of note, and we have been working to document this trend in the Labrador Sea. The increased hydrologic cycle seen in North America is one related event, and the invasion of increasing amounts of Atlantic water into the Arctic (possibly due to the systematically stronger Icelandic Low Pressure center) may be another. Simple warming of the Arctic may be a third related event. The flooding of downwelling sites with surface fresh water, as an inhibition of deep convection and sinking for the meridional overturning, is a classic idea (going back to L.V.Worthington and others in the 1960s). Yet the idea has recently been exercised through coarse numerical circulation models which are still having difficulty getting any of the detail of high latitude processes correct. And, contrary to current models, the recent 25-year decrease in salinity is accompanied by an increase in density of the intermediate and deep water masses.
This is a new ball-game, or one might say, mine-field. The opportunity for Theory to do Good is there, and is what we want, but the new surges of power, influence, the dazzling lights of the entertainment industry can so easily distort the truth that it is not a place for the timid. The nuclear physics community in WW II rose to the challenge of applying their intellect to building bombs. Perhaps there is an Oppenheimer-foil among us who can organize the results of our research in a way that will actually help humanity, and who can bear intense forms of public scrutiny (e.g., quote from The Heat is On, below).
These parallel streams, the powerful discoveries of basic natural science, and the impending global disaster, suggest that the conduct of theoreticians should change. I suggest a 50:50 split of our energies between the abstract and applied, and that im proved connectivity between the two be developed.

CONCLUSION

Theory is strong in our teaching, strong in neighboring scientific fields, and strong in providing dynamical basis for the environmentally important ENSO and extratropical climate variability. Yet there is some sign of lost coherence in 'straight physical oceanography' or in its connectivity with big gcms and big observational programs. Sometimes large, specially organized and funded oceanographic programs appear to be egalitarian, organized, with an articulate set of goals, while small or individual research projects appear as elitist, remote, unclear in goals and possibly even irrelevant, when they are not. Measurement of T, S, velocity, and surface height fields down to the last molecule of ocean is not necessarily the way to understanding, any more than one understands the functions of the body by mindless dissection, nor would a computer model of the ocean with infinite resolution necessarily, by itself, teach us very much. Theory, and dynamical computer modelling were omitted from programs li ke Woce, whereas the first big oceanographic experiment, MODE, had a healthier mix, despite being a quirky menagerie of personalities. We are seeing the consequences of this short-sighted separation of theory from global observation and simulation now.
There are, however, positive signs of theory finding new modes of interaction with numerics and observations, infiltrating the analysis of observations and interpretation of numerical models in new forms, as described above. 'Full-time theory' of a mor e classical nature nevertheless needs to continue too.

APPENDIX: MISCELLANEOUS QUOTATIONS

*Daedalus (Nature 390, p 127): 'I almost weep to think of all the potentially fruitful, creative minds who get hooked on compulsive computer nerdery, and are thenceforth lost to civilization. Analysts look in vain for any increase in productivity or eco nomic value from all this digital churning.'

*Associated Press, 28 Nov. 1997: GASES THREATEN OCEAN CURRENTS, RESEARCH SAYS Washington - Currents flowing like rivers from pole to pole and from ocean to ocean help keep the Earth's weather in a steady state, but the buildup of greenhouse gases in the atmosphere is threatening this circulation and could dump Europe into a deep fr eeze, a research says. The dependable pattern of ocean circulation is a key factor in controlling the Earth's weather and keeping it predictable, said Wallace Broecker of the Lamont-Doherty Earth Observatory of Columbia University in Palisades, N.Y. But this has only been true for the past 8,000 years. Before that ocean currents altered about every 1000 years and scrambled the Earth's climate, Broecker says in a study to be published today in the journal Science. "We live in a climate system that can jump abruptly from one state to another," Broecker said. By dumping into the atmosphere huge amounts of greenhouse gases, such as carbon dioxide from the burning of fossil fuels, "we are conducting an experiment that could have devastating effects," he added. "We're playing with an angry beast - a climate system that has been shown to be very sensitive". The findings come as representatives from more than 140 nations prepare to gather in Kyoto, Japan, next week in hopes of forging an agreement binding industrial nations to specific reductions of greenhouse gases, especially carbon dioxide from burning fossil fuels. Broecker said studies of ice cores that date back 110,000 years show that about once a millenium, the Earth's climate abruptly changes and within 10 to 20 years can cause such things as increased glaciers, halting of rainfall or crippling declines in temperature. Ocean currents are controlled by the temperature and salt content of the water, according to the researcher. Cold, salty water is heavy and drops to the ocean bottom, while warm, fresh water rises. This creates what Broecker calls a conveyor current that spans the globe. Cold, salty water in the North Atlantic sinks, working like a plunger to drive an ocean current from near North America to Europe. Warm surface waters borne by this current help to keep Europe's climate mild. Without the current, Broecker said, "Europe would be a deep freeze" with average winter temperatures dropping by 20 degrees F or more. The climate of Dublin or London would be like that of Spitsbergen, Norway, which is 600 miles north of the Arctic Circle, he said. The conveyor now flows past Europe, into the South Atlantic and then around Antarctica. The waters cool and pick up more salt, giving the current another boost. From the South Pole, the currents fan out into the Indian and Pacific Oceans and into the Atlantic to complete the cycle. Broecker said the currents help to bring seasonal cycles of moisture that farmers count on to plant crops. If the currents are disrupted, he said, agriculture would suffer. With a changing climate, there would be crop failures until farmers learned to cope with the changes. Broecker said his studies suggest the conveyor is the "Achilles' heel of the climate system" and a fragile phenomenon that can change rapidly for reasons not understood.
end of AP text

*Ross Gelpspan, in The Heat is On, describing congressional hearings on global warming, gives some flavor of the bitterness between the anthropogenic global warmers and their opponents. ( I include this as an example of the 'heat' that comes with highl y visible science.) This lately focuses on the IPCC climate report ( Climate Change 1995-The Science of Climate Change: Cambridge Univ. Press, 1996). Jerry Mahlman is director of GFDL, Princeton: "Mahlman: I simply do not accept the conspiratorial tone of Michael's [Patrick Michael, a global warming skeptic] assertions about the IPCC process. First, imperfections in the models are widely and openly acknowledged...Michael's assertion of a virtual IPCC cover-up is totally implausible, given the very open style of this process."

*"Hey Dad," Kern said. "'Youngest aviators ever to fly America coast-to-coast?' Don't you think this is bull?" "Ah c'mon Kern," my father said. "Learn to relax. When you get right down to it everything's bull? Who cares? This is what the papers are saying so this is what's true. Milk it? Get used to it. Christ, you're famous!" (Flight of Passage, R. Buck, Hyperion Press, 1997).

*Henry Stommel, a voracious after-hours reader, came into the Oceanographic one day in 1973 with a copy of the New Yorker magazine, and showed us an article on the physicist I.I.Rabi. Rabi described some advice he had given to a young colleague, a laboratory experimentalist [here, read 'observational oceanographer']; to paraphrase: ' Don't go to the theoreticians to discuss your experiments. If you ask them 'what shall I measure' they will tell you something and you will go away and measure it. Then you will have to return to them and ask, 'what have I measured?'.