GFD-1 LAB #7 ROSSBY WAVES
P.B.Rhines, E.G.Lindahl
Rossby waves are information-carriers of the atmosphere and ocean. They
transport energy and angular momentum, often driving the kind of banded zonal
jets seen on Jupiter and Earth.
click on the Rossby wave
This is a polar beta-plane experiment, with rapidly rotating (omega=3.2
sec^-1)
homogeneous fluid with a free surface. The 1m diameter cylinder has a wavemaker
located in the lower-left quadrant, in the form of a horizontal disk (10 cm diameter)
oscillated slowly up and down. It produces Rossby waves, most visibly the short
waves propagating east from the wavemaker. The green wavecrests have phase
propagation westward toward the wavemaker, yet group velocity eastward, away
from it. The longer waves propagate west, and are less visible. The sequence shows
the development of the eastern wavetrain (with group velocity about 5 cm/sec, and
the induction of systematic bands of zonal flow by the wave's potential vorticity flux.
Westward mean flow occurs both north and south of the wavemaker (the deep blue
and green bands), while an eastward jet (faint blue) develops at the latitudes
encompassing the forcing. This jet was discovered in Whitehead's landmark
experiments (Tellus, 1974). Because of bottom-frictional dissipation, fluid does
traverse across latitude circles, for example connecting the eastward jet sucked into
the wavemaker with a westward jet further north.
Yet, at this high rotation rate the potential vorticity 'barrier' to meridional flow is
strong, as is the 'Rossby wave elasticity'. Orange fluid at the North Pole remains
unmixed, like an 'ozone-hole' region in the stratosphere, for the duration of the
experiment.
Stirring of potential vorticity leads to the predictable polar anticyclone, almost
regardless of the detailed nature of the Rossby waves or geostrophic turbulence.
Low pv from lower latitudes mixes poleward, replacing the high pv of the polar cap,
and since the planetary vorticity is unchanged this must appear as anticyclonic
(easterly, westward) zonal acceleration. Beautiful numerical experiments of Yoden
and Yamada (J.Atmos.Sci. 1993, Phys.Fluids 1997) show this, and the general
arguments are given by Rhines (The Sea, 1977, Dyn. Atmos. Oceans 1979,
Ann.Revs. Fluid Mech. 1979, Geophys.Astrophys.Fluid Dyn. 1983). This particular
wavemaker also generates small scale vortices, which flow with the induced
circulation northwestward.
Annular modes observed in both hemispheres of the atmosphere have much in
common with these zonal jets. They have significant barotropic components, and
time-variation of meridional and vertical pv flux is known to be active in driving
them (e.g., Hartmann DL, 2000: The key role of lower-level meridional shear in
baroclinic wave life cycles J. Atm. Sci., 57, 389-401; DeWeaver, E., and S. Nigam,
2000: Do stationary waves drive the zonal-mean jet anomalies of the Northern
Winter? J. Climate, in press). Vertical propagation of Rossby waves in the stratified
atmosphere occurs along ray paths that are sensitive to the presence of the annular
modes: this introduces the idea of a 'self-tuning wave-guide'. Dave Thompson has
established a website
for annular modes.