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.