We consider quasi-stationary planetary waves that are excited by midlatitude orographic forcing in a shallow-water model on the sphere. These waves propagate towards subtropical regions where the basic flow is weak and the waves are therefore likely to break. Earlier studies using finite-amplitude, wave-activity diagnostics have found that given enough forcing such waves will be reflected from the low-latitude, wave-breaking region back toward midlatitudes, both in shallow-water flows and in fully three-dimensional, primitive-equations flows. (A theoretical bound on the absorption in the wave-breaking region is only available for two-dimensional balanced flow.) Introducing thermal damping with timescales as low as 5 days does not inhibit the nonlinear reflection. However, we have found that the large scale-selective hyperdiffusion needed for our numerical experiments at horizontal resolution corresponding to T21 and lower, inhibits the nonlinear reflection.
Here we extend this line of investigation further by examining the effect of the Hadley cell on the nonlinear reflection. Not only will the meridional component of the velocity tend to oppose the propagation of stationary Rossby waves to low latitudes, but the Hadley circulation may act to maintain the low-latitude gradients of potential vorticity, thus violating one of the key assumptions required for the theoretical bound that is valid in two-dimensional vortex dynamics and hence inhibiting reflection. Nonconservative effects associated with the Hadley cell may also inhibit reflection by acting directly to dissipate wave activity at low latitudes. Some of the effects of the Hadley circulation have been considered by Held and Phillips (1990) who studied the interactions of a stationary Rossby wave with a zonally symmetric Hadley circulation in a single-layer model. Here we expand on their work, both in generalizing some of the assumptions made and in taking advantage of the finite-amplitude, wave-activity diagnostics in analyzing numerical results. We find that nonlinear reflection is not hindered when a Hadley cell is included in our numerical experiments.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics