Nadejda Dikovskaya

On the Arrest of Inverse Energy Cascade and the Rhines Scale

Abstract The notion of the cascade arrest in a β-plane turbulence in the context of continuously forced flows is revised in this paper using both theoretical analysis and numerical simulations. It is demonstrated that the upscale energy propagation cannot be stopped by a β effect and can only be absorbed by friction. A fundamental dimensional parameter in flows with a β effect, the Rhines scale, LR, has traditionally been associated with the cascade arrest or with the scale that separates turbulence and Rossby wave–dominated spectral ranges. It is shown that rather than being a measure of the inverse cascade arrest, LR is a characteristic of different processes in different flow regimes. In unsteady flows, LR can be identified with the moving energy front propagating toward the decreasing wavenumbers. When large-scale energy sink is present, β-plane turbulence may attain several steady-state regimes. Two of these regimes are highlighted: friction-dominated and zonostrophic. In the former, LR does not have...

Rossby waves and zonons in zonostrophic turbulence

Two-dimensional, small-scale forced turbulent flows on the surface of a rotating sphere, along with the familiar Rossby-Haurwitz waves, reveal a new class of waves termed zonons. The zonons form non-dispersive wave packets that propagate in the westward direction with the velocity equal to the phase speed of the most energetic Rossby-Haurwitz wave. Zonons preserve their identity even after the forcing is switched off and the flow undergoes structural reorganization. Zonons reside in locations with the maximum meridional shear and are engaged in strong energy exchange with themean flow. These physical properties of zonons point to their identitywith Rossby solitary waves. The symbiosis between themean flow and the solitarywaves plays an important role in the large-scale dynamics.