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Jet formation in decaying two-dimensional turbulence on a rotating sphere

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The Nature of High Reynolds Number Turbulence

Jet formation in decaying two-dimensional turbulence on a rotating sphere is reviewed from the view point of wave mean-flow interaction for both shallow-water case and non-divergent case as the limit of Fr (Froude number) going to zero.

A series of computations are performed to confirm the behavior of zonal mean zonal flow generation on the parameter space of the rotation rate Omega and Fr. When the flow is non-divergent and Omega is large, intense retrograde circumpolar jets tend to emerge in addition to a banded structure of mean zonal flows with alternating flow directions. As Fr increases, circumpolar jets disappear and a retrograde jet emerges in the equatorial region.

The appearance of the intense retrograde jets can be understood by the angular momentum transport associated with the generation, propagation, and absorption of Rossby waves. When the flow is non-divergent, long Rossby waves tend to be absorbed near the poles. In contrast, when Fr is large, Rossby waves can hardly propagate poleward and tend to be absorbed near the equator.

The direction of the equatorial jet, however, is not always retrograde. Our ensemble experiments showed the emergence of a prograde jet, though less likely. This result is contrasted with the previous studies that reported retrograde equatorial jets in all the cases for shallow-water turbulence. Furthermore, a mean zonal flow induced by wave-wave interactions was examined using a weakly nonlinear model to investigate the acceleration mechanisms of the equatorial jet. The second-order acceleration is induced by the Rossby and mixed Rossby-gravity waves and its mechanisms can be categorized into two types.

This talk is part of the Isaac Newton Institute Seminar Series series.

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