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Geophysical turbulence; beyond slow vortices and fast waves

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Thursday, December 10, 2015 - 2:00pm

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ECCR 257

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A major achievement of mid-twentieth century meteorology and oceanography was to simplify the Navier-Stokes equations considerably (using two time scales) to obtain the quasigeostrophic set describing flow that is dominated by earth's rotation and the background density stratification. ÌýOf course, it has always been known that these simplifications were not valid for small-scale phenomenon such as thunderstorms or boundary-layer turbulence. ÌýAs the emphasis remains on ever more detailed knowledge and prediction of smaller-scale atmospheric and oceanic flows, it is now time to ask how these simplified flows break down into more general fluid mechanics.

Various explorations involving the transition from large-scale quasigeostrophic turbulence, through a scale range exhibiting the breakdown of this balance, to stratified turbulence with negligible rotation will be discussed. ÌýThe latter has recently been demonstrated to be inherently unbalanced in that linear wave time scales are not fast with respect to the nonlinear variablity of the turbulence. In this setting the small-scale turbulence follows a shallow -5/3 spectrum with respect to the horizontal wavenumber in contrast to the considerably steeper spectra of quasigeostrophic turbulence in the potential-enstrophy cascade range. ÌýIn addition, the spontaneous emergence of unbalanced small-scale turbulence from balanced initial conditions also manifests itself via a shallow -5/3 range at high wavenumbers in the horizontal energy spectrum. These results will be related to observations of atmospheric and oceanic spectra with the caveat that statistically homogeneous turbulence is studied here without boundaries.