Wave Turbulence in Atmospheric and Oceanic Flows

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Smith0071937 The investigator studies the mechanisms responsible for thegeneration of slow, large-scale motions from fast, small-scalemotions in stratified turbulence and rotating, stratifiedturbulence. Because the earth's atmosphere and oceans arestratified fluids in a rotating frame, the work is highlyrelevant to geophysical applications. Many aspects ofwave-turbulence interactions are yet to be understood. Forexample, it is not clear if, when and how small-scale 3Dturbulence in the presence of waves can organize into large-scalecoherent structures (as in 2D flows). In purely rotating flow,the investigator previously showed that white-noise forcing atsmall scales leads to the generation of slow, large-scale,cyclonic vortical columns, if the Rossby number is below acritical value of order one. This is surprising because recentwork using multiple scales analysis shows, at first order,decoupling between fast, small-scale motions and slow,large-scale motions for a variety of wave-turbulence systemsincluding rotating flow. Several second-order mechanisms may beresponsible for the upscale energy transfer to slow modes inrotating turbulence. This project goes a step further towardsunderstanding the large-scale dynamics in geophysical flows, byinvestigation of upscale energy transfer in 3D stratified androtating, stratified turbulence. The investigator explores thenecessary conditions leading to such upscale transfer and seeksto identify the underlying mechanisms. Simplified systems ofdispersive wave turbulence are used to test understanding and forthe development of statistical models. To complement numericalsimulations and analysis, she has also planned laboratoryexperiments in a rotating tank, where the turbulence is driven bydifferentially-rotating, rough top and bottom plates. Over relatively short time periods in rotating and/orstratified flows, there is both experimental evidence andmathematical support for the decoupling of slow, large-scalemotions from fast, small-scale motions. This means that, on timescales of perhaps days in the atmosphere and weeks in the oceans,large-scale eddies and currents evolve independently fromsmall-scale turbulence. Another implication is that short-termclimate change is independent from rapid fluctuations of theconditions in the atmosphere and oceans. Our numericalsimulations for longer times, however, show the generation oflarge-scale, coherent structures from small-scale turbulence, andthis coupling may be important for long-term weather prediction,ocean circulaton and climate change. In the context of theatmosphere, one might ask, can small-scale cumulus convection atlength scales of about ten kilometers generate large-scale eddiesof several thousand kilometers in extent? The transfer of energyfrom fast, small-scale motions to slow, large-scale motions inthree-dimensional, wave-turbulence systems such as rotating andstratified flows has only recently been discovered, even thoughsuch transfer has been studied for decades in two-dimensionalflows. The present study involves numerical simulations, modelingand analysis, and laboratory experiments in a rotating tank. Thegoals are to deepen our understanding and improve our capabilityto predict geophysical phenomena.