Wave Turbulence in Atmospheric and Oceanic Flows

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Smith 0071937 The investigator studies the mechanisms responsible for the generation of slow, large-scale motions from fast, small-scale motions in stratified turbulence and rotating, stratified turbulence. Because the earth's atmosphere and oceans are stratified fluids in a rotating frame, the work is highly relevant to geophysical applications. Many aspects of wave-turbulence interactions are yet to be understood. For example, it is not clear if, when and how small-scale 3D turbulence in the presence of waves can organize into large-scale coherent structures (as in 2D flows). In purely rotating flow, the investigator previously showed that white-noise forcing at small scales leads to the generation of slow, large-scale, cyclonic vortical columns, if the Rossby number is below a critical value of order one. This is surprising because recent work 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 systems including rotating flow. Several second-order mechanisms may be responsible for the upscale energy transfer to slow modes in rotating turbulence. This project goes a step further towards understanding the large-scale dynamics in geophysical flows, by investigation of upscale energy transfer in 3D stratified and rotating, stratified turbulence. The investigator explores the necessary conditions leading to such upscale transfer and seeks to identify the underlying mechanisms. Simplified systems of dispersive wave turbulence are used to test understanding and for the development of statistical models. To complement numerical simulations and analysis, she has also planned laboratory experiments in a rotating tank, where the turbulence is driven by differentially-rotating, rough top and bottom plates. Over relatively short time periods in rotating and/or stratified flows, there is both experimental evidence and mathematical support for the decoupling of slow, large-scale motions from fast, small-scale motions. This means that, on time scales of perhaps days in the atmosphere and weeks in the oceans, large-scale eddies and currents evolve independently from small-scale turbulence. Another implication is that short-term climate change is independent from rapid fluctuations of the conditions in the atmosphere and oceans. Our numerical simulations for longer times, however, show the generation of large-scale, coherent structures from small-scale turbulence, and this coupling may be important for long-term weather prediction, ocean circulaton and climate change. In the context of the atmosphere, one might ask, can small-scale cumulus convection at length scales of about ten kilometers generate large-scale eddies of several thousand kilometers in extent? The transfer of energy from fast, small-scale motions to slow, large-scale motions in three-dimensional, wave-turbulence systems such as rotating and stratified flows has only recently been discovered, even though such transfer has been studied for decades in two-dimensional flows. The present study involves numerical simulations, modeling and analysis, and laboratory experiments in a rotating tank. The goals are to deepen our understanding and improve our capability to predict geophysical phenomena.