Wave Turbulence in Atmospheric and Oceanic Flows

Smith0071937研究人员研究了在分层湍流和旋转分层湍流中由快速、小尺度情绪产生缓慢、大规模运动的机制。由于地球大气和海洋是旋转框架中的分层流体，这项工作与地球物理应用高度相关。波浪-湍流相互作用的许多方面尚不清楚。例如，在波浪存在的情况下，小尺度的三维湍流是否、何时以及如何组织成大尺度的相干结构(如在2D流动中)尚不清楚。在纯旋转流动中，研究人员先前表明，如果Rossby数低于一阶临界值，小尺度上的白噪声强迫会导致缓慢的大尺度气旋式涡柱的产生。这是令人惊讶的，因为最近使用多尺度分析的工作表明，对于包括旋转流在内的各种波动-湍流系统，一阶的快速、小尺度运动和慢的、大尺度运动之间是解耦的。在旋转湍流中，几种二阶机制可能是导致高阶能量传递到慢模的原因。该项目通过研究三维分层和旋转分层湍流中的高层能量传递，进一步了解地球物理流动中的大尺度动力学。研究人员探索了导致这种高级转移的必要条件，并试图确定潜在的机制。简化的频散波湍流系统被用来检验对统计模型的理解和发展。为了补充数值模拟和分析，她还计划在旋转水槽中进行实验室实验，在旋转水槽中，湍流由不同旋转的粗糙顶板和底板驱动。在旋转和/或分层流动中，在相对较短的时间内，有实验证据和数学支持将缓慢的大规模情绪与快速的小规模运动分离。这意味着，在大气中可能是几天，在海洋中可能是几周的时间尺度上，大尺度的漩涡和洋流是从小尺度的湍流中独立演化出来的。另一个含义是，短期气候变化独立于大气和海洋条件的快速波动。然而，我们的较长时间的数值模拟表明，小尺度湍流产生了大尺度的相干结构，这种耦合对长期天气预报、海洋环流和气候变化可能是重要的。在大气的背景下，有人可能会问，大约十公里长的小尺度积云对流能产生几千公里的大范围涡流吗？在旋转和分层流等三维波动湍流系统中，能量从快速的小尺度运动到慢的大尺度运动的转移是最近才被发现的，尽管这种转移在二维流中已经研究了几十年。本研究包括数值模拟、建模和分析，以及旋转槽内的实验室实验。目标是加深我们的理解，提高我们预测地球物理现象的能力。

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.