Wave Turbulence in Atmospheric and Oceanic Flows

研究者研究了在分层湍流和旋转分层湍流中由快速、小规模情绪产生缓慢、大规模运动的机制。由于地球的大气和海洋是旋转框架中的分层流体，因此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还有待了解。例如，目前尚不清楚波浪存在下的小尺度三维湍流是否、何时以及如何组织成大尺度的相干结构（如二维流动）。在纯旋转流中，研究者先前表明，如果罗斯比数低于一阶的临界值，小尺度的白噪声强迫会导致缓慢的、大尺度的、旋涡状柱的产生。这是令人惊讶的，因为最近使用多尺度分析的工作表明，在一阶，快速、小尺度运动和缓慢、大尺度运动之间的解耦，适用于各种波湍流系统，包括旋转流。在旋转湍流中，一些二阶机制可能是导致能量向慢模态转移的原因。该项目通过研究三维分层和旋转分层湍流中的高级能量传递，进一步了解地球物理流动的大规模动力学。研究者探讨了导致这种高档转移的必要条件，并试图确定潜在的机制。色散波湍流的简化系统被用来测试理解和统计模型的发展。为了补充数值模拟和分析，她还计划在一个旋转罐中进行实验室实验，其中湍流是由微分旋转的粗糙的顶部和底部板驱动的。在旋转和/或分层流的相对较短的时间内，有实验证据和数学支持慢的、大规模的情绪从快速的、小规模的运动中解耦。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，大规模的涡流和洋流独立于小规模的湍流演变而来。另一个暗示是，短期气候变化与大气和海洋条件的快速波动无关。然而，我们长时间的数值模拟显示，小规模湍流产生了大规模的相干结构，这种耦合可能对长期天气预报、海洋环流和气候变化很重要。有人可能会问，在大气的背景下，长度约为十公里的小尺度积云对流能否产生范围达几千公里的大尺度涡旋？在旋转和分层流等三维波动湍流系统中，能量从快速、小尺度运动到缓慢、大尺度运动的转移直到最近才被发现，尽管这种转移在二维流中已经研究了几十年。目前的研究包括数值模拟、建模和分析，以及在旋转槽中的实验室实验。目标是加深我们对地球物理现象的理解，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.