Wave Turbulence in Atmospheric and Oceanic Flows

史密斯0071937 研究人员研究了分层湍流和旋转分层湍流中由快速小尺度运动产生缓慢大尺度运动的机制。 由于地球的大气和海洋是旋转框架中的分层流体，这项工作与地球物理应用高度相关。 波与湍流相互作用的许多方面还有待了解。 例如，目前还不清楚是否，何时以及如何小规模的三维湍流在波的存在下可以组织成大规模的相干结构（如在二维流）。 在纯旋转流中，研究者先前表明，如果Rossby数低于一阶临界值，则小尺度下的白噪声强迫会导致产生缓慢的、大尺度的气旋性涡列。 这是令人惊讶的，因为最近的工作使用多尺度分析显示，在一阶，快速，小尺度运动和缓慢，大尺度运动之间的解耦的各种波湍流systemsincluding旋转流。 在旋转湍流中，高阶能量向慢模的传递可能是由几种二阶机制引起的。 本项目通过研究三维分层旋转、分层湍流中的高阶能量传递，进一步理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水平转移的必要条件，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，她还计划在旋转槽中进行实验室实验，其中湍流由差动旋转的粗糙顶板和底板驱动。 在相对较短的时间内，在旋转和/或分层流，有实验证据和数学支持的解耦缓慢，大规模的情绪从快速，小规模的运动。 这意味着，在大气中可能是几天的时间尺度上，在海洋中可能是几周的时间尺度上，大尺度的漩涡和洋流的演变独立于小尺度的湍流。 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，我们对更长时间的数值模拟表明，小尺度湍流产生大尺度相干结构，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。 在大气层中，人们可能会问，长度约为10公里的小尺度积云对流能产生数千公里范围的大尺度涡旋吗？ 在三维、波-湍流系统（如旋转流和分层流）中，能量从快速、小尺度运动向缓慢、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。 本研究包括数值模拟、建模和分析以及旋转槽中的实验室实验。 目的是加深我们的理解，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.