Wave Turbulence and Mixing

这项合作工作解决了流体系统中出现的两个封闭问题：描述通过大量波动模式传递的湍流能量，以及确定分层环境中内部破碎波的混合量。所提出的方法包括将复杂的偏微分方程组渐近化为更简单的系统，动力学方程的数值模拟，物理原理的临界分析，以及理论和计算与物理实验室实验的比较。我们预计，这项工作将产生物理见解和有趣的新数学。湍流能量传递、耗散和混合是流体动力学问题中的关键过程，从水波的风生到气候动力学。海洋混合最终决定了海面温度，而海面温度又影响着大气的风、温度和湿度。众所周知，向上传播的破碎波的混合在大气层下层和上层之间的动量交换中起着重要的作用。在海洋中，湍流波作用负责将能量从非常大的风暴尺度转移到发生耗散的小尺度上。预计这里提出的研究将有助于理解这些重要现象背后的基本物理机制，从而提高我们预测和量化气候变化的能力。这项建议还将产生强大的教育影响，通过培养研究生，为本科生开发研究学院，教授具有挑战性的本科生课程，以及让本科生参与专注于研究的暑期项目。

This collaborative effort addresses two closure problems arisingin fluid systems: the description of turbulent energy transferthrough a large number of wave modes, and the determination of theamount of mixing at internal breaking waves in a stratifiedenvironment. The methodology proposed includes the asymptoticreduction of complex partial differential equations to simplersystems, the numerical simulation of dynamic equations, thecritical analysis of physical principles, and the comparison oftheory and computations with physical laboratory experiments. Weanticipate that the work will yield both physical insights andinteresting new mathematics.Turbulent energy transfer, dissipation and mixing are keyprocesses in fluid dynamical problems ranging from the windgeneration of water waves to climate dynamics. Ocean mixing ultimatelydetermines the sea--surface temperature, which, in turn, affectsatmospheric winds, temperature and humidity. Mixing by upward propagatingbreaking waves is known to play a significant role in the exchange ofmomentum between the lower and the upper layers of the atmosphere. In theocean, turbulent wave action is responsible for the transfer of energy fromthe very large scales of storms to the small scales at whichdissipation takes place. It is expected that the research proposedhere will contribute to the understanding of fundamental physicalmechanisms behind these important phenomena, and hence improveour capability to predict and quantify climate changes.This proposal will also have a strong educational impact, throughthe training of graduate students, the development of a research seminarfor undergraduate students, the teaching of challenging undergraduate classes,and by having undergraduate students participate in summer projects focused onthe research.