Wave Turbulence and Mixing

这一合作努力解决了流体系统中出现的两个闭合问题：通过大量波浪模式描述湍流能量传递，以及确定分层环境中内部破碎波的混合量。所提出的方法包括复杂偏微分方程的渐近化简，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。湍流能量的传递、耗散和混合是从水波的风力形成到气候动力学等流体动力学问题的关键过程。海洋混合最终决定了海洋表面温度，而海洋表面温度反过来又影响了大气的风、温度和湿度。由向上传播的破碎波引起的混合，在低层和高层大气之间的动量交换中起着重要的作用。在海洋中，湍流波的作用负责能量从非常大尺度的风暴转移到发生耗散的小尺度。预计本文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。该提案还将通过培养研究生、为本科生开展研究研讨会、教授具有挑战性的本科课程以及让本科生参与以研究为重点的暑期项目，产生强大的教育影响。

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.