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。例如，在海洋中，风驱动的海浪导致海洋混合，最终决定了海洋--表面温度，这反过来又影响大气风、温度和湿度。湍流波作用负责能量在极大范围的风暴和发生消散的小尺度风浪之间的转移。在一个大气例子中，向上传播的破碎波的混合在大气下层和上层之间的动力耦合中起着重要的作用。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。该建议还将产生强大的教育影响，通过培训研究生，为本科生开发研究研讨会，教授具有挑战性的本科生班级，并让本科生参与以研究为重点的暑期项目。

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. In the ocean, forexample, wind driven ocean waves leads to ocean mixing, ultimatelydetermining the sea--surface temperature, which, in turn, affectsatmospheric winds, temperature and humidity. Turbulent wave actionis responsible for the transfer of energy between the very largescales of storms and the small scales of wind ripples at whichdissipation takes place. In an atmospheric example, mixing byupward propagating breaking waves plays a significant role in thedynamical coupling between the lower and the upper layers of theatmosphere. The research proposed here will contribute to theunderstanding of fundamental physical mechanisms behind theseimportant phenomena, and hence improve our capability to predictand quantify climate changes. The proposal will also have a strongeducational impact, through the training of graduate students, thedevelopment of a research seminar for undergraduate students, theteaching of challenging undergraduate classes, and by havingundergraduate students participate in summer projects focused onthe research.