Title: Statistical State Dynamics based study of Langmuir Turbulence Show Chinese title

Title: 基于统计状态动力学的朗缪尔湍流研究

Abstract: The dynamics of the ocean mixed layer is of central importance in determining the fluxes of momentum, heat, gases, and particulates between the ocean and the atmosphere. A prominent component of mixed layer dynamics is the appearance of a spanwise ordered array of streamwise oriented roll/streak structures (RSS), referred to as Langmuir circulations, that form in the presence of surface wind stress. The coherence and long-range order of the Langmuir circulations are strongly suggestive of an underlying modal instability, and surface wind stress produces the necessary Eulerian shear to provide the required kinetic energy. Unfortunately, there is no instability with RSS form supported solely by Eulerian surface stress-driven shear. However, in the presence of velocity fluctuations in the water column, either in the form of a surface gravity wave velocity field and/or a background field of turbulence, there are two instabilities of the required form. These are the Craik-Leibovich CL2 instability arising from interaction of the Eulerian shear vorticity with the Stokes drift of a surface gravity wave velocity field and the Reynolds stress (RS) torque instability arising from the organization of turbulent Reynolds stresses by a perturbing RSS. The CL2 instability is familiar as an explanation for the RSS of the Langmuir circulation, while the RS torque instability is familiar as an explanation for the RSS in wall-bounded shear flows. In this work, we show that these instabilities act synergistically in the mixed layer of the ocean to form a comprehensive theory for both the formation and equilibration of Langmuir circulations. Show Chinese abstract

Abstract: 海洋混合层的动力学在确定海洋与大气之间动量、热量、气体和颗粒物通量方面具有中心重要性。 混合层动力学的一个显著组成部分是出现沿流向排列的横向有序的滚流/条纹结构（RSS），称为朗缪尔环流，在表面风应力存在的情况下形成。 朗缪尔环流的相干性和远距离有序强烈表明存在一种基本的模态不稳定性，而表面风应力提供了必要的欧拉剪切以提供所需的动能。 不幸的是，仅由欧拉表面应力驱动的剪切无法支持RSS形式的不稳定性。 然而，在水柱中存在速度波动的情况下，无论是以表面重力波速度场的形式，还是以湍流背景场的形式，都存在两种所需形式的不稳定性。 这些是由于欧拉剪切涡度与表面重力波速度场的斯托克斯漂移相互作用而产生的Craik-Leibovich CL2不稳定性，以及由于扰动RSS对湍流雷诺应力的组织而产生的雷诺应力（RS）扭矩不稳定性。 CL2不稳定性作为朗缪尔环流RSS的解释是众所周知的，而RS扭矩不稳定性作为壁面受限剪切流中RSS的解释也是众所周知的。 在本研究中，我们表明这些不稳定性在海洋混合层中协同作用，为朗缪尔环流的形成和平衡提供了一个全面的理论。