Zonal flows

纬向气流对小扰动的不稳定性巩固了我们对行星大气和海洋中的运动尺度及其可预测性的理解。自从查尼(1947)和伊迪(1949)的开创性工作以来，许多论文都探讨了这个问题的各个方面。准地转公式只适用于小Rossby数和大Richardson数，并要求基本态的分层与纬度无关。直到最近，更普遍有效的公式一直局限于忽略地球曲率的横向均匀气流。最近，Bell(2017)描述了一种简单但新颖的方法来研究热风平衡中任何纬向气流的稳定性：线性化的原始方程简化为只包含一个变量的偏微分方程组，气压扰动；方程在气压扰动中是线性的，但在复杂的相速度中是非线性的，它设置了不稳定的增长率。这种方法可以用来研究基本态分层随高度和纬度变化、运动可以是非静力的、流体可以是可压的球体上的射流的稳定性。可以研究与不同类型的临界层有关的不稳定性，以及对称的和开尔文的Helmholz不稳定性。我们将研究赤道附近层结纬向喷流的不稳定性，在那里Rossby数很大，地球的曲率具有重要的意义。例如，这些流动表现出一些不稳定性，导致热带不稳定波的形成，由此产生的热量输送对于确定海洋结构和吸热至关重要，并对热带气候产生广泛影响。因此，了解这些赤道气流的稳定特性对于了解热带气候对人为强迫的响应至关重要。增长率对平均态轮廓的依赖性将在一个逐渐复杂的纬向气流层次中进行研究。在NEMO海洋模式模拟中，将计算不稳定波的热量和动量输送，并与热带不稳定波的输送进行比较。学生将利用Blumen(1979)的基本态研究近表面海洋混合层内的三类不稳定：对称不稳定、斜压不稳定和朗缪尔不稳定。学生将诊断海洋环流模式中的不稳定，探索一系列纬向流动的数值解，考虑对不稳定和标志稳定转变的中立模的积分约束等理论方面，并计算不稳定的非线性或弱非线性发展。数值解的初步研究表明，除非使用非常精细的垂直网格间距，否则某些不稳定的增长率被高估了：学生还将研究海洋环流模型所需的垂直分辨率，以避免错误地描述不同类别的不稳定。

The instability of zonal flows to small disturbances underpins our understanding of the scales of motion and theirpredictability in planetary atmospheres and oceans. Numerous papers have explored aspects of this problem since thepioneering work of Charney (1947) and Eady (1949). The quasi-geostrophic formulation is only valid for small Rossbynumbers and large Richardson numbers and requires the stratification of the basic state to be independent of latitude.Formulations with more general validity have until recently been restricted to laterally uniform flows neglecting the Earth'scurvature.Recently, Bell (2017) has described a simple but novel method for studying stability of any zonal flow that is in thermal windbalance: the linearised primitive equations are reduced to a partial differential equation involving only a single variable, thepressure perturbation; the equation is linear in the pressure perturbation, but nonlinear in the complex phase speed whichsets the growth rate of the instability. The method can be used to study the stability of jets on a sphere in which thestratification of the basic state varies with height and latitude, the motions can be non-hydrostatic and the fluid can becompressible. Instabilities associated with different types of critical layers and symmetric and Kelvin Helmholz instabilitiescan be studied. Integral constraints on the instabilities can also be derived.We will investigate the instability of stratified zonal jets near the equator where the Rossby number is large and the Earth'scurvature of fundamental importance. These flows exhibit a number of instabilities that lead, for example, to the formationof tropical instability waves, the heat transport by which is of fundamental importance in setting ocean structure and heatuptake with widespread impact on tropical climate. Understanding the stability properties of these equatorial flows istherefore crucial for understanding the response of tropical climate to anthropogenic forcing.The dependence of growth rates on the profile of the mean state will be investigated in a hierarchy of progressively morecomplex zonal flows. The heat and momentum transports by the unstable waves will be calculated and compared withthose of tropical instability waves in NEMO ocean model simulations. Three classes of instabilities within the near-surfaceocean mixed layer will be studied: symmetric, baroclinic and Langmuir instabilities using the basic state of Blumen (1979)The student will diagnose the instabilities in ocean circulation models, explore numerical solutions for a hierarchy of zonalflows, consider theoretical aspects such as integral constraints on the instabilities and neutral modes which mark stabilitytransitions, and calculate the non-linear or weakly nonlinear development of the instabilities. Preliminary investigations ofnumerical solutions indicate that the growth rates of some instabilities are overestimated unless very fine vertical gridspacing is used: the student will also investigate the vertical resolution that is required for ocean circulation models to avoidmisrepresenting the different classes of instabilities.