Zonal flows

分区流

• 批准号: 2285630
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2285630
• 关键词: Zonal; flows

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.

纬向流到小扰动的不稳定性支撑了我们对运动尺度的理解，以及它们在行星大气和海洋中的可预测性。自Charney（1947）和Eady（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较小的罗斯比数和较大的理查德森数，并且要求基本状态的分层与纬度无关。直到最近，具有更普遍有效性的公式还局限于横向均匀流动，而忽略了地球的曲率。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的任何纬向流的稳定性：线性化的原始方程被简化为只涉及单个变量（压力扰动）的偏微分方程；该方程在压力扰动下是线性的，而在决定不稳定性增长速率的复相速度下是非线性的。该方法可用于研究基本状态分层随高度和纬度变化、非静力运动和流体可压缩的球体上射流的稳定性。可以研究与不同类型的临界层以及对称和开尔文亥姆霍兹不稳定性相关的不稳定性。还可以推导出不稳定性的积分约束。我们将研究赤道附近层状纬向喷流的不稳定性，那里罗斯比数很大，地球的曲率具有根本的重要性。这些流动表现出许多不稳定性，例如，导致热带不稳定波的形成，热输送在确定海洋结构和热吸收方面具有根本的重要性，对热带气候具有广泛的影响。因此，了解这些赤道气流的稳定性对于理解热带气候对人为强迫的响应至关重要。增长率对平均状态剖面的依赖性将在逐渐复杂的地带性流的层次中进行研究。在NEMO海洋模式模拟中，计算了不稳定波的热量和动量输运，并与热带不稳定波进行了比较。本文将研究近地表海洋混合层内的三类不稳定性：学生将诊断海洋环流模式中的不稳定性，探索纬向流层次的数值解，考虑理论方面，如不稳定性的积分约束和标志着稳定性过渡的中性模式，并计算不稳定性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，否则某些不稳定性的增长率被高估了。该学生还将研究海洋环流模式所需的垂直分辨率，以避免错误地表示不同类别的不稳定性。