Inertia-Gravity Waves in Geophysical Flows

SmithDMS-1008396该项目旨在更好地了解非重力波在物理流体动力学中两个高度相关问题中的作用：(1)观测到的海浪频谱的来源；(2)热带气旋生成和飓风发展的先决条件状态。这两个研究都涉及到一个相似的动力学核心，即具有强层结的旋转Boussinesq方程。以前，在弱湍流模式下，通过考虑精确的三波共振，已经在理解海洋光谱方面取得了理论进展。在这里，研究人员研究了包含所有三波相互作用的新的偏微分方程模型，从而捕捉到了更完整的物理学。通过明确推导的非线性耦合系数，对旋转、层结和静力平衡的影响进行了解析推导。数值模拟表征了能谱和切变的产生。将简化的云动力学(水的凝结和蒸发)添加到Boussinesq核心，可以对飓风胚胎进行研究。后一个项目涉及包括快速波在内的最小活跃湿度模式的数值实施和开发，利用施加的热源将湿过程纳入平衡模式(不包括快速波)，从而扩展了最近的工作。惯性重力波是地球自转和大气和海洋密度分层的结果。惯性重力波的作用是多种多样的，例如，波可以自组织形成自然界中广泛观察到的大尺度相干结构，如气旋和/或反气旋、东西急流和水平切变层。然而，有一种非常重要的流动，其非重力波的动力作用还没有一个完全自洽的数学理论来描述。该项目使用分析和数值计算相结合的方法解决了两个基本应用问题：(1)海洋中波能的尺度分布；(2)热带气旋生成(也称为飓风胚胎问题)。在海洋中，潮汐和风力强迫产生内部重力波破裂，最终在小规模混合和全球环流之间建立平衡。对于热带气旋发生的问题，以前的数学模型已经过滤掉了快波，关于快波在低空气旋垂直涡度的出现和稳定中的作用，最终导致飓风的形成，有很多需要了解的东西。这些主题涉及海洋混合和海洋-大气相互作用，这些都是气候的重要因素。

SmithDMS-1008396 The project aims to better understand the role ofinertia-gravity waves in two highly relevant problems ingeophysical fluid dynamics: (i) the origin of observed ocean wavespectra, and (ii) tropical cyclogenesis and the preconditionedstate for the development of hurricanes. Both studies involve asimilar dynamical core, namely, the rotating Boussinesq equationswith strong stratification. Previous theoretical progress towardunderstanding ocean spectra has been made by considering exactthree-wave resonances under the weak turbulence paradigm. Herethe investigator studies new partial-differential equation modelsincluding all three-wave interactions, thus capturing morecomplete physics. Effects of rotation, stratification andhydrostatic balance are deduced analytically through explicitlyderived, nonlinear coupling coefficients. Numerical simulationscharacterize energy spectra and generation of shear. Addingsimplified cloud dynamics (condensation and evaporation of water)to the Boussinesq core allows for investigation of the hurricaneembryo. The latter project involves numerical implementation andexploration of a minimal, active moisture model including fastwaves, extending recent work using imposed heat sources toincorporate moist processes within the context of balanced models(excluding fast waves). Inertia-gravity waves result from the earth's rotation anddensity stratification of the atmosphere and oceans. The effectsof inertia-gravity waves are varied, for example, waves canself-organize to form large-scale coherent structures widelyobserved in nature, such as cyclones and/or anticyclones,east-west jets, and horizontal shear layers. Yet there arecritically important flows for which the dynamical role ofinertia-gravity waves is yet to be described by a fullyself-consistent mathematical theory. The project addresses twosuch fundamental application problems using a combination ofanalytical and numerical calculations: (i) the scale distributionof wave energy in the oceans, and (ii) tropical cyclogenesis(also known as the hurricane embryo problem). In the oceans,tidal and wind forcing generate internal gravity-wave breaking,ultimately establishing the balance between small-scale mixingand global circulation. For the problem of tropicalcyclogenesis, previous mathematical models have filtered out thefast waves, and there is much to learn about the role of fastwaves for the emergence and stability of low-altitude cyclonicvertical vorticity, leading ultimately to the formation of ahurricane. The topics involve ocean mixing and ocean-atmosphereinteractions, which are important factors in climate.