Inertia-Gravity Waves in Geophysical Flows

SmithDMS-1008396 该项目旨在更好地了解惯性重力波在地球物理流体动力学中两个高度相关问题中的作用：（i）观测到的海洋波谱的起源，以及（ii）热带气旋生成和飓风发展的先决条件。 这两项研究都涉及到一个类似的动力学核心，即具有强分层的旋转Boussinesq方程。 以前的理论进展，了解海洋光谱已考虑exactthree-wave共振下弱湍流范例。 在这里，研究人员研究新的偏微分方程模型，包括所有的三波相互作用，从而捕捉更完整的物理。 旋转，分层和流体静力平衡的影响推导解析通过显式推导，非线性耦合系数。 数值模拟表征能谱和剪切的产生。 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调查。 后一个项目涉及数值实现和探索的最小，积极的水分模式，包括快波，扩展最近的工作，使用强加的热源纳入潮湿的过程中的平衡模式（不包括快波）。 惯性重力波是地球自转和大气、海洋密度分层的结果。 重力惯性波的作用是多种多样的，例如，重力惯性波可以自组织形成大尺度相干结构，如在自然界中广泛观测到的气旋和反气旋、东西向急流和水平剪切层等。 然而，有一个非常重要的流动，惯性重力波的动力学作用还没有被完全自洽的数学理论所描述。 该项目使用分析和数值计算相结合的方法解决了两个这样的基本应用问题：（i）海洋中波浪能量的尺度分布，和（ii）热带气旋生成（也称为飓风胚胎问题）。 在海洋中，潮汐和风的作用力产生内部重力波的破碎，最终在小尺度混合和全球环流之间建立平衡。 对于热带气旋生成的问题，以前的数学模型已经过滤掉了快波，关于快波对低空气旋垂直涡度的出现和稳定性的作用，还有很多东西要学，最终导致飓风的形成。 主题涉及海洋混合和海洋-大气相互作用，这是气候的重要因素。

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.