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Stochastic Wave–Current Interaction in Thermal Shallow Water Dynamics
Journal of Nonlinear Science ( IF 3 ) Pub Date : 2021-03-02 , DOI: 10.1007/s00332-021-09682-9
Darryl D. Holm , Erwin Luesink

Holm (Proc R Soc A Math Phys Eng Sci 471(2176):20140963, 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin’s circulation theorem, while also allowing for dispersive nonlinear wave propagation, both within a stratified fluid and at its free surface. The present paper combines asymptotic expansions and vertical averaging with the stochastic variational framework to formulate a new approach for developing stochastic parametrisation schemes for nonlinear waves in fluid dynamics. The approach is applied to two sequences of shallow water models which descend from Euler’s three-dimensional fluid equations with rotation and stratification under approximation by asymptotic expansions and vertical averaging. In the entire family of nonlinear stochastic wave–current interaction equations derived here using this approach, Kelvin’s circulation theorem reveals a barotropic mechanism for wave generation of horizontal circulation or convection (cyclogenesis) which is activated whenever the gradients of wave elevation and/or topography are not aligned with the gradient of the vertically averaged buoyancy.



中文翻译:

浅水热动力学中的随机波-电流相互作用

Holm(Proc R Soc A Math Phys Eng Sci 471(2176):20140963,2015)引入了一种变分框架,用于随机参数化未解决的水动力运动尺度。这种变化的框架保留了流体动力学的基本特征,例如开尔文的循环定理,同时还允许在分层流体内部及其自由表面传播色散非线性波。本文将渐近展开和垂直平均与随机变分框架相结合,为开发流体动力学非线性波的随机参数化方案提供了一种新方法。该方法适用于两个浅水模型序列,这些模型是由Euler的三维流体方程派生而来的,它们具有在渐近展开和垂直平均近似的情况下进行旋转和分层的过程。在此方法推导的整个非线性随机波-流相互作用方程组中,开尔文环流定理揭示了水平波或对流波(回旋作用)的正压机制,只要波高和/或地形的梯度为零,该正压机制就会被激活。与垂直平均浮力的梯度不一致。

更新日期:2021-03-02
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