论文标题
流体波流相互作用的随机变异公式
Stochastic Variational Formulations of Fluid Wave-Current Interaction
论文作者
论文摘要
我们正在对波流相互作用（WCI）中的多尺度，多物理不确定性进行建模。为了模拟WCI中的不确定性，我们将随机性引入了WCI的两个经典模型的波动力学。也就是说，广义的拉格朗日平均值（GLM）模型和craik-leibovich（CL）模型。 GLM方法的关键思想是汉密尔顿原理中拉格朗日（Fluid）和欧拉（Wave）自由度的分离。这是通过将Euler-Poincaré{\ IT耦合为当前流量的Lagrangian}和波段{\ IT相位空间Lagrangian}来完成。 GLM模型中的WCI涉及哈密顿波浪子系统的频率的非线性多普勒移动，这是因为在电流的拉格朗日均值速度的运动框架内传播波。相比之下，CL模型中的WCI之所以出现，是因为流体速度是相对于Stokes平均漂移速度的运动框架定义的，该速度通常被视为处方，时间独立和外部驱动。我们通过将它们都放入旋转框架中的3D Euler- boussinesq（EB）流体的随机汉密尔顿原理的一般框架中来比较GLM和CL理论。在其他示例中，我们还应用GLM和CL方法将波浪物理和随机性添加到熟悉的1d和2d浅水流模型中。可以通过比较两个模型的开尔文循环定理来观察到GLM和CL模型的随机性类型的差异。 GLM模型在其Lagrangian运输速度中获得了随机性的随机性，并在其群体速度中获得了波浪的随机性。开尔文循环定理随机CL模型可以接受其积分和其循环回路的拉格朗日传输速度的随机性。
We are modelling multi-scale, multi-physics uncertainty in wave-current interaction (WCI). To model uncertainty in WCI, we introduce stochasticity into the wave dynamics of two classic models of WCI; namely, the Generalised Lagrangian Mean (GLM) model and the Craik--Leibovich (CL) model. The key idea for the GLM approach is the separation of the Lagrangian (fluid) and Eulerian (wave) degrees of freedom in Hamilton's principle. This is done by coupling an Euler--Poincaré {\it reduced Lagrangian} for the current flow and a {\it phase-space Lagrangian} for the wave field. WCI in the GLM model involves the nonlinear Doppler shift in frequency of the Hamiltonian wave subsystem, which arises because the waves propagate in the frame of motion of the Lagrangian-mean velocity of the current. In contrast, WCI in the CL model arises because the fluid velocity is defined relative to the frame of motion of the Stokes mean drift velocity, which is usually taken to be prescribed, time independent and driven externally. We compare the GLM and CL theories by placing them both into the general framework of a stochastic Hamilton's principle for a 3D Euler--Boussinesq (EB) fluid in a rotating frame. In other examples, we also apply the GLM and CL methods to add wave physics and stochasticity to the familiar 1D and 2D shallow water flow models. The differences in the types of stochasticity which arise for GLM and CL models can be seen by comparing the Kelvin circulation theorems for the two models. The GLM model acquires stochasticity in its Lagrangian transport velocity for the currents and also in its group velocity for the waves. The Kelvin circulation theorem stochastic CL model can accept stochasticity in its both its integrand and in the Lagrangian transport velocity of its circulation loop.
