Abstract

The mean drift in a permeable homogeneous bottom layer caused by internal gravity waves in an overlying stratified fluid, is investigated theoretically. We apply a Lagrangian formulation, together with the long-wave approximation, for the motion in the fluid and the fluid-saturated permeable layer. In the stratified fluid, we assume a constant Brunt-Väisälä frequency and inviscid flow. In the permeable bed, the density is constant. Here we apply a simple macroscopic version of Darcy’s law. For internal waves with frequency $\omega ,$ a fundamental small parameter in the permeable bed is $R=\omega K/{\nu }_2.$ Here $K$ is the effective permeability, and ${\nu }_2$ is the overall eddy viscosity, representing the small-scale turbulence of the interstitial fluid. The Lagrangian mean flow in each layer is weakly damped, with a damping rate proportional to $R,$ and composed of contributions from an infinite, but discrete set of eigen-modes. For each mode the mean drift in the permeable bed is an order $R^2$ smaller than the Stokes drift in internal waves at the bottom of the fluid layer. For spatially damped waves, it is particularly interesting that the wave-induced Eulerian mean current in the permeable bed may exceed the Stokes drift if the bed thickness is smaller than the upper layer thickness. It is suggested that the explored wave-induced particle drift in the permeable bottom layer could provide a physical model for the slow net transport of bio aerosols and smoke particles in the tropical rainforest.

摘要

理论上研究了由内部重力波在上覆分层流体中引起的可渗透均质底层的平均漂移。我们将拉格朗日公式与长波近似一起应用于流体和流体饱和渗透层中的运动。在分层流体中，我们假设Brunt-Väisälä频率恒定且无粘性。在渗透床中，密度是恒定的。在这里，我们应用达西定律的简单宏观形式。对于具有频率的内部波$\omega ，$ 渗透床的基本参数是 $\mathrm{[R}=\omega ķ/{\nu }_2。$ 这里 $ķ$ 是有效渗透率，并且 ${\nu }_2$是整体涡流粘度，代表组织液的小规模湍流。每层中的拉格朗日平均流量是弱阻尼的，阻尼率与$\mathrm{[R}，$由来自无限但离散的本征模式集的贡献组成。对于每种模式，渗透床中的平均漂移为一个阶${\mathrm{[R}}^2$小于斯托克斯在流体层底部内部波中的漂移。对于空间阻尼波，特别有趣的是，如果床层的厚度小于上层的厚度，则可渗透床中的波感应欧拉平均电流可能会超过斯托克斯漂移。有人认为，在可渗透的底层探索的波引起的颗粒漂移可以为热带雨林中生物气溶胶和烟尘颗粒的缓慢净运输提供物理模型。