标题： 高雷诺数下两个振动平面之间的稳态流 显示英文标题

标题： Steady streaming between two vibrating planes at high Reynolds numbers

摘要： 我们考虑在两个横向振动的固体壁之间的不可压缩流动，并构建纳维-斯托克斯方程解的渐近展开式，当振动幅度和斯托克斯层厚度都较小时且具有相同的量级。我们的渐近展开式在流动边界处仍然有效。特别是，我们推导了平均流动的方程和边界条件。在主导阶，平均流动由带有额外项的定常纳维-斯托克斯方程描述，该额外项包含主导阶的斯托克斯漂移速度。在稍有不同的背景下（对于由振荡保守体力引起的流动），同样的方程之前已由Riley（2001）推导出来。一般理论被应用于两个特定例子，即由壁面横向振动产生的稳态射流，这些振动以驻波和行波形式出现。特别是，在波同方向传播的情况下，诱导的流动是平面平行的，拉格朗日速度剖面可以解析计算。这个例子可以看作是将蠕动泵理论扩展到高雷诺数的情况。 显示英文摘要

摘要： We consider incompressible flows between two transversely vibrating solid walls and construct an asymptotic expansion of solutions of the Navier-Stokes equations in the limit when both the amplitude of vibrations and the thickness of the Stokes layer are small and have the same order of magnitude. Our asymptotic expansion is valid up to the flow boundary. In particular, we derive equations and boundary conditions, for the averaged flow. In the leading order, the averaged flow is described by the stationary Navier-Stokes equations with an additional term which contains the leading-order Stokes drift velocity. In a slightly different context (for a flow induced by an oscillating conservative body force), the same equations had been derived earlier by Riley (2001). The general theory is applied to two particular examples of steady streaming induced by transverse vibrations of the walls in the form of standing and travelling plane waves. In particular, in the case of waves travelling in the same direction, the induced flow is plane-parallel and the Lagrangian velocity profile can be computed analytically. This example may be viewed as an extension of the theory of peristaltic pumping to the case of high Reynolds numbers.