A model for transitional plane Couette flow

Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy Pub Date : 2000-02-01 DOI:10.1016/S1287-4620(00)00113-7

Paul Manneville, Fabien Locher

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引用次数: 13

Abstract

A simplified model of plane Couette flow is derived by means of a cross-stream (y) Galerkin expansion in terms of trigonometric functions appropriate for idealized stress-free boundary conditions at the plates. A set of partial differential equations is obtained, governing the in-plane (x–z) space-dependence of a velocity field taken in the form: u=U₀(x,z,t)+[1+U₁(x,z,t)]sin(πy/2), v=V₁(x,z,t)cos(πy/2), w=W₀(x,z,t)+W₁(x,z,t)sin(πy/2). Beyond Lorenz-like Waleffe's modeling (Waleffe 1997), this Swift–Hohenberg type of approach is expected to give an access to the microscopic mechanism of spatiotemporal intermittency typical of the transition to turbulence in plane Couette flow (Pomeau 1986, Bergé et al. 1998).

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过渡平面库埃特流模型

利用适于板上理想无应力边界条件的三角函数，用横流(y)伽辽金展开导出了平面库埃特流的简化模型。得到了速度场平面内(x - z)空间依赖方程:u=U0(x,z,t)+[1+U1(x,z,t)]sin(πy/2)， v=V1(x,z,t)cos(πy/2)， w=W0(x,z,t)+W1(x,z,t)sin(πy/2)。除了Lorenz-like Waleffe的模型(Waleffe 1997)之外，这种Swift-Hohenberg类型的方法有望为平面Couette流过渡到湍流的时空间歇性的微观机制提供途径(Pomeau 1986, berg et al. 1998)。

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Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy

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