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A model for transitional plane Couette flow

Paul Manneville 1, * Fabien Locher 1 
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(py/2), v = V1 (x, z, t) cos(py/2), w = W0(x,z,t) + W1 (x, z, t) sin(py/2). Beyond Lorenzlike 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, Berge et al. 1998). (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
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Paul Manneville, Fabien Locher. A model for transitional plane Couette flow. Comptes rendus de l’Académie des sciences. Série 2, 2000, 328 (2), pp.159-164. ⟨10.1016/s1287-4620(00)00113-7⟩. ⟨hal-01025353⟩



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