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The effect of the boundary slip on the stability of shear flow
Author(s) -
He Qiaolin,
Wang XiaoPing
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800020
Subject(s) - slip (aerodynamics) , hagen–poiseuille equation , reynolds number , mathematics , shear flow , mechanics , slip line field , boundary value problem , hydrodynamic stability , slip ratio , physics , shear (geology) , mathematical analysis , geometry , flow (mathematics) , shear stress , geology , thermodynamics , turbulence , petrology
We study the linearized stability of shear flow satisfying Navier slip boundary conditions. The Orr‐Sommerfeld equation for the plane Poiseuille flow with Navier slip boundary conditions is solved numerically by the Chebyshev collocation method. Our numerical results show that slip at the boundary increases the critical Reynolds number R c for instability. The dependence of the this critical Reynolds number on the slip length l s is found to be R c (l s )‐ R c (0) ≈ C l s 2 .