Journal of Fluid Mechanics

Finite-amplitude steady waves in plane viscous shear flows

F. A.  Milinazzo a1p1 and P. G.  Saffman a1
a1 Applied Mathematics, California Institute of Technology, Pasadena, CA 91125

Article author query
milinazzo fa   [Google Scholar] 
saffman pg   [Google Scholar] 


Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

(Published Online April 20 2006)
(Received January 7 1985)
(Revised May 14 1985)

p1 Present address: Royal Roads Military College, Victoria, B.C., Canada.