On the role of viscosity in shear instabilities

This paper aims al investigating the viscous corrections to mode selection and associated growth rate in the inflectional instability of shear layers. While, in the inviscid limit, the most unstable mode and its growth rate are fully determined by the initial thickness of the layer 2L and the velocity jump 2u it experiences, we show here that these quantities are modified by a factor {1 + [(a/0.2)/Re](2)}(-1/2) in the small Reynolds number Re = uL/v limit, with a a constant depending on the detailed shape of the initial velocity profile. This result agrees well with early numerical computations of Betchov and Szewczyk [Phys. Fluids 6, 1391 (1963)] and its interest is discussed in several different contexts. (C) 1998 American Institute of Physics.