Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow

We examine the excitation of inviscid stationary cross ow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modi ed to a signi cant extent. This behavior contrasts sharply with earlier ndings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the cross ow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for ow reversal to occur in the canonical solution. We also nd that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to cross ow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed. The work of MC was supported by NASA Langley Research Center under contract number NAS1-20059. The research of the second author was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while he was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001.