Linear and nonlinear spatial developments of twohyphen;dimensional wall jets on curved surfaces are computed using pseudospectralhyphen;finite difference methods. Inviscid analysis shows that the instability originates from the inner/outer region on a concave/convex wall; the shear layer is thus always unstable regardless of the curvature. This primary instability is a steady spanwise vortex structure similar to Gouml;rtler instability in a Blasius flow. In the present study, a perturbation of prescribed wave number agr; is assumed. In the limit of high Reynolds number (Re) and small curvature (egr;), a parabolic set of nonlinear equations describes the spatial evolution of the disturbance. Direct marching simulation of the perturbation and a parabolic stability approach are employed. Both give the same results with different computational efficiencies. For the concave case at low Gouml;rtler numbers (G2=egr;sqrt;Re), perturbations are unstable for small agr;. Their energy reaches a maximum and then decays. At highG, the most unstable disturbance occurring at larger agr; will grow exponentially and reach saturation. The convex case is the most unstable situation. But as for the concave case, the most dangerous disturbance moves from small to larger agr; asGincreases. The numerical results are able to capture the primary instability as observed in the experiment of Matsson lsqb;Phys. Fluids7, 3048 (1995)rsqb;. copy;1996 American Institute of Physics.
展开▼
