EFFECT OF CROSS-FLOW ON GORTHER INSTABILITY IN INCOMPRESSIBLE BOUNDARY-LAYERS

Linear stability theory is used to study the effect of cross-flow on G ortler instability in incompressible boundary layers. The results cove r a wide range of sweep angle, pressure gradient, and wall curvature p arameters. It is shown that the cross-how stabilizes Gortler disturban ces by reducing the maximum growth rate and shrinking the unstable ban d of spanwise wave numbers. On the other hand, the effect of concave w all curvature on cross-flow instability is destabilizing. Calculations show that the changeover from Gortler to cross-flow instabilities is a function of Gortler number, pressure gradient, and sweep angle. The results demonstrate that Gortler instability may still be relevant in the transition process on swept wings even at large angles of sweep if the pressure gradient is sufficiently small. The influence of pressur e gradient and sweep can be combined by defining a cross-flow Reynolds number. Thus, the changeover from Gortler to cross-flow instability t akes place at some critical cross-flow Reynolds number whose value inc reases with Gortler number. (C) 1995 American Institute of Physics.