NONPARALLEL WAVE INSTABILITY ANALYSIS OF BOUNDARY-LAYER FLOWS

Abstract

An order-of-magnitude approach is employed to analyze the linear nonparallel wave instability of boundary-layer flows. This analysis removes the restriction imposed by previous investigators on the weak dependence of the streamwise variation of disturbance quantities. A superposition technique along with a modified Thomas trans-formation is employed to solve the resulting nonhomogeneous equation for the amplitude function of the disturbance without the use of an adjoint eigenfunction, which is needed in conventional approaches. All of the eigenfuncrions are treated in their general forms. The growing rate of the disturbance intensity is found to depend on both streamwise and transverse coordinates. At a local observation point × (or Re_×), the growing rate of the disturbance intensity has a maximum value near y = Y = Ylpar;U_∞/ vX)^½ = 3 for Blasiusflow. The neutral stability curve can then be defined by letting the maximum growing rate of the disturbance intensity be zero. Excellent agreement is found between the present results and available experimental data.