Stability Analysis of Unsteady Nonparallel Flows via Separation of Variables: Synthesis of Analytical and Numerical Computations

摘要

Problems of hydrodynamic stability are of great theoretical and practical interest, as evidenced by the number of publications devoted to this subject. The classical linear stability theory of viscous incompressible flows [1] is concerned with the development in space and time of infinitesimal perturbations around a given basic flow. Then small disturbances are resolved into normal modes which, for a steady-state basic flow, depend on time exponentially with a complex exponent X. For parallel shear basic flows, further separation of variables in the governing stability equations leads to a set of ordinary differential equations which, with taking recourse to Squire's theorem and considering only 2-D disturbances, reduces to the Orr-Sommerfeld equation. When this equation is solved with proper boundary conditions, the problem of linear stability of parallel flows is reduced to a 2-point boundary (eigen) value problem.