Orr Sommerfeld Solver Using Mapped Finite Di?erence Scheme for Plane Wake Flow

Abstract

Linear stability analysis of the three dimensional plane wake flow is performed using a mapped finite di?erence scheme in a domain which is doubly infinite in the cross–stream direction of wake flow. The physical domain in cross–stream direction is mapped to the computational domain using a cotangent mapping of the form y = ?cot(??). The Squire transformation [2], proposed by Squire, is also used to relate the three–dimensional disturbances to the equivalent two– dimensional disturbances. The compact finite di?erence scheme of Lele [3] and the chain rule of di?erentiation are used to solve the Orr Sommerfeld equation. The results of linear stability analysis indicates that streamwise and the span- wise component of velocity eigenmodes are antisymmetric and the cross stream velocity eigenmode is symmetric. This is consistent with the DNS requirement of plane wake flow pertaining to solvability conditions[5]