Orr Sommerfeld Solver Using Mapped Finite Difference Scheme for Plane Wake Flow

Linear stability analysis of the three dimensional plan e wake flow is performed using a mapped finite difference scheme in a domain which is doubly infinite in the cross- stream direction of wake flow. Thephysical domain in cross - stream direction is mapped to the computational domain using a cotangent mapping of the form y = - (Beta)cot (Pi Zeta) . The Squire transformation (2], proposed by Squire,is also used to relate the three- dimension al disturbances to the equivalent two dimensional disturban ces. The compact finite difference scheme of Lele [3]and the chain rule of differentiation are used to solve the Orr Sommerfeldequation. The results of linear stability analysis indicates that streamwiseand the spanwise component of velocity eigenmodes are antisymmetric and theCross stream velocity eigenmode is symmetric . This is consistent with the DNSrequiremeni of plane wake flow pertaining to solvability conditions [5].