A novel method for determination of convective velocity of coherent structures in high speed flows

A novel method to determine the average convection velocity of coherent structures in the shear layer of supersonic jets is presented in this paper. The method is based on the Proper Orthogonal Decomposition (POD) of a flow field and the standard advection equation. Substitution of a function satisfying the advection equation with its POD representation followed by the utilization of the fundamental properties of POD modes and coefficients yields an expression for the convection velocity in terms of the derivatives and the inner products of modes. The method is suitable for experimental data (like PIV) as it does not require the data set to be time resolved. For validation and practical applicability of the method, a sensitivity analysis has been performed using a synthetic data set followed by the application of the technique on the simulation data of a realistic research problem.