Resolvent analysis allows for the extraction of the dominant input-output behavior of a fluid flow near a mean state, which can be used to advise potential applications to flow control. A significant hurdle in the adoption of resolvent analysis is the singular value decomposition (SVD) of the large linear operators involved. A matrix sketching algorithm is used to extract the primary forcing and response modes, with their associated gain. The formulation of an iterative algorithm is shown to be able to calculate the SVD of the resolvent operator with greater accuracy. The sources of error due to the selection of a test vector are discussed and it is shown that an accurate calculation of the forcing and response modes can be obtained by utilizing a test vector corresponding to a single point. The strength of this algorithm is shown by calculating the resolvent modes for a flow over a NACA 0012 airfoil at a Reynolds number of 23,000. This method is shown to converge for an arbitrary selection of test vector, obtaining results in agreement with past studies of this flow.

This method is used to perform windowed resolvent analysis on a two-dimensional turbulent flow of over a Honda sports utility vehicle (SUV) at $Re\approx 2.5\times 10^4$ to propose a flow control strategy for drag reduction. The force characteristics of the SUV are highly dependent on the wake structures and large structures in the wake region near the rear end of the vehicle are responsible for increase in drag of an SUV. We characterize the flow physics and modal analysis of the shear layer on the roof and the role of shear layer physics leading to the large structures in the wake dynamics. A moving window approach to investigate the windowed response modes of the resolvent operator over the roof of SUV is performed. The location of maximum gain shifts to the rear of the car as the spanwise wavenumer is reduced indicating the transition from small structures in the shear layer to large structures in the wake region. We use a body constrained window for forcing modes to investigate the optimum location of forcing to achieve desired response along the roof of the vehicle. An optimal forcing strategy about the placement of actuators and the frequency and direction of forcing is suggested after investigating the forcing modes at different frequencies and wave numbers.