Efficient global resolvent analysis via the one-way Navier–Stokes equations

Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes with more than one inhomogeneous spatial coordinate remains computationally expensive. In this two-part paper, we show how efficient accurate approximations can be obtained using well-posed marching method that contain slowly varying direction. first part the derive convergent one-way equation describing downstream-traveling waves supported by linearized Navier-Stokes equations. Integrating these equations, which requires significantly less CPU memory resources direct solution approximates action operator on forcing vector. This capability leveraged 2 paper to compute approximate modes. The validated demonstrated examples simple acoustics problem supersonic jet.