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A linear analysis of the mean flow of an isothermal ideally-expanded Mach 1.5 turbulent jet is conducted. Optimal response modes describing the fluctuating hydrodynamic and acoustic fields are obtained in a computationally efficient way by spatially marching the linearized One-Way Navier-Stokes equations. For this purpose, an adjoint-based optimization framework is proposed and demonstrated for calculating optimal boundary conditions and optimal volumetric forcing. The optimal modes are validated against modes obtained in terms of global resolvent analysis. Two scenarios are considered in the present analysis. In the first case, no restrictions are applied to the spatial forcing distribution. In the second scenario, the forcing is restricted to the nozzle plane. The resulting optimal and suboptimal modes are compared to spectral proper orthogonal modes obtained from a high-fidelity large eddy simulation. The implications of these observations are discussed in detail.

One Way Navier-Stokes and resolvent analysis for modeling coherent structures in a supersonic turbulent jet