Stochastic receptivity analysis of boundary layer flow

TL;DR

This paper introduces a stochastic receptivity analysis method for boundary layer flows using linearized Navier-Stokes equations, providing insights into flow response to free-stream turbulence without costly simulations.

Contribution

It develops a stochastic receptivity framework that combines local and global linearized models to analyze boundary layer response to turbulence, advancing beyond traditional resolvent analysis.

Findings

Locally parallel analysis captures key mechanisms and length-scales.

Global analysis predicts cascade of streamwise scales.

Modal decomposition of velocity covariance reveals flow structures.

Abstract

We utilize the externally forced linearized Navier-Stokes equations to study the receptivity of pre-transitional boundary layers to persistent sources of stochastic excitation. Stochastic forcing is used to model the effect of free-stream turbulence that enters at various wall-normal locations and the fluctuation dynamics are studied via linearized models that arise from locally parallel and global perspectives. In contrast to the widely used resolvent analysis that quantifies the amplification of deterministic disturbances at a given temporal frequency, our approach examines the steady-state response to stochastic excitation that is uncorrelated in time. In addition to stochastic forcing with identity covariance, we utilize the spatial spectrum of homogeneous isotropic turbulence to model the effect of free-stream turbulence. Even though locally parallel analysis does not account for the effect of the spatially evolving base flow, we demonstrate that it captures the essential mechanisms and the prevailing length-scales in stochastically forced boundary layer flows. On the other hand, global analysis, which accounts for the spatially evolving nature of the boundary layer flow, predicts the amplification of a cascade of streamwise scales throughout the streamwise domain. We show that the flow structures that can be extracted from a modal decomposition of the resulting velocity covariance matrix, can be closely captured by conducting locally parallel analysis at various streamwise locations and over different wall-parallel wavenumber pairs. Our approach does not rely on costly stochastic simulations and it provides insight into mechanisms for perturbation growth including the interaction of the slowly varying base flow with streaks and Tollmien-Schlichting waves.