Estimating large-scale structures in wall turbulence using linear models

Abstract

A dynamical systems approach is used to devise a linear estimation tool for channel flow at a friction Reynolds number of Reτ = 1000. The estimator uses time-resolved velocity measurements at a single wall-normal location to estimate the velocity field at other wall-normal locations (the data coming from direct numerical simulations). The estimation tool builds on the work of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336-382) by using a Navier-Stokes-based linear model and treating any nonlinear terms as unknown forcings to an otherwise linear system. In this way nonlinearities are not ignored, but instead treated as an unknown model input. It is shown that, while the linear estim..