Optimal estimation of log-layer turbulence using surface pressure measurements

The estimation and control of wall-bounded flows often relies on practical sensing capabilities that are physically bound to the wall. Wall-pressure sensors provide such capabilities while maintaining a robust measurement signal in detecting flow variations away from the wall. Prior studies have investigated the efficacy of data-driven projection schemes such as linear stochastic estimation in tracking the evolution of attached eddies using wall-pressure sensing. This approach, however, relies on strong correlations between wall pressure and the velocity field in the log layer. We present an alternative framework that leverages persistently strong two-point correlations between the pressure field in the measurement and estimation planes. In this approach, said projection schemes are first used to infer pressure fluctuations in the log layer from the wall pressure. The target velocity field is subsequently obtained as the solution of the pressure Poisson equations. We demonstrate the efficacy of this approach in the context of Kalman filtering for real-time estimation of log-layer turbulence whereby wall-pressure measurements are used to correct the predictions of the stochastically forced linearized Navier-Stokes equations. The spatio-temporal coloring of the stochastic forcing is identified using the noise-modeling approach of Zare et al. (J. Fluid Mech., vol. 812, 2017) to ensure statistical consistency of the model with the results of direct numerical simulations.