Estimating near-wall turbulence using adjoint-variational data assimilation

Experimental measurements of near-wall turbulence are challenging to acquire. Using adjoint-variational data assimilation (4DVar), we augment incomplete measurements that do not sample the viscous or buffer layer. The time series is divided into a sequence of shorter assimilation horizons, and 4DVar is performed within each window to estimate the flow within the gap, between the first measurement point and the wall, at full spatial resolution. The accuracy of the estimation is first verified using synthetic measurements from an independent direct numerical simulation. When the full system is simulated and the first measurement plan is near y⁺= 50, the predictions of the wall shearstresses and pressure are accurate. Spectral analysis of the errors in the estimation is interpreted in terms of the influence, or lack thereof, of near-wall eddies on the observation in the core of the channel.We then proceed to examine the case where the assimilation is performed in truncated sub-domains of the channel, where the boundary conditions are unknown. This configuration is designed to model application to experimental measurements, where we wish to predict the instantaneous wall shear stresses and pressure at high Reynolds numbers within truncated simulation domains.