Adjoint-variational reconstruction of turbulence in isothermal and stratified channel flow*

In many canonical and engineering turbulent flows, measurements are challenging and limited in resolution. Accurate reconstruction of the full flow state, which can significantly enhance our scientific understanding and inform engineering objectives, is a challenging inverse problem. Recent work explored adjoint-variational data assimilation to reconstruct the velocity field in isothermal turbulent channel flow from sparse data (M. Wang and T. Zaki, 2021, J. Fluid Mech. 917, A9). The results demonstrated that accurate flow reconstruction at all scales is possible when the spatio-temporal resolution of measurements satisfies criteria set by the Taylor microscale and the Lyapunov timescale. Whether stratification simply modifies these scales or also alters the criteria for accurate reconstruction is not known, and will be examined using numerical experiments. Observations are extracted at various resolutions from independent, fully resolved simulations, and the accuracy of the adjoint-variational reconstruction will be assessed against the hidden truth.