Assimilation of under-resolved velocity observations in the wake of a towed sphere

Reconstruction of the wake behind a towed sphere from sparse data is performed using an adjoint-variational data assimilation. As the sphere is towed at the free-stream speed, under-resolved velocity measurements are collected in a stationary sub-volume of the wake, at moderate Reynolds number. The forward-adjoint Navier-Stokes solver reconstructs the flow state within the volume (Wang, Wang & Zaki, J. Compu. Phys. 396, 2019) and has been extended to also estimate the time-dependent boundary conditions on the surfaces of the sub-volume. Tests using independent simulations as surrogate for experimental measurements are used to highlight important considerations of the data assimilation procedure. The dispersion properties of the numerical solver must be taken into consideration when performing these numerical tests. We demonstrate that data assimilation can accurately predict the full flow state of the wake within the observation sub-domain. The error reduction is assessed for the velocity fields which are observed but under-resolved in the data, as well as for unobserved quantities such as vorticity and pressure. The results highlight the potential of infusing measurements from laboratory experiments with numerical simulations to overcome limitations of both techniques.