State estimation in transitional and turbulent cylindrical-Couette flow*

Transitional and turbulent cylindrical-Couette flows are very sensitive to initial conditions and the start-up process. As a result, in numerical simulations, it is difficult to prescribe appropriate initial conditions that achieve target flow states, and comparisons to experiments become challenging. This problem is addressed using an adjoint-variational state-estimation algorithm. By combining simulations with limited measurements, we predict the appropriate initial conditions that track the correct flow states. We first consider estimation of a superposition of saturated wavy vortices from wall measurements. The computed initial condition contains all the relevant modes, and accurately reproduces the true energy spectra, mean-flow distortion and flow structures within the time intervals where measurements are available. We subsequently investigate the more challenging turbulent case with coarse-grained velocity data. The velocity field is reconstructed on a much finer simulation grid. The estimation error is 70% lower than space-time interpolation, with a better prediction of large-scale structures and vorticity.