An inverse problem for the estimation of upstream velocity profiles in an incompressible turbulent boundary layer

An inverse problem is solved for the estimation of upstream velocity profiles in an incompressible turbulent boundary layer over a smooth flat plate. The inverse analysis is based on the boundary layer morphology, making use of the law of the wall and the law of the wake to estimate boundary layer parameters from measured velocity histories. The direct problem of the turbulent boundary layer equations is solved by using finite difference method with the Cebeci–Smith turbulence model. The numerical solution of the direct problem is validated by experimental data obtained through the hotwire anemometry in a low-speed wind tunnel. The friction velocity, Von Kármán constant, law of the wall constant, Coles’s wake-strength parameter and boundary layer thickness for the initial profile are determined as unknown parameters by the Levenberg–Marquardt algorithm. The estimated upstream velocity profiles compare favourably with hotwire anemometry measurements at the same location.