Stochastic estimation of cavity shear layer and fully developed turbulent channel flows: linear and non linear multi-time-delay analyses

Abstract

A nonlinear extension of the multi-time-delay linear stochastic estimation technique is presented. In order to highlight the potentialities of the proposed methodology, results of its application to two different flows are discussed. The first application is the estimation of the temporal dynamics of the velocity fluctuations in a cavity shear layer in low subsonic conditions from wall-pressure measurements. The second application is the estimation of the streamwise velocity fluctuations in the buffer layer of a fully developed turbulent channel flow from wall-shear stress measurements. It is shown that the accuracy of the nonlinear technique is application dependent, i.e. it is significantly affected by the underlying nonlinear nature of the flow investigated. In particular, we show that for the cavity shear layer case investigated, the improvement is marginal and it appears not to be worth the additional computational complexity of solving the nonlinear problem. On the other hand, the improvement in accuracy of the nonlinear estimation of the velocity fluctuations in the buffer layer is significant, owing to the strong nonlinearity of the dynamics in the wall bounded flow.