Pressure/velocity coupling induced by a near wall wake

A combined wall pressure/velocity analysis of the wake of a disk located in the vicinity of a flat wall is presented in this paper. One gap ratio only is selected. In this situation, the footprint of the flow unsteadiness on the magnitude of the wall fluctuating pressure is significant while the natural vortex shedding properties of the wake are only slightly altered. Spatio-temporal velocity and pressure/velocity correlations are analyzed. They carry the signature of the large-scale coherence and periodicity associated with vortex shedding and exhibit characteristic phase relations. Advanced statistical analysis techniques are adapted and developed. A conditional phase averaging of the pressure and velocity fields is obtained. The proper orthogonal decomposition of a spatio-temporal pressure data set on the axis of the near wake is shown to be efficient (1) to determine the phase of the spatio-temporal pressure field projected on the two first modes and (2) to distinguish between quiescent random signatures and more energetic phases. Conditional statistics show very clearly that the large-scale structures interact with the flat wall. Finally, a linear stochastic estimation (LSE) of the velocity field is computed from the fluctuating pressure data. We show the superiority of the spatio-temporal LSE over the spatial LSE in predicting the kinetic energy and the coherent spectral properties of the fluctuating velocity field. Moreover, the linear stochastic estimation is very good in predicting the phase-averaged conditional velocity field.