Self-sustained instability, transition, and turbulence induced by a long separation bubble in the footprint of an internal solitary wave. II. Flow statistics

The statistical properties of the self-sustained turbulent wake downstream of a long, high-aspect-ratio, laminar separation bubble are studied. The primary focus is on the relaxation of turbulent wake to a zero pressure gradient (ZPG) turbulent boundary layer, in terms of mean flow, Reynolds stresses, and turbulent kinetic energy (TKE) budget. The bubble is initiated by the strong adverse pressure gradient (APG) induced by a large-amplitude, laboratory-scale internal solitary wave of depression propagating against an oncoming barotropic current. The high-resolution large eddy simulation data generated in Part I of this two-part article is used for analysis. It is shown that the wake development in the early stage, following the breakdown of coherent vortices toward the trailing region of the separation bubble, possesses a statistical character similar to that of a self-similar plane mixing layer. The mean streamwise velocity profile relaxes to that of a ZPG turbulent boundary layer at 15 water column depths form the wave trough. This relaxation distance normalized by the bubble length is equal to 5 which is shorter than reported by Alam and Sandham's short bubble [J. Fluid Mech. 403, 223 (2000)] that is induced by a stronger APG. In regions further downstream of the bubble, distributions of the Reynolds stresses resemble those of channel flow. The relaxation of the TKE budget to that of a ZPG turbulent boundary layer is slower far away from the wall and faster near the wall, as compared to the relaxation of the mean flow to that of a ZPG turbulent boundary layer. Large bed stresses beneath the shed vortices and persistent near-bed turbulence offer an insight into frequently observed sediment resuspension events in coastal seas.