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

The development of a separated bottom boundary layer in the footprint of a large-amplitude internal solitary wave of depression, propagating against an oncoming barotropic current, is examined in detail using high-resolution implicit large eddy simulation. The wave is supported by a continuous two-layer stratification. The Reynolds number based on the water column height is 1.6 x 10(5). This numerical simulation is the first to reproduce the self-sustained three-dimensional vortex shedding, resultant transition, and turbulence under an ISW, which have long been hypothesized to occur in field experiments. No artificial noise is inserted into the flow domain. Part I of this study focuses on a structural description of the sequence of flow regimes developing from a wave-induced, long, high-aspect-ratio, laminar separation bubble. Three illuminating topological features are identified. (a) The spatial development of the self-sustained turbulence is composed of three transitional stages: (i) spontaneous excitation of a global instability in the separation bubble that emanates trailing vortices, (ii) vortex breakup and degeneration into turbulent clouds, and (iii) relaxation to a spatially developing turbulent boundary layer. (b) In the separation bubble, there exists a three-dimensional linear global oscillator, which is primarily excited by the two-dimensional absolute instability of the separated shear layer. This global mode possesses a transverse coherent structure. The transverse perturbation subsequently excites an elliptic instability mode inside the shed vortex, resulting in an axial distortion of the vortex core. (c) A shortwave secondary instability is excited in the form of a series of coherent streamwise vortex streaks that wrap around each shed vortex, leading to rapid break up and burst of the vortex.