Receptivity and transition in a wave boundary layer over random bottom topography

TL;DR

This study uses direct numerical simulations to explore how a solitary wave boundary layer over random bottom topography responds to perturbations, revealing complex transition mechanisms influenced by streaks and vortices.

Contribution

It uncovers the nonlinear feedback loop between streaks and vortices and identifies three distinct transition scenarios depending on streak amplitude.

Findings

Boundary layer exhibits selective response to broadband bottom perturbations.

High-amplitude streaks indirectly amplify vortices, intensifying the boundary layer.

Three transition scenarios: 2D wave instabilities, inner shear-layer, and outer shear-layer instabilities.

Abstract

Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective response to broadband perturbations from the bottom, and develops streamwise-elongated streaks. When the streaks reach high amplitudes, they indirectly amplify streamwise-elongated vortices through modulating small-scale fluctuations and pressure fields. These stronger vortices in turn stir the boundary layer more effectively and further intensify streaks via the lift-up mechanism. This nonlinear feedback loop increases the sensitivity of the boundary layer to the roughness level and yields dramatic variations among cases sharing the same Reynolds number with differing roughness height. Three different local breakdown scenarios are observed depending on the amplitude of the streaks: (i) two-dimensional wave instabilities in the regions with weak streaks; (ii) inner shear-layer instabilities in the regions with moderate-amplitude streaks; (iii) rapidly growing outer shear-layer instabilities in the regions with highly elevated high-amplitude streaks. Inner instabilities have the slowest growth rate among all transition paths, which confirms the previous predictions on the stabilising role of moderate-amplitude streaks (\"Onder & Liu, J. Fluid. Mech., vol. 896, 2020, A20).