Roughness-induced boundary layer instability beneath internal solitary waves*

We investigate the effects of bottom roughness on the bottom boundary layer (BBL) instability beneath internal solitary waves (ISWs) of depression. Applying both 2D numerical simulations and linear stability theory, an extensive parametric study explores the effect of the Reynolds number, pressure gradient, roughness (bump) height h_b, and roughness wavelength λ_b on the BBL instability. The simulations show that small roughness heights h_b on the scale of laboratory flume materials (∼100 times less than the thickness of the viscous sublayer δ_v) can destabilize the BBL and trigger vortex shedding, at critical Reynolds numbers much lower than what occurs for numerically smooth surfaces. We identify two mechanisms of vortex shedding, depending on h_b/δ_v. For h_b/δ_v>≈1, vortices are forced directly by local flow separation in the lee of each bump. Conversely, for h_b/δ_v<≈10^-1, roughness seeds perturbations in the BBL, which are amplified by the BBL flow. Roughness wavelengths close to that of the most unstable mode of the BBL, as predicted by linear instability theory, are preferentially amplified. This resonator-like nature of the BBL flow beneath ISWs has also been reported for the BBL driven by surface solitary waves and by periodic monochromatic waves. Our results show that including surface roughness, or more generally an appropriate level of amplification seed noise, is necessary to reconcile the discrepancies between the instability threshold in the lab versus those predicted by 2D spectral simulations.