Low-Reynolds-number oscillating boundary layers on adiabatic slopes

The presence of a no-slip, impermeable, adiabatic, sloped boundary in an otherwise quiescent, stably stratified, Boussinesq flow generates baroclinic vorticity within diffusive layer. Such conditions are typical the oscillating layers on adiabatic abyssal slopes, lake bathymetry, and coastal bathymetry absence high-wavenumber internal waves, mean flows, far-field turbulence larger scales, resonant tidal-bathymetric interaction. We investigate linear stability non-dimensional parameter space $M_2$ tide hydraulically smooth, mid-latitude slopes through Floquet analysis. dynamics depend three variables: Reynolds number for Stokes' second problem (Re), Prandtl number, frequency ratio that accounts resonance (C, criticality) buoyant restoring force tidal forcing. analysis results suggest laminar increasingly unstable as criticality parameter, and/or spanwise disturbance wavenumber increased. also show two-dimensional instability necessarily three-dimensional vorticity, which suggests evolution gravitational instabilities may be nonlinear $t\rightarrow\infty$.