Linear stability analysis of inclined two-layer stratified flows

Two-layer stratified flows are commonly observed in geophysical and environmental contexts. At the interface between the two layers, both velocity shear and buoyancy interplay, resulting in various modes of instability. Results from a temporal linear stability analysis of a two-layer stratified exchange flow under the action of a mean advection are presented, investigating the effect of a mild bottom slope on the stability of the interface. The spatial acceleration is directly included in the governing stability equations. The results demonstrate that increasing the bottom slope has a similar effect on the stability of the flow as does increasing the ratio R of the thickness of the velocity mixing layer δν to that of the density layer δρ as it causes the flow to be more unstable to the Kelvin–Helmholtz instabilities. The transition from Kelvin–Helmholtz modes to stable flow occurs at lower Richardson numbers and wavenumbers compared to the horizontal two-layer flow. Kelvin–Helmholtz modes are decreasingly amplified for 1