Investigation of the interfacial instability in a non-Boussinesq density stratified flow using linear stability theory

Abstract

Abstract The main goal of this study is investigating the interfacial instability in the shear density stratified flow in non-Boussinesq regime using linear stability theory. In the current study, the pseudospectral collocation method employed Chebyshev polynomials is applied to solve two coupled eigenvalue equations. Using the linear stability analysis in the temporal framework, the effects of various parameters on the flow instability have been studied. Obtained results in the present paper are showing that increasing the bed slope, the flow becomes more unstable; also at R = 1, Kelvin–Helmholtz and Holmboe waves appear. Furthermore, Holmboe waves were not observed only at θ = 0. This study shows that at R ≠ 1, in addition to observing Kelvin–Helmholtz and Holmboe waves with higher growth rates, by increasing the bed slope, the growth rate and the number of Kelvin–Helmholtz modes increase. With an improved understanding of the instability mechanisms and features with including the non-Boussinesq effects, one can confirm some of the previous experimental results and offer new indications to observations that have not been fully explained. In designing laboratory experiments to observe Holmboe waves and estimating their wavelengths and phase speeds the results of present paper are also could be useful.