Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes and have an important role in the mixing process. In this work, the linear stability analysis in the temporal framework is used to study the stability characteristics of a particle-laden stratified two-layer flow for two different background density profiles: smooth (hyperbolic tangent) and piecewise linear. The effect of parameters, such as bed slope, viscosity, and particle size, on the stability is also considered. The pseudospectral collocation method employing Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, there are some differences in the stability characteristics of the two density profiles. In the case of R = 1 (R is the ratio of the shear layer thickness to the density layer thickness), the stability boundary in smooth profile is the transition from the unstable flow (where the dominant unstable mode is Kelvin–Helmholtz) to the stable one where in the piecewise linear profile this boundary is the transition from Kelvin–Helmholtz to the Holmboe mode. It is also shown that the unstable region increases with the bed slope and unstable modes amplify as the bed slope increases. For R = 5 the flow does not become stable by increasing the stratification in nonzero bed slope, and in some wavenumbers the Kelvin–Helmholtz and Holmboe modes coexist. In addition, by increasing the bed slope the growth rate of the Holmboe mode and the range of its existence decrease. As expected, the viscosity makes the current more stable, and for large values of the viscosity (small Reynolds number) the flow becomes stable at long waves (small wave numbers) for all bulk Richardson numbers. Existence of small particles does not change the instability characteristics so much, however, large particles make the flow more unstable.
First Measurement of Electron Temperature and Density Profiles for Spherical Tokamak Plasmas Sustained by Lower Hybrid Waves
