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

Figures & data

Figure 1. Schematic of the problem under study with velocity profiles U (y) and the base concentration of ρ (y) of a two-layer flow. δ_ρ is the density layer thickness and δ_V is the shear layer thickness. g is gravitational acceleration and θ is the bed slope

Figure 2. Changes of (a) growth rate and (b) phase speed for ${\alpha }_r=0.3$ and $\theta =0$

Figure 3. Changes of (a) growth rate and (b) phase speed (the legend is same as part a) for ${\alpha }_r=0.3$ and $\theta =0.2$. Solid line is the first mode (Kelvin–Helmholtz) and dotted line is the second mode (Holmboe) of instability

Figure 4. Changes of (a) growth rate and (b) phase speed for ${\alpha }_r=0.5$ and $\theta =0$

Figure 5. Changes of (a) growth rate and (b) phase speed for ${\alpha }_r=0.5$ and $\theta =0.2$

Figure 6. Temporal growth rate in terms of Richardson number for R = 3 and Ө = 0

Figure 7. Time growth rate in terms of Richardson number for R = 5 and Ө = 0.2.. Solid line is the first mode (Kelvin–Helmholtz) and dotted line is the second mode (Holmboe) of instability. The legend is same as Figure 3