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Instability of two-layer flows with viscosity and density stratification. (English) Zbl 1479.76035

Summary: The three-dimensional linear stability characteristics of two-layer immiscible fluid with a free surface are considered, wherein a Newtonian fluid contains a small amount of sediment particles, and overlies a lower fluid that contents hyperconcentration of sediment. Rheological experiments are carried out on three kinds of artificial sediments with different silt-kaolin mixing ratios to study the rheological properties of the lower fluid. The results show that the rheological properties of the lower fluid conform to the power-law model. Based on this, the modified N-S and Squire equations in each layer are derived for the gravity-driven flow, which are calculated by using the finite difference method. The effect of various dimensionless parameters, such as the viscosity ratio \((c_m)\), the density ratio \((s)\), the power-law index \((n)\), and the thickness ratio \((h_s)\) on the instability characteristics of the flow is investigated. It is observed that increasing \(c_m, s\) and \(h_s\) is stabilizing for both long and short waves, which leads to an increase of the critical Reynolds number \((\text{Re}_\text{wcr})\), and a decrease of the bandwidth of the unstable wavenumbers. The disturbed velocities \((u\) and \(w)\) are also decreased. Decreasing the shear-thinning tendency (increasing \(n)\) of the lower fluid is destabilizing for both long and short waves, which leads to a decrease of \((\text{Re}_\text{wcr})\) and an increase of the disturbed velocities.

MSC:

76E05 Parallel shear flows in hydrodynamic stability
76D50 Stratification effects in viscous fluids
76-10 Mathematical modeling or simulation for problems pertaining to fluid mechanics
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