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Effect of Schmidt number on the structure and propagation of density currents. (English) Zbl 1178.76115

Summary: The results of a numerical study of two- and three-dimensional Boussinesq density currents are described. They are aimed at exploring the role of the Schmidt number on the structure and dynamics of density driven currents. Two complementary approaches are used, namely a spectral method and a finite-volume interface capturing method. They allow for the first time to describe density currents in the whole range of Schmidt number \(1 \leq Sc \leq \infty \) and Reynolds number \(10^{2} \leq Re \leq 10^{4}\). The present results confirm that the Schmidt number only weakly influences the structure and dynamics of density currents provided the Reynolds number of the flow is large, say of \(O(10^{4})\) or more. On the contrary low- to moderate-\(Re\) density currents are dependant on \(Sc\) as the structure of the mixing region and the front velocities are modified by diffusion effects. The scaling of the characteristic density thickness of the interface has been confirmed to behave as \((ScRe)^{ - 1/2}\). Three-dimensional simulations suggest that the patterns of lobes and clefts are independent of \(Sc\). In contrast the Schmidt number is found to affect dramatically (1) the shape of the current head as a depression is observed at high-\(Sc\), (2) the formation of vortex structures generated by Kelvin-Helmholtz instabilities. A criterion is proposed for the stability of the interface along the body of the current based on the estimate of a bulk Richardson number. This criterion, derived for currents of arbitrary density ratio, is in agreement with present computed results as well as available experimental and numerical data.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76M22 Spectral methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
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