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A settling-driven instability in two-component, stably stratified fluids

Published online by Cambridge University Press:  06 March 2017

A. Alsinan ,
E. Meiburg Open the ORCID record for E. Meiburg [Opens in a new window]  and
P. Garaud
A. Alsinan
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
E. Meiburg*
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
P. Garaud
Affiliation:
Department of Applied Mathematics and Statistics, Baskin School of Engineering, University of California at Santa Cruz, Santa Cruz, CA 95064, USA
*
†Email address for correspondence: [email protected]
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Abstract

We analyse the linear stability of stably stratified fluids whose density depends on two scalar fields where one of the scalar fields is unstably stratified and involves a settling velocity. Such conditions may be found, for example, in flows involving the transport of sediment in addition to heat or salt. A linear stability analysis for constant-gradient base states demonstrates that the settling velocity generates a phase shift between the perturbation fields of the two scalars, which gives rise to a novel, settling-driven instability mode. This instability mechanism favours the growth of waves that are inclined with respect to the horizontal. It is active for all density and diffusivity ratios, including for cases in which the two scalars diffuse at identical rates. If the scalars have unequal diffusivities, it competes with the elevator mode waves of the classical double-diffusive instability. We present detailed linear stability results as a function of the governing dimensionless parameters, including for lateral gradients of the base state density fields that result in predominantly horizontal intrusion instabilities. Highly resolved direct numerical simulation results serve to illustrate the nonlinear competition of the various instabilities for such flows in different parameter regimes.

JFM classification

Convection: Double diffusive convection Geophysical and Geological Flows: Sediment transport Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 816 , 10 April 2017 , pp. 243 - 267
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Copyright
© 2017 Cambridge University Press 

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Alsinan et al. supplementary movie

Sediment concentration perturbation field from a two-dimensional simulation for $Pr=7$, $\tau=1$, $R_{\rho}=1.5$, $\phi=0$ and $W_{st}=1$, with white noise as initial condition.

Download Alsinan et al. supplementary movie(Video)
Video 31.8 MB

Alsinan et al. supplementary movie

Sediment concentration perturbation field from a two-dimensional simulation for $Pr=7$, $\tau=0.01$, $R_{\rho}=150$, $\phi=0$ and $W_{st}=5$, initiated by white noise.

Download Alsinan et al. supplementary movie(Video)
Video 11.1 MB

Alsinan et al. supplementary movie

Sediment concentration perturbation field from a two-dimensional simulation for $Pr=7$, $\tau=5$, $R_{\rho}=1.5$, $\phi=0.1$ and $W_{st}=0$, initiated by white noise.

Download Alsinan et al. supplementary movie(Video)
Video 50.2 MB

Alsinan et al. supplementary movie

Sediment concentration perturbation field from a two-dimensional simulation for $Pr=7$, $\tau=5$, $R_{\rho}=1.5$, $\phi=0.1$ and $W_{st}=0.5$, initiated by white noise.

Download Alsinan et al. supplementary movie(Video)
Video 40.4 MB