Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-30T20:17:06.521Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alldredge, A. & Cohen, Y. 1987 Can microscale chemical patches persist in the sea? Microelectrode study of marine snow, fecal pellets. Science 235 (4789), 689–691.CrossRefGoogle ScholarPubMed
Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients. J. Fluid Mech. 37, 289–306.Google Scholar
Burns, P. & Meiburg, E. 2012 Sediment-laden fresh water above salt water: linear stability analysis. J. Fluid Mech. 691, 279–314.CrossRefGoogle Scholar
Burns, P. & Meiburg, E. 2015 Sediment-laden fresh water above salt water: nonlinear simulations. J. Fluid Mech. 762, 156–195.CrossRefGoogle Scholar
Carazzo, G. & Jellinek, A. M. 2013 Particle sedimentation and diffusive convection in volcanic ash-clouds. J. Geophys. Res. 118 (4), 1420–1437.Google Scholar
Carey, S. 1997 Influence of convective sedimentation on the formation of widespread tephra fall layers in the deep sea. Geology 25 (9), 839–842.Google Scholar
Chen, C. F. 1997 Particle flux through sediment fingers. Deep-Sea Res. I 44 (9), 1645–1654.CrossRefGoogle Scholar
Davarpanah, J. S. & Wells, M. G. 2016 Enhanced sedimentation beneath particle-laden flows in lakes and the ocean due to double-diffusive convection. Geophys. Res. Lett. 43 (20), 10883–10890.Google Scholar
Green, T. 1987 The importance of double diffusion to the settling of suspended material. Sedimentology 34 (2), 319–331.CrossRefGoogle Scholar
Green, T. & Diez, T. 1995 Vertical plankton transport due to self-induced convection. J. Plankton Res. 17 (9), 1723–1730.Google Scholar
Holyer, J. Y. 1983 Double-diffusive interleaving due to horizontal gradients. J. Fluid Mech. 137, 347–362.CrossRefGoogle Scholar
Hoyal, D., Bursik, M. & Atkinson, J. 1999a The influence of diffusive convection on sedimentation from buoyant plumes. Mar. Geol. 159 (1), 205–220.CrossRefGoogle Scholar
Hoyal, D., Bursik, M. & Atkinson, J. 1999b Settling-driven convection: a mechanism of sedimentation from stratified fluids. J. Geophys. Res. 104 (C4), 7953–7966.Google Scholar
Lampitt, R., Achterberg, E., Anderson, T., Hughes, J. A., Iglesias-Rodriguez, M. D., Kelly-Gerreyn, B. A., Lucas, M., Popova, E. E., Sanders, R., Shepherd, J. G. et al. 2008 Ocean fertilization: a potential means of geoengineering? Phil. Trans. R. Soc. Lond. A 366 (1882), 3919–3945.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.CrossRefGoogle Scholar
Manville, V. & Wilson, C. J. N. 2004 Vertical density currents: a review of their potential role in the deposition and interpretation of deep-sea ash layers. J. Geol. Soc. 161 (6), 947–958.Google Scholar
Manzella, I., Bonadonna, C., Phillips, J. C. & Monnard, H. 2015 The role of gravitational instabilities in deposition of volcanic ash. Geology 43 (3), 211–214.CrossRefGoogle Scholar
Maxworthy, T. 1999 The dynamics of sedimenting surface gravity currents. J. Fluid Mech. 392, 27–44.CrossRefGoogle Scholar
Medrano, M., Garaud, P. & Stellmach, S. 2014 Double-diffusive mixing in stellar interiors in the presence of horizontal gradients. Astrophys. J. Lett. 792 (2), L30.CrossRefGoogle Scholar
Parsons, J., Bush, J. & Syvitski, J. 2001 Hyperpycnal plume formation from riverine outflows with small sediment concentrations. Sedimentology 48 (2), 465–478.Google Scholar
Parsons, J. & García, M. 2000 Enhanced sediment scavenging due to double-diffusive convection. Intl J. Sedim. Res. 70 (1), 47–52.Google Scholar
Radko, T. 2013 Double-diffusive Convection. Cambridge University Press.Google Scholar
Reali, J. F., Garaud, P., Alsinan, A. & Meiburg, E. 2017 Layer formation in sedimentary fingering convection. J. Fluid Mech. 816, 268–305.Google Scholar
Rouhnia, M. & Strom, K. 2015 Sedimentation from flocculated suspensions in the presence of settling-driven gravitational interface instabilities. J. Geophys. Res. 120 (9), 6384–6404.CrossRefGoogle Scholar
Ruddick, B. R. & Turner, J. S. 1979 The vertical length scale of double-diffusive intrusions. Deep-Sea Res. A 26 (8), 903–913.Google Scholar
Sánchez, X. & Roget, E. 2007 Microstructure measurements and heat flux calculations of a triple-diffusive process in a lake within the diffusive layer convection regime. J. Geophys. Res. 112 (C2), C02012.Google Scholar
Scheu, K. R., Fong, D. A., Monismith, S. G. & Fringer, O. B. 2015 Sediment transport dynamics near a river inflow in a large alpine lake. Limnol. Oceanogr. 60 (4), 1195–1211.Google Scholar
Schulte, B., Konopliv, N. & Meiburg, E. 2016 Clear salt water above sediment-laden fresh water: Interfacial instabilities. Phys. Rev. Fluids 1 (1), 012301.Google Scholar
Segre, P. N., Liu, F., Umbanhowar, P. & Weitz, D. A. 2001 An effective gravitational temperature for sedimentation. Nature (London) 409, 594.Google Scholar
Stern, M. E. 1960 The salt-fountain and thermohaline convection. Tellus 12 (2), 172–175.Google Scholar
Stern, M. E. 1967 Lateral mixing of water masses. In Deep Sea Research and Oceanographic Abstracts, vol. 14, pp. 747–753. Elsevier.Google Scholar
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.Google Scholar
Turner, J. S. 1985 Multicomponent convection. Annu. Rev. Fluid Mech. 17 (1), 11–44.Google Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35 (1), 48–56.CrossRefGoogle Scholar
Yu, X., Hsu, T. & Balachandar, S. 2013 Convective instability in sedimentation: linear stability analysis. J. Geophys. Res. 118 (1), 256–272.Google Scholar
Yu, X., Hsu, T. & Balachandar, S. 2014 Convective instability in sedimentation: 3-d numerical study. J. Geophys. Res. 119 (11), 8141–8161.Google Scholar

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