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Dynamics of fingering convection. I. Small-scale fluxes and large-scale instabilities. (English) Zbl 1241.76229

Summary: Double-diffusive instabilities are often invoked to explain enhanced transport in stably stratified fluids. The most-studied natural manifestation of this process, fingering convection, commonly occurs in the ocean’s thermocline and typically increases diapycnal mixing by 2 orders of magnitude over molecular diffusion. Fingering convection is also often associated with structures on much larger scales, such as thermohaline intrusions, gravity waves and thermohaline staircases. In this paper, we present an exhaustive study of the phenomenon from small to large scales. We perform the first three-dimensional simulations of the process at realistic values of the heat and salt diffusivities and provide accurate estimates of the induced turbulent transport. Our results are consistent with oceanic field measurements of diapycnal mixing in fingering regions. We then develop a generalized mean-field theory to study the stability of fingering systems to large-scale perturbations using our calculated turbulent fluxes to parameterize small-scale transport. The theory recovers the intrusive instability, the collective instability and the \(\gamma \)-instability as limiting cases. We find that the fastest growing large-scale mode depends sensitively on the ratio of the background gradients of temperature and salinity (the density ratio). While only intrusive modes exist at high density ratios, the collective and \(\gamma \) instabilities dominate the system at the low density ratios where staircases are typically observed. We conclude by discussing our findings in the context of staircase-formation theory.

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
76E06 Convection in hydrodynamic stability
76F25 Turbulent transport, mixing
86A05 Hydrology, hydrography, oceanography
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References:

[1] DOI: 10.1029/2007GC001778
[2] DOI: 10.1111/j.2153-3490.1960.tb01295.x
[3] DOI: 10.1051/0004-6361:20066891
[4] DOI: 10.1175/1520-0485(1992)022<1158:SOTGOM>2.0.CO;2
[5] DOI: 10.1088/2041-8205/728/2/L30
[6] DOI: 10.1175/1520-0485(1999)029<1404:TCOSFT>2.0.CO;2
[7] DOI: 10.1007/s10236-003-0060-9
[8] DOI: 10.1175/2009JPO4297.1
[9] DOI: 10.1051/0004-6361:20077274
[10] DOI: 10.1175/JPO3000.1
[11] Canuto, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (2007) · Zbl 1121.76001
[12] DOI: 10.1175/1520-0485(2004)034<1723:DIOAFT>2.0.CO;2
[13] DOI: 10.1103/PhysRevE.73.035301
[14] DOI: 10.1063/1.868596 · Zbl 1032.76549
[15] DOI: 10.1126/science.1108678
[16] DOI: 10.1017/S0022112069000553
[17] DOI: 10.1146/annurev.fl.26.010194.001351
[18] DOI: 10.1063/1.864419 · Zbl 0523.76074
[19] DOI: 10.1175/1520-0485(1981)011<1015:FOTTSR>2.0.CO;2
[20] DOI: 10.1016/0198-0149(79)90083-9
[21] DOI: 10.1016/S0377-0265(99)00021-4
[22] DOI: 10.1016/0198-0149(79)90104-3
[23] DOI: 10.1016/S0079-6611(03)00028-4
[24] DOI: 10.1175/1520-0485(1998)028<0589:SOTGMO>2.0.CO;2
[25] DOI: 10.1016/S0079-6611(03)00029-6
[26] DOI: 10.1016/S0967-0637(02)00099-7
[27] DOI: 10.1017/S0022112008002127 · Zbl 1147.76058
[28] DOI: 10.1175/1520-0485(2000)030<2231:DDIITP>2.0.CO;2
[29] DOI: 10.1017/S0022112004002290 · Zbl 1065.76087
[30] DOI: 10.1175/1520-0485(1995)025<0348:DDITIO>2.0.CO;2
[31] DOI: 10.1017/S0022112003006785 · Zbl 1065.76086
[32] DOI: 10.1016/j.dsr.2007.02.002
[33] DOI: 10.1086/382668
[34] Peyret, Spectral Methods for Incompressible Viscous Flow (2002) · Zbl 1005.76001
[35] DOI: 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
[36] DOI: 10.1088/2041-8205/728/2/L29
[37] DOI: 10.1175/1520-0485(1985)015<1542:DDIPIF>2.0.CO;2
[38] DOI: 10.1016/0079-6611(81)90003-3
[39] DOI: 10.1175/1520-0485(1985)015<1532:DDIPIL>2.0.CO;2
[40] DOI: 10.1038/231178a0
[41] DOI: 10.1016/S0079-6611(03)00027-2
[42] Tait, Deep-Sea Res. 15 pp 275– (1968)
[43] DOI: 10.1357/002224087788326885
[44] DOI: 10.1357/002224001762842244
[45] DOI: 10.1017/S0022112003004166 · Zbl 1032.76505
[46] Stern, Deep-Sea Res. 16 pp 97– (1969)
[47] Kluikov, Double-Diffusive Convection, Geophysical Monograph pp 287– (1995)
[48] DOI: 10.1017/S0022112005004416 · Zbl 1074.76024
[49] DOI: 10.1357/002224008787157467
[50] DOI: 10.1175/1520-0485(2002)032<3638:IWOPBS>2.0.CO;2
[51] DOI: 10.1017/S0022112081000682 · Zbl 0484.76057
[52] DOI: 10.1017/S0022112069001066 · Zbl 0164.28802
[53] DOI: 10.1029/2007JC004455
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.