Double-diffusive convection in the finger regime is studied using direct numerical simulations in a confined domain. For narrow (1–4 mm horizontal extent) domains, we demonstrate active instabilities that are uniquely double-diffusive, or in other words that no instabilities develop when differential diffusion is not present. The novel double-diffusive instabilities are influenced by the boundaries, but demonstrate complex time-dependent evolution down to lateral extents of 1.25 mm. We quantify the energetics, the horizontal asymmetry, and the buoyancy flux due to the instability. We utilize these results to characterize the instability within regimes and point out that while coherent instabilities associated with larger gaps are well characterized by the ratio of diffusive effects to buoyancy forces (the time dependent Grashof number), for smaller gap widths, regime characterization is more difficult. Nevertheless, even at a gap of 1.25 mm, the instability remains robust, and thus it can be concluded that double diffusion can be employed to drive localized mixing in highly confined settings for which single constituent Rayleigh–Taylor does not manifest.
References
1.
D.
Brydon
, S.
Sun
, and R.
Bleck
, “A new approximation of the equation of state for seawater, suitable for numerical ocean models
,” J. Geophys. Res.: Oceans
104
, 1537
–1540
, (1999
).2.
T. J.
McDougall
, D. R.
Jackett
, D. G.
Wright
, and R.
Feistel
, “Accurate and computationally efficient algorithms for potential temperature and density of seawater
,” J. Atmos. Oceanic Technol.
20
, 730
–741
(2003
).3.
4.
M. E.
Stern
, “The ‘salt-fountain’ and thermohaline convection
,” Tellus
12
, 172
–175
(1960
).5.
R. W.
Schmitt
, “Double diffusion in oceanography
,” Annu. Rev. Fluid Mech.
26
, 255
–285
(1994
).6.
J.
Turner
, “Double-diffusive phenomena
,” Annu. Rev. Fluid Mech.
6
, 37
–54
(1974
).7.
R. W.
Schmitt
, “The characteristics of salt fingers in a variety of fluid systems, including stellar interiors, liquid metals, oceans, and magmas
,” Phys. Fluids
26
, 2373
–2377
(1983
).8.
J.
Carpenter
, T.
Sommer
, and A.
Wüest
, “Simulations of a double-diffusive interface in the diffusive convection regime
,” J. Fluid Mech.
711
, 411
–436
(2012
).9.
S.
Kimura
and W.
Smyth
, “Direct numerical simulation of salt sheets and turbulence in a double-diffusive shear layer
,” Geophys. Res. Lett.
34
, L21610
, (2007
).10.
P. H.
Sichani
, C.
Marchioli
, F.
Zonta
, and A.
Soldati
, “Shear effects on scalar transport in double diffusive convection
,” J. Fluids Eng.
142
, 121105
(2020
).11.
W.
Smyth
, J.
Nash
, and J.
Moum
, “Differential diffusion in breaking Kelvin–Helmholtz billows
,” J. Phys. Oceanogr.
35
, 1004
–1022
(2005
).12.
T.
Radko
, J.
Ball
, J.
Colosi
, and J.
Flanagan
, “Double-diffusive convection in a stochastic shear
,” J. Phys. Oceanogr.
45
, 3155
–3167
(2015
).13.
T.
Radko
, Double-Diffusive Convection
(Cambridge University Press
, 2013
).14.
W.
Jevons
, “II. On the cirrous form of cloud
,” London, Edinburgh, Dublin Philos. Mag. J. Sci.
14
, 22
–35
(1857
).15.
F. J.
Merceret
, “A possible manifestation of double diffusive convection in the atmosphere
,” Boundary-Layer Meteorol.
11
, 121
–123
(1977
).16.
W.
Baines
and J.
Turner
, “Turbulent buoyant convection from a source in a confined region
,” J. Fluid Mech.
37
, 51
–80
(1969
).17.
T. J.
McDougall
, “Double-diffusive plumes in unconfined and confined environments
,” J. Fluid Mech.
133
, 321
–343
(1983
).18.
O.
Kerr
, “Double-diffusive instabilities at a sloping boundary
,” J. Fluid Mech.
225
, 333
–354
(1991
).19.
O. S.
Kerr
, “Double-diffusive instabilities at a horizontal boundary after the sudden onset of heating
,” J. Fluid Mech.
859
, 126
–159
(2019
).20.
O. S.
Kerr
, “Double-diffusive instabilities at a vertical sidewall after the sudden onset of heating
,” J. Fluid Mech.
909
, A11
(2021
).21.
K.
Ghorayeb
and A.
Mojtabi
, “Double diffusive convection in a vertical rectangular cavity
,” Phys. Fluids
9
, 2339
–2348
(1997
).22.
X.
Zhang
, L.-l.
Wang
, H.
Zhu
, and C.
Zeng
, “Modeling of salt finger convection through a fluid-saturated porous interface: Representative elementary volume scale simulation and effect of initial buoyancy ratio
,” Phys. Fluids
32
, 082109
(2020
).23.
X.
Zhang
, L.-l.
Wang
, H.
Zhu
, and C.
Zeng
, “Pore-scale simulation of salt fingers in porous media using a coupled iterative source-correction immersed boundary-lattice Boltzmann solver
,” Appl. Math. Modell.
94
, 656
–675
(2021
).24.
A.
Mohamad
, R.
Bennacer
, and J.
Azaiez
, “Double diffusion natural convection in a rectangular enclosure filled with binary fluid saturated porous media: The effect of lateral aspect ratio
,” Phys. Fluids
16
, 184
–199
(2004
).25.
A.
Koberinski
, A.
Baglaenko
, and M.
Stastna
, “Schmidt number effects on Rayleigh-Taylor instability in a thin channel
,” Phys. Fluids
27
, 084102
(2015
).26.
J.
Penney
and M.
Stastna
, “Direct numerical simulation of double-diffusive gravity currents
,” Phys. Fluids
28
, 086602
(2016
).27.
D. A.
Nield
and A.
Benken
, Convection in Porous Media
(Springer International Publishing
, 2017
).28.
S.
Alqatari
, T. E.
Videbæk
, S. R.
Nagel
, A.
Hosoi
, and I.
Bischofberger
, “Confinement-induced stabilization of the Rayleigh-Taylor instability and transition to the unconfined limit
,” Sci. Adv.
6
, eabd6605
(2020
).29.
A.
Coutino
, “Hydrodynamics of the Yucatan peninsula carbonate aquifer: Surface flow, inland propagation and mixing
,” Ph.D. thesis (University of Waterloo
, 2021
).30.
W. R.
Wilcox
, “Transport phenomena in crystal growth from solution
,” Prog. Cryst. Growth Charact. Mater.
26
, 153
–194
(1993
).31.
H. E.
Huppert
and R. S. J.
Sparks
, “Double-diffusive convection due to crystallization in magmas
,” Annu. Rev. Earth Planet. Sci.
12
, 11
–37
(1984
).32.
J. S.
Turner
and L.
Gustafson
, “The flow of hot saline solutions from vents in the sea floor; some implications for exhalative massive sulfide and other ore deposits
,” Econ. Geol.
73
, 1082
–1100
(1978
).33.
M. G.
Rosevear
, B.
Gayen
, and B. K.
Galton-Fenzi
, “The role of double-diffusive convection in basal melting of antarctic ice shelves
,” Proc. Natl. Acad. Sci.
118
, e2007541118
(2021
).34.
M.
Gregg
and C.
Cox
, “The vertical microstructure of temperature and salinity
,” in Deep Sea Research and Oceanographic Abstracts
(Elsevier
, 1972
), Vol. 19
, pp. 355
–376
.35.
A. J.
Love
, C. T.
Simmons
, and D.
Nield
, “Double-diffusive convection in groundwater wells
,” Water Resour. Res.
43
, W08428
, (2007
).36.
A. I.
Mizev
, E. A.
Mosheva
, and A. V.
Shmyrov
, “Double-diffusive convection in the continuous flow microreactors
,” J. Phys.: Conf. Ser.
1945
, 012036
(2021
).37.
C. J.
Subich
, K. G.
Lamb
, and M.
Stastna
, “Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method
,” Int. J. Numer. Methods Fluids
73
, 103
–129
(2013
).38.
S.
Harnanan
, N.
Soontiens
, and M.
Stastna
, “Internal wave boundary layer interaction: A novel instability over broad topography
,” Phys. Fluids
27
, 016605
(2015
).39.
D.
Deepwell
, M.
Stastna
, M.
Carr
, and P. A.
Davies
, “Interaction of a mode-2 internal solitary wave with narrow isolated topography
,” Phys. Fluids
29
, 076601
(2017
).40.
D.
Caldwell
and S.
Eide
, “Soret coefficient and isothermal diffusivity of aqueous solutions of five principal salt constituents of seawater
,” Deep Sea Res., Part A
28
, 1605
–1618
(1981
).41.
A. C.
Ribeiro
, O.
Ortona
, S. M.
Simoes
, C. I.
Santos
, P. M.
Prazeres
, A. J.
Valente
, V. M.
Lobo
, and H. D.
Burrows
, “Binary mutual diffusion coefficients of aqueous solutions of sucrose, lactose, glucose, and fructose in the temperature range from (298.15 to 328.15) K
,” J. Chem. Eng. Data
51
, 1836
–1840
(2006
).42.
C.
Angeli
and E.
Leonardi
, “The effect of thermodiffusion on the stability of a salinity gradient solar pond
,” Int. J. Heat Mass Transfer
48
, 4633
–4639
(2005
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.
