Layering and vertical transport in sheared double-diffusive convection in the diffusive regime

A sequence of two- and three-dimensional simulations are conducted for the double-diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, with early-time coarsening of the observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear significantly spatio-temporally modifies the vertical transport of the various scalars. The flux ratio $\gamma ^*$ (i.e. the ratio between the density fluxes due to the total salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistent with the physical model proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, 1978, pp. 417–432) and the variational arguments presented by Stern (J. Fluid Mech., vol. 114, 1982, pp. 105–121) for unsheared double-diffusive convection.

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Acoustic Detection of Oceanic Double-Diffusive Convection: A Feasibility Study

Journal of Atmospheric and Oceanic Technology ◽

10.1175/2009jtecho696.1 ◽

2010 ◽

Vol 27 (3) ◽

pp. 580-593 ◽

Cited By ~ 3

Author(s):

Tetjana Ross ◽

Andone Lavery

Keyword(s):

Acoustic Scattering ◽

Double Diffusive Convection ◽

Western Antarctic Peninsula ◽

Acoustic Detection ◽

Acoustic Backscattering ◽

Diffusive Regime ◽

Diffusive Convection ◽

In Situ Observations ◽

Double Diffusive

Abstract The feasibility of using high-frequency acoustic scattering techniques to map the extent and evolution of the diffusive regime of double-diffusive convection in the ocean is explored. A scattering model developed to describe acoustic scattering from double-diffusive interfaces in the laboratory, which accounted for much of the measured scattering in the frequency range from 200 to 600 kHz, is used in conjunction with published in situ observations of diffusive-convection interfaces to make predictions of acoustic scattering from oceanic double-diffusive interfaces. Detectable levels of acoustic scattering are predicted for a range of different locations in the world’s oceans. To corroborate these results, thin acoustic layers detected near the western Antarctic Peninsula using a multifrequency acoustic backscattering system are shown to be consistent with scattering from diffusive-convection interfaces.

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Applicability and failure of the flux-gradient laws in double-diffusive convection

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.244 ◽

2014 ◽

Vol 750 ◽

pp. 33-72 ◽

Cited By ~ 8

Author(s):

Timour Radko

Keyword(s):

Large Scale ◽

Numerical Models ◽

Vertical Transport ◽

Double Diffusive Convection ◽

Flux Gradient ◽

Salinity Gradients ◽

Diffusive Convection ◽

Small Scales ◽

New Formulation ◽

Double Diffusive

AbstractDouble-diffusive flux-gradient laws are commonly used to describe the development of large-scale structures driven by salt fingers – thermohaline staircases, collective instability waves and intrusions. The flux-gradient model assumes that the vertical transport is uniquely determined by the local background temperature and salinity gradients. While flux-gradient laws adequately capture mixing characteristics on scales that greatly exceed those of primary double-diffusive instabilities, their accuracy rapidly deteriorates when the scale separation between primary and secondary instabilities is reduced. This study examines conditions for the breakdown of the flux-gradient laws using a combination of analytical arguments and direct numerical simulations. The applicability (failure) of the flux-gradient laws at large (small) scales is illustrated through the example of layering instability, which results in the spontaneous formation of thermohaline staircases from uniform temperature and salinity gradients. Our inquiry is focused on the properties of the ‘point-of-failure’ scale ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H_{pof}$) at which the vertical transport becomes significantly affected by the non-uniformity of the background stratification. It is hypothesized that$H_{pof} $can control some key characteristics of secondary double-diffusive phenomena, such as the thickness of high-gradient interfaces in thermohaline staircases. A more general parametrization of the vertical transport – the flux-gradient-aberrancy law – is proposed, which includes the selective damping of relatively short wavelengths that are inadequately represented by the flux-gradient models. The new formulation is free from the unphysical behaviour of the flux-gradient laws at small scales (e.g. the ultraviolet catastrophe) and can be readily implemented in theoretical and large-scale numerical models of double-diffusive convection.

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Double diffusive convection in the diffusive regime

Applied Scientific Research ◽

10.1007/bf00389267 ◽

1982 ◽

Vol 39 (4) ◽

pp. 301-319 ◽

Cited By ~ 5

Author(s):

Sheng-Ming Chang ◽

Seppo A. Korpela ◽

Yee Lee

Keyword(s):

Double Diffusive Convection ◽

Diffusive Regime ◽

Diffusive Convection ◽

Double Diffusive

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Transport and profile measurements of the diffusive interface in double diffusive convection with similar diffusivities

Journal of Fluid Mechanics ◽

10.1017/s002211207300100x ◽

1973 ◽

Vol 57 (1) ◽

pp. 27-43 ◽

Cited By ~ 52

Author(s):

T. G. L. Shirtcliffe

Keyword(s):

Molecular Diffusion ◽

Flux Ratio ◽

Optical Measurements ◽

Salt Flux ◽

Density Anomaly ◽

Diffusive Convection ◽

Diffusive Interface ◽

Double Diffusive ◽

Vertical Gradients ◽

Diffusivity Ratio

The transport properties of a diffusive interface with diffusivity ratio $\kappa_S/\kappa_T = {\textstyle\frac{1}{3}}$ have been measured, using salt and sugar as the diffusing components. The flux ratio is constant and equal to (κS/κT)½. The normalized salt flux is related to the density anomaly ratio Rρ = βΔS/αΔT by the power law F*T = 2·59Rρ−12.6 over four decades. Optical measurements show that the vertical gradients of concentration of salt and sugar within the interface are those required if molecular diffusion is to account for the whole flux of each component.

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Layered double-diffusive convection in porous media

Journal of Fluid Mechanics ◽

10.1017/s0022112081002619 ◽

1981 ◽

Vol 102 ◽

pp. 221-248 ◽

Cited By ~ 80

Author(s):

R. W. Griffiths

Keyword(s):

Porous Medium ◽

Flux Ratio ◽

Geothermal System ◽

Double Diffusive Convection ◽

Salinity Gradients ◽

Diffusive Convection ◽

Diffusive Interface ◽

Convection In Porous Media ◽

And Diffusion ◽

Double Diffusive

In this paper it is shown that layered double-diffusive convection of a fluid within a porous medium is possible. A thin ‘diffusive’ interface was observed in a Hele Shaw cell and in a laboratory porous medium, with salt and sugar or heat and salt as the diffusing components. Heat–salt and salt–sugar fluxes through two-layer convection systems were measured and are compared with predictions of a model. For the thermohaline system the salt and heat buoyancy fluxes are approximately in the ratio r ≃ ετm½, where ε is the porosity and Tm is the appropriate ratio of diffusivities. The behaviour of the heat flux is explained in terms of a coupling between purely thermal convection within each convecting layer and diffusion through the density interface. Salinity gradients are important only within the interface. The presence of a ‘diffusive’ interface in the Wairakei geothermal system is postulated. The ratio of heat and salt fluxes (that can be estimated from existing observations) through this convection system is consistent with the laboratory flux ratio.

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The influence of a third diffusing component upon the onset of convection

Journal of Fluid Mechanics ◽

10.1017/s0022112079000811 ◽

1979 ◽

Vol 92 (4) ◽

pp. 659-670 ◽

Cited By ~ 45

Author(s):

R. W. Griffiths

Keyword(s):

Stability Analysis ◽

Rayleigh Number ◽

Small Amplitude ◽

Double Diffusive Convection ◽

Onset Of Convection ◽

Molecular Diffusivity ◽

Diffusive Convection ◽

Wide Range ◽

Straight Lines ◽

Double Diffusive

The small amplitude stability analysis for the onset of double-diffusive convection when the density gradient is gravitationally stable is extended to include a third diffusing component. Special attention is given to systems with κ1 [Gt ] κ2, κ3 and Pr [Gt ] κ/κ1, where κi is the molecular diffusivity of the ith component and Pr is the Prandtl number based on the largest of the Ki. It is found that the boundary for the onset of overstability is approximated by two straight lines in a Rayleigh number plane. Small concentrations of a third property with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities, the magnitude of this effect being proportional to κ1/Ki. Oscillatory and direct ‘salt-finger’ modes are found to be simultaneously unstable under a wide range of conditions when the density gradients due to the components with the greatest and smallest diffusivities are of the same sign.

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