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

1973 ◽  
Vol 57 (1) ◽  
pp. 27-43 ◽  
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.

scholarly journals Simulations of a double-diffusive interface in the diffusive convection regime

2012 ◽  
Vol 711 ◽  
pp. 411-436 ◽  
Author(s):  
J. R. Carpenter ◽  
T. Sommer ◽  
A. Wüest
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Molecular Diffusion ◽  
Layer Structure ◽  
Previous Theory ◽  
Convection Regime ◽  
Graphic Interface ◽  
Diffusive Convection ◽  
Diffusive Interface ◽  
Double Diffusive

AbstractThree-dimensional direct numerical simulations are performed that give us an in-depth account of the evolution and structure of the double-diffusive interface. We examine the diffusive convection regime, which, in the oceanographically relevant case, consists of relatively cold fresh water above warm salty water. A ‘double-boundary-layer’ structure is found in all of the simulations, in which the temperature ($T$) interface has a greater thickness than the salinity ($S$) interface. Therefore, thin gravitationally unstable boundary layers are maintained at the edges of the diffusive interface. The $TS$-interface thickness ratio is found to scale with the diffusivity ratio in a consistent manner once the shear across the boundary layers is accounted for. The turbulence present in the mixed layers is not able to penetrate the stable stratification of the interface core, and the $TS$-fluxes through the core are given by their molecular diffusion values. Interface growth in time is found to be determined by molecular diffusion of the $S$-interface, in agreement with a previous theory. The stability of the boundary layers is also considered, where we find boundary layer Rayleigh numbers that are an order of magnitude lower than previously assumed.

Experimental investigation of double-diffusive groundwater fingers

1988 ◽  
Vol 188 ◽  
pp. 363-382 ◽  
Author(s):  
Paul T. Imhoff ◽  
Theodore Green
Keyword(s):  
Experimental Investigation ◽  
Viscous Fluid ◽  
Molecular Diffusion ◽  
Saturated Porous Medium ◽  
Flux Ratio ◽  
Buoyancy Flux ◽  
Tank Model ◽  
Density Anomaly ◽  
Double Diffusive ◽  
Good Agreement

Using a sand-tank model and the salt-sugar system, double-diffusive fingers formed in a saturated porous medium. In contrast to the quasi-steady fingering typically observed in a viscous fluid, the fingering here was quite unsteady. The fingers’ structure was observed, and measurements of the sugar flux indicate that double-diffusive groundwater fingers can transport solutes at rates as much as two orders of magnitude larger than those associated with molecular diffusion in motionless groundwater. The buoyancy-flux ratio, r = αFT/βFS, increased from r = 0.65 ± 0.02 (at Rρ = 1.02) to r = 0.81 ± 0.06 (at Rρ = 1.50), where Rρ is the density-anomaly ratio. (Using the salt-sugar system in a viscous fluid, r was previously shown to decrease with increasing Rρ.) The buoyancy flux due to sugar varied approximately as R−5.6ρ, which is almost identical with the variation found for salt-sugar fingers in a viscous fluid. The model of Green (1984) was applied to the experiments and predicted buoyancy-flux ratios and finger widths that were in fairly good agreement with the measured values, although the predicted buoyancy fluxes due to sugar were significantly larger than the measured fluxes.

Layered double-diffusive convection in porous media

1981 ◽  
Vol 102 ◽  
pp. 221-248 ◽  
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.

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

2021 ◽  
Vol 933 ◽  
Author(s):  
Yantao Yang ◽  
Roberto Verzicco ◽  
Detlef Lohse ◽  
C.P. Caulfield
Keyword(s):  
Initial Perturbation ◽  
Flux Ratio ◽  
Vertical Transport ◽  
Salt Flux ◽  
Double Diffusive Convection ◽  
Control Parameters ◽  
Diffusive Regime ◽  
Diffusive Convection ◽  
Wide Range ◽  
Double Diffusive

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.

The Influence of Coupled Molecular Diffusion on Double-Diffusive Convection in a Porous Medium

1986 ◽  
Vol 108 (4) ◽  
pp. 872-876 ◽  
Author(s):  
N. Rudraiah ◽  
M. S. Malashetty
Keyword(s):  
Porous Medium ◽  
Molecular Diffusion ◽  
Normal Mode Analysis ◽  
Finite Amplitude ◽  
Mode Analysis ◽  
Double Diffusive Convection ◽  
Amplitude Analysis ◽  
Cross Diffusion ◽  
Diffusive Convection ◽  
Double Diffusive

The effect of coupled molecular diffusion on double-diffusive convection in a horizontal porous medium is studied using linear and nonlinear stability analyses. In the case of linear theory, normal mode analysis is employed incorporating two cross diffusion terms. It is found that salt fingers can form by taking cross-diffusion terms of appropriate sign and magnitude even when both concentrations are stably stratified. The conditions for the diffusive instability are compared with those for the formation of fingers. It is shown that these two types of instability will never occur together. The finite amplitude analysis is used to derive the condition for the maintenance of fingers. The stability boundaries are drawn for three different combinations of stratification and the effect of permeability is depicted.

Shear Effects on Scalar Transport in Double Diffusive Convection1

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Pejman Hadi Sichani ◽  
Cristian Marchioli ◽  
Francesco Zonta ◽  
Alfredo Soldati
Keyword(s):  
Fluid Layer ◽  
Density Ratio ◽  
Lewis Number ◽  
Scalar Transport ◽  
Confined Fluid ◽  
Fluid Instability ◽  
Diffusive Convection ◽  
Diffusive Fluxes ◽  
Double Diffusive ◽  
Diffusivity Ratio

Abstract In this article, we examine the effect of shear on scalar transport in double diffusive convection (DDC). DDC results from the competing action of a stably stratified, rapidly diffusing scalar (temperature) and an unstably stratified, slowly diffusing scalar (salinity), which is characterized by fingering instabilities. We investigate, for the first time, the effect of shear on the diffusive and convective contributions to the total scalar transport flux within a confined fluid layer, examining also the associated fingering dynamics and flow structure. We base our analysis on fully resolved numerical simulations under the Oberbeck–Boussinesq condition. The problem has five governing parameters: The salinity Prandtl number, Prs (momentum-to-salinity diffusivity ratio); the salinity Rayleigh number, Ras (measure of the fluid instability due to salinity differences); the Lewis number, Le (thermal-to-salinity diffusivity ratio); the density ratio, Λ (measure of the effective flow stratification), and the shear rate, Γ. Simulations are performed at fixed Prs, Ras, Le, and Λ, while the effect of shear is accounted for by considering different values of Γ. Preliminary results show that shear tends to damp the growth of fingering instability, leading to highly anisotropic DDC dynamics associated with the formation of regular salinity sheets. These dynamics result in significant modifications of the vertical transport rates, giving rise to negative diffusive fluxes of salinity and significant reduction of the total scalar transport, particularly of its convective part.

Experimental Study on Double-Diffusive Convection During Solidification of NH4Cl-H2O Hypereutectic Solution in Cylinder Cavity

2008 ◽  
Author(s):  
Bofeng Bai ◽  
Jun Lu ◽  
Lei Zhang ◽  
Heng Li
Keyword(s):  
Experimental Study ◽  
Cylindrical Cavity ◽  
Particle Image ◽  
Solidification Process ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Image Velocimetry ◽  
Diffusive Interface ◽  
Contrary Direction ◽  
Double Diffusive

In order to reveal the law of double-diffusive convection of multi-compound solution in cylindrical cavity, experimental study on solidification of NH4Cl-H2O hypereutectic solution has been performed by using particle image velocimetry (PIV). The influencing factors of flow patterns and intensity are also analyzed. The results show that: 1) There are two approximately symmetric main convection cells in the liquid which are down along the sidewall and up along the center of the cylindrical cavity. Meanwhile, there are also two secondary cells on the bottom corner of cylindrical cavity, which flow in contrary direction to that of the main ones; 2) Due to the release of water during the solidification process, solute layers and diffusive interface are developed in the liquid and will be disappeared in the end; 3) The cooling temperature and the initial concentration have significantly effects on the flow velocity, solute layers and diffusive interface.

Temperature Modulation of Double Diffusive Convection in a Horizontal Fluid Layer

2006 ◽  
Vol 61 (7-8) ◽  
pp. 335-344 ◽  
Author(s):  
Beer Singh Bhadauria
Keyword(s):  
Rayleigh Number ◽  
Fluid Layer ◽  
Thermosolutal Convection ◽  
Periodic Part ◽  
Temperature Modulation ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Horizontal Fluid Layer ◽  
Double Diffusive ◽  
Diffusivity Ratio

Linear stability analysis is performed for the onset of thermosolutal convection in a horizontal fluid layer with rigid-rigid boundaries. The temperature field between the walls of the fluid layer consists of two parts: a steady part and a time-dependent periodic part that oscillates with time. Only infinitesimal disturbances are considered. The effect of temperature modulation on the onset of thermosolutal convection has been studied using the Galerkin method and Floquet theory. The critical Rayleigh number is calculated as a function of frequency and amplitude of modulation, Prandtl number, diffusivity ratio and solute Rayleigh number. Stabilizing and destabilizing effects of modulation on the onset of double diffusive convection have been obtained. The effects of the diffusivity ratio and solute Rayleigh number on the stability of the system are also discussed.

Two-dimensional effects in double-diffusive convection

1974 ◽  
Vol 63 (3) ◽  
pp. 577-592 ◽  
Author(s):  
J. S. Turner ◽  
C. F. Chen
Keyword(s):  
Two Dimensional ◽  
Double Diffusive Convection ◽  
Mechanism Of Formation ◽  
Concentration Gradients ◽  
One Dimensional ◽  
Horizontal Gradients ◽  
Diffusive Convection ◽  
Similar Density ◽  
Double Diffusive ◽  
Vertical Gradients

The limitations of existing one-dimensional experiments on double-diffusive convection are discussed, and a variety of new two-dimensional phenomena are described. We have used the sugar-salt system and shadowgraph photography to make exploratory studies of motions which can arise in a fluid with two smooth, opposing, vertical concentration gradients, with and without horizontal gradients. Many different effects have been observed, the most important of which are the following, (a) In the ‘finger’ case, local disturbances can propagate rapidly as wave motions, which cause a simultaneous breakdown to convection over large horizontal distances. (b) Layers formed in the’ diffusive’ sense overturn locally to produce fingers, but propagate more slowly, as convective rather than wave motions, (c) A series of layers, separated by diffusive interfaces, can become unstable, in the sense that successive layers merge in time as their densities become equal, (d) The presence of horizontally separated sources of water of similar density but differentT,Scharacteristics can lead to the development of strong vertical gradients and extensive quasi-horizontal layering.Most of our results are qualitative, but it is hoped that they will stimulate further quantitive work on each of the new processes described. It is already clear that much more needs to be done before the mechanism of formation of layers observed in the ocean can be regarded as properly understood.

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