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.

scholarly journals Stability of a Double-Diffusive Interface in the Diffusive Convection Regime

2012 ◽  
Vol 42 (5) ◽  
pp. 840-854 ◽  
Author(s):  
J. R. Carpenter ◽  
T. Sommer ◽  
A. Wüest
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Boundary Layers ◽  
Linear Stability Analysis ◽  
Direct Numerical Simulations ◽  
Diffusive Convection ◽  
Diffusive Interface ◽  
Double Diffusive

Abstract In this paper, the authors explore the conditions under which a double-diffusive interface may become unstable. Focus is placed on the case of a cold, freshwater layer above a warm, salty layer [i.e., the diffusive convection (DC) regime]. The “diffusive interface” between these layers will develop gravitationally unstable boundary layers due to the more rapid diffusion of heat (the destabilizing component) relative to salt. Previous studies have assumed that a purely convective-type instability of these boundary layers is what drives convection in this system and that this may be parameterized by a boundary layer Rayleigh number. The authors test this theory by conducting both a linear stability analysis and direct numerical simulations of a diffusive interface. Their linear stability analysis reveals that the transition to instability always occurs as an oscillating diffusive convection mode and at boundary layer Rayleigh numbers much smaller than previously thought. However, these findings are based on making a quasi-steady assumption for the growth of the interfaces by molecular diffusion. When diffusing interfaces are modeled (using direct numerical simulations), the authors observe that the time dependence is significant in determining the instability of the boundary layers and that the breakdown is due to a purely convective-type instability. Their findings therefore demonstrate that the relevant instability in a DC staircase is purely convective.

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 Nonlinear Double-diffusive Convection in a Low Prandtl Number Fluid

1980 ◽  
Vol 33 (1) ◽  
pp. 59 ◽  
Author(s):  
N Riahi
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Layer Structure ◽  
Solute Concentration ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Solute Fluxes ◽  
Boundary Layer Method ◽  
Double Diffusive

Nonlinear double-diffusive convection is studied using the modal equations of cellular convection. The boundary layer method is used by assuming a large Rayleigh number R for a fluid of low Prandtl number (J, and different ranges of the diffusivity ratio 7: and. the solute Rayleigh number Rs. The heat and solute fluxes are found to increase with R(J and decrease with Rs. The effect of the solute is stabilizing, although the convection in a fluid with large (J is less affected by the solute concentration. The flow is shown to have a solute layer which thickens as (J, R, .-1 or R;l decreases. It is proved that it is only for this layer that the solute affects the boundary layer structure.

The Relationship Between Atmospheric Boundary Layer Structure, Brown Haze, and Air Pollution in Auckland, New Zealand

2021 ◽  
Author(s):  
Hannah Marley ◽  
Kim Dirks ◽  
Andrew Neverman ◽  
Ian McKendry ◽  
Jennifer Salmond
Keyword(s):  
Boundary Layer ◽  
Air Pollution ◽  
New Zealand ◽  
Atmospheric Boundary Layer ◽  
Boundary Layers ◽  
Layer Structure ◽  
High Surface ◽  
Residual Layer ◽  
Pollution Levels ◽  
Haze Formation

<p><span><span>A brown air pollution haze that forms over some international cities during the winter has been found to be associated with negative health outcomes and high surface air pollution levels. Previous research has demonstrated a well-established link between the structure of the atmospheric boundary layer (ABL) and surface air quality; however, the degree to which the structure of the ABL influences for formation of local-</span></span><span><span>scale</span></span><span><span> brown haze is unknown. Using continuous ceilometer data covering seven consecutive winters, we investigate the influence of the structure of the ABL in relation to surface air pollution and brown haze formation over an urban area of complex coastal terrain in the Southern Hemisphere city of Auckland, New Zealand. Our results suggest the depth and evolution of the ABL has a strong influence on severe brown haze formation. When days with severe brown haze are compared with those when brown haze is expected but not observed (based on favorable meteorology and high surface air pollution levels), days with severe brown haze are found to coincide with significantly shallower daytime convective boundary layers (~ 48% lower), and the nights preceding brown haze formation are found to have significantly shallower nocturnal boundary layers (~ 28% lower). On severe brown haze days the growth rate during the morning transition phase from a nocturnal boundary layer to a convective daytime boundary layer is found to be significantly reduced (70 m h</span></span><sup><span><span>-1</span></span></sup><span><span>) compared to days on which brown haze is expected but not observed (170 m h</span></span><sup><span><span>-1</span></span></sup><span><span>). Compared with moderate brown haze, severe brown haze conditions are found to be associated with a significantly higher proportion of days with a distinct residual layer present in the ceilometer profiles, suggesting the entrainment of residual layer pollutants may contribute to the severity of the haze. This study illustrates the complex interaction between the ABL structure, air pollution, and the presence of brown haze, and demonstrates the utility of a ceilometer instrument in understanding and predicting the occurrence of brown haze events. </span></span></p>

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.

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.

Does Rotation Influence Double-Diffusive Fluxes in Polar Oceans?

2014 ◽  
Vol 44 (1) ◽  
pp. 289-296 ◽  
Author(s):  
J. R. Carpenter ◽  
M.-L. Timmermans
Keyword(s):  
Arctic Ocean ◽  
Heat Fluxes ◽  
Small Scale ◽  
Previous Theory ◽  
Thermal Interface ◽  
Diffusive Convection ◽  
Polar Oceans ◽  
Diffusive Fluxes ◽  
Mixed Layers ◽  
Double Diffusive

Abstract The diffusive (or semiconvection) regime of double-diffusive convection (DDC) is widespread in the polar oceans, generating “staircases” consisting of high-gradient interfaces of temperature and salinity separated by convectively mixed layers. Using two-dimensional direct numerical simulations, support is provided for a previous theory that rotation can influence DDC heat fluxes when the thickness of the thermal interface sufficiently exceeds that of the Ekman layer. This study finds, therefore, that the earth’s rotation places constraints on small-scale vertical heat fluxes through double-diffusive layers. This leads to departures from laboratory-based parameterizations that can significantly change estimates of Arctic Ocean heat fluxes in certain regions, although most of the upper Arctic Ocean thermocline is not expected to be dominated by rotation.

Melting heat transfer in the stagnation-point flow of Maxwell fluid with double-diffusive convection

2014 ◽  
Vol 24 (3) ◽  
pp. 760-774 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Farooq ◽  
Ahmad Alsaedi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Stagnation Point ◽  
Boundary Layer Thickness ◽  
Double Diffusive Convection ◽  
Content Type ◽  
Diffusive Convection ◽  
Double Diffusive

Purpose – The purpose of this paper is to analyze the melting heat transfer in the stagnation-point flow with double-diffusive convection. Design/methodology/approach – Series solutions for velocity, temperature and concentration are constructed via homotopy analysis method. Findings – The authors observed that the behaviors of N, ?2 and M on the velocity and boundary layer thickness are qualitatively similar. Further, for A<1 the velocity profile and boundary layer thickness increase with the increase of A. However, when A>1 then the velocity profile increases but the boundary layer thickness decreases when A is increased. Originality/value – This analysis has not been discussed in the literature previously.

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