Equilibrium transport in double-diffusive convection

2011 ◽  
Vol 692 ◽  
pp. 5-27 ◽  
Author(s):  
Timour Radko ◽  
D. Paul Smith
Keyword(s):  
Linear Growth ◽  
Density Ratio ◽  
Molecular Characteristics ◽  
Diffusive Transport ◽  
Salt Fingers ◽  
Diffusive Convection ◽  
Wide Range ◽  
Secondary Instabilities ◽  
Double Diffusive

AbstractA theoretical model for the equilibrium double-diffusive transport is presented which emphasizes the role of secondary instabilities of salt fingers in saturation of their linear growth. Theory assumes that the fully developed equilibrium state is characterized by the comparable growth rates of primary and secondary instabilities. This assumption makes it possible to formulate an efficient algorithm for computing diffusivities of heat and salt as a function of the background property gradients and molecular parameters. The model predicts that the double-diffusive transport of heat and salt rapidly intensifies with decreasing density ratio. Fluxes are less sensitive to molecular characteristics, mildly increasing with Prandtl number $(\mathit{Pr})$ and decreasing with diffusivity ratio $(\tau )$. Theory is successfully tested by a series of direct numerical simulations which span a wide range of $\mathit{Pr}$ and $\tau $.

Mixing in a Moderately Sheared Salt-Fingering Layer

2011 ◽  
Vol 41 (7) ◽  
pp. 1364-1384 ◽  
Author(s):  
W. D. Smyth ◽  
S. Kimura
Keyword(s):  
Turbulent Mixing ◽  
Linear Growth ◽  
Density Ratio ◽  
Effective Diffusivity ◽  
Shear Instability ◽  
Bulk Richardson Number ◽  
Additional Energy ◽  
Salt Fingers ◽  
Salt Fingering ◽  
Secondary Instabilities

Abstract Mixing due to sheared salt fingers is studied by means of direct numerical simulations (DNS) of a double-diffusively unstable shear layer. The focus is on the “moderate shear” case, where shear is strong enough to produce Kelvin–Helmholtz (KH) instability but not strong enough to produce the subharmonic pairing instability. This flow supports both KH and salt-sheet instabilities, and the objective is to see how the two mechanisms work together to flux heat, salt, and momentum across the layer. For observed values of the bulk Richardson number Ri and the density ratio Rρ, the linear growth rates of KH and salt-sheet instabilities are similar. These mechanisms, as well as their associated secondary instabilities, lead the flow to a fully turbulent state. Depending on the values of Ri and Rρ, the resulting turbulence may be driven mainly by shear or mainly by salt fingering. Turbulent mixing causes the profiles of temperature, salinity, and velocity to spread; however, in salt-sheet-dominated cases, the net density (or buoyancy) layer thins over time. This could be a factor in the maintenance of the staircase and is also an argument in favor of an eventual role for Holmboe instability. Fluxes are scaled using both laboratory scalings for a thin layer and an effective diffusivity. Fluxes are generally stronger in salt-sheet-dominated cases. Shear instability disrupts salt-sheet fluxes while adding little flux of its own. Shear therefore reduces mixing, despite providing an additional energy source. The dissipation ratio Γ is near 0.2 for shear-dominated cases but is much larger when salt sheets are dominant, supporting the use of Γ in the diagnosis of observed mixing phenomena. The profiler approximation Γz, however, appears to significantly overestimate the true dissipation ratio.

scholarly journals Reply

2008 ◽  
Vol 65 (3) ◽  
pp. 1095-1097 ◽  
Author(s):  
David M. Schultz ◽  
Adam J. Durant ◽  
Jerry M. Straka ◽  
Timothy J. Garrett
Keyword(s):  
Volcanic Ash ◽  
Effective Means ◽  
Double Diffusive Convection ◽  
Vertical Temperature ◽  
Effective Mechanism ◽  
Gravitational Forces ◽  
Salt Fingers ◽  
Diffusive Convection ◽  
Double Diffusive

Abstract Doswell has proposed a mechanism for mammatus called double-diffusive convection, the mechanism responsible for salt fingers in the ocean. The physics of salt fingers and mammatus are different. Unlike the ocean where the diffusivity is related to molecular motions within solution, the hydrometeors in clouds are affected by inertial and gravitational forces. Doswell misinterprets the vertical temperature profiles through mammatus and fails to understand the role of settling in volcanic ash clouds. Furthermore, given that mixing is a much more effective means of transferring heat in the atmosphere and given idealized numerical model simulations of mammatus showing that the destabilizing effect of subcloud sublimation is an effective mechanism for mammatus, this reply argues that double-diffusive convection is unlikely to explain mammatus, either in cumulonimbus anvils or in volcanic ash clouds.

scholarly journals From convection rolls to finger convection in double-diffusive turbulence

2015 ◽  
Vol 113 (1) ◽  
pp. 69-73 ◽  
Author(s):  
Yantao Yang ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Temperature Gradient ◽  
Large Scale ◽  
Salinity Gradient ◽  
Density Ratio ◽  
Lewis Number ◽  
Salt Fingers ◽  
Wide Range ◽  
Ocean Flows ◽  
Convection Rolls ◽  
Double Diffusive

Double-diffusive convection (DDC), which is the buoyancy-driven flow with fluid density depending on two scalar components, is ubiquitous in many natural and engineering environments. Of great interests are scalars' transfer rate and flow structures. Here we systematically investigate DDC flow between two horizontal plates, driven by an unstable salinity gradient and stabilized by a temperature gradient. Counterintuitively, when increasing the stabilizing temperature gradient, the salinity flux first increases, even though the velocity monotonically decreases, before it finally breaks down to the purely diffusive value. The enhanced salinity transport is traced back to a transition in the overall flow pattern, namely from large-scale convection rolls to well-organized vertically oriented salt fingers. We also show and explain that the unifying theory of thermal convection originally developed by Grossmann and Lohse for Rayleigh–Bénard convection can be directly applied to DDC flow for a wide range of control parameters (Lewis number and density ratio), including those which cover the common values relevant for ocean flows.

scholarly journals Finger puzzles

2012 ◽  
Vol 692 ◽  
pp. 1-4 ◽  
Author(s):  
R. W. Schmitt
Keyword(s):  
Growth Rate ◽  
Finite Amplitude ◽  
Double Diffusive Convection ◽  
Magma Chambers ◽  
Fluid Systems ◽  
Salt Fingers ◽  
Diffusive Convection ◽  
Stellar Interiors ◽  
Secondary Instabilities ◽  
Double Diffusive

AbstractSalt fingers are a form of double-diffusive convection that can occur in a wide variety of fluid systems, ranging from stellar interiors and oceans to magma chambers. Their amplitude has long been difficult to quantify, and a variety of mechanisms have been proposed. Radko & Smith (J. Fluid Mech., this issue, vol. 692, 2012, pp. 5–27) have developed a new theory that balances the basic growth rate with that of secondary instabilities that act on the finite amplitude fingers. Their approach promises a way forward for computationally challenging systems with vastly different scales of decay for momentum, heat and dissolved substances.

scholarly journals Multiple states and transport properties of double-diffusive convection turbulence

2020 ◽  
Vol 117 (26) ◽  
pp. 14676-14681 ◽  
Author(s):  
Yantao Yang ◽  
Wenyuan Chen ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Large Range ◽  
Local Density ◽  
Density Ratio ◽  
Single Layer ◽  
Multiple Equilibrium ◽  
Double Diffusive Convection ◽  
Flow Parameters ◽  
Diffusive Convection ◽  
Sharp Interfaces ◽  
Double Diffusive

When fluid stratification is induced by the vertical gradients of two scalars with different diffusivities, double-diffusive convection (DDC) may occur and play a crucial role in mixing. Such a process exists in many natural and engineering environments. Especially in the ocean, DDC is omnipresent since the seawater density is affected by temperature and salinity. The most intriguing phenomenon caused by DDC is the thermohaline staircase, i.e., a stack of alternating well-mixed convection layers and sharp interfaces with very large gradients in both temperature and salinity. Here we investigate DDC and thermohaline staircases in the salt finger regime, which happens when warm saltier water lies above cold fresher water and is commonly observed in the (sub)tropic regions. By conducting direct numerical simulations over a large range of parameters, we reveal that multiple equilibrium states exist in fingering DDC and staircases even for the same control parameters. Different states can be established from different initial scalar distributions or different evolution histories of the flow parameters. Hysteresis appears during the transition from a staircase to a single salt finger interface. For the same local density ratio, salt finger interfaces in the single-layer state generate very different fluxes compared to those within staircases. However, the salinity flux for all salt finger interfaces follows the same dependence on the salinity Rayleigh number of the layer and can be described by an effective power law scaling. Our findings have direct applications to oceanic thermohaline staircases.

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.

scholarly journals Scaling laws and flow structures of double diffusive convection in the finger regime

2016 ◽  
Vol 802 ◽  
pp. 667-689 ◽  
Author(s):  
Yantao Yang ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Density Ratio ◽  
Copper Ion ◽  
Double Diffusive Convection ◽  
Parallel Plates ◽  
Diffusive Convection ◽  
Prandtl Numbers ◽  
Salinity Difference ◽  
Double Diffusive

Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates. The Prandtl numbers, i.e. the ratios between the viscosity and the molecular diffusivities of scalars, are similar to the values of seawater. The DDC flow is driven by an unstable salinity difference (here across the two plates) and stabilized at the same time by a temperature difference. For these conditions the flow can be in the finger regime. We develop scaling laws for three key response parameters of the system: the non-dimensional salinity flux $\mathit{Nu}_{S}$ mainly depends on the salinity Rayleigh number $\mathit{Ra}_{S}$, which measures the strength of the salinity difference and exhibits a very weak dependence on the density ratio $\unicode[STIX]{x1D6EC}$, which is the ratio of the buoyancy forces induced by two scalar differences. The non-dimensional flow velocity $Re$ and the non-dimensional heat flux $\mathit{Nu}_{T}$ are dependent on both $\mathit{Ra}_{S}$ and $\unicode[STIX]{x1D6EC}$. However, the rescaled Reynolds number $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ and the rescaled convective heat flux $(\mathit{Nu}_{T}-1)\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{T}^{eff}}$ depend only on $\mathit{Ra}_{S}$. The two exponents are dependent on the fluid properties and are determined from the numerical results as $\unicode[STIX]{x1D6FC}_{u}^{eff}=0.25\pm 0.02$ and $\unicode[STIX]{x1D6FC}_{T}^{eff}=0.75\pm 0.03$. Moreover, the behaviours of $\mathit{Nu}_{S}$ and $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ agree with the predictions of the Grossmann–Lohse theory which was originally developed for the Rayleigh–Bénard flow. The non-dimensional salt-finger width and the thickness of the velocity boundary layers, after being rescaled by $\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}/2}$, collapse and obey a similar power-law scaling relation with $\mathit{Ra}_{S}$. When $\mathit{Ra}_{S}$ is large enough, salt fingers do not extend from one plate to the other and horizontal zonal flows emerge in the bulk region. We then show that the current scaling strategy can be successfully applied to the experimental results of a heat–copper–ion system (Hage & Tilgner, Phys. Fluids, vol. 22, 2010, 076603). The fluid has different properties and the exponent $\unicode[STIX]{x1D6FC}_{u}^{eff}$ takes a different value $0.54\pm 0.10$.

Equilibration of weakly nonlinear salt fingers

2010 ◽  
Vol 645 ◽  
pp. 121-143 ◽  
Author(s):  
TIMOUR RADKO
Keyword(s):  
Asymptotic Expansion ◽  
Linear Growth ◽  
Mean Field ◽  
Vertical Shear ◽  
Weakly Nonlinear ◽  
Salinity Gradients ◽  
Salt Fingers ◽  
Wide Range ◽  
Shear Effects ◽  
The Mean

An analytical model is developed to explain the equilibration mechanism of the salt finger instability in unbounded temperature and salinity gradients. The theory is based on the weakly nonlinear asymptotic expansion about the point of marginal instability. The proposed solutions attribute equilibration of salt fingers to a combination of two processes: (i) the triad interaction and (ii) spontaneous development of the mean vertical shear. The non-resonant triad interactions control the equilibration of linear growth for moderate and large values of Prandtl number (Pr) and for slightly unstable parameters. For small Pr and/or rigorous instabilities, the mean shear effects become essential. It is shown that, individually, neither the mean field nor the triad interaction models can accurately describe the equilibrium patterns of salt fingers in all regions of the parameter space. Therefore, we propose a new hybrid model, which represents both stabilizing effects in a single framework. The resulting solutions agree with the fully nonlinear numerical simulations over a wide range of governing parameters.

scholarly journals Video: Salt fingers in double diffusive convection bounded by two parallel plates

2014 ◽  
Author(s):  
Yantao Yang ◽  
Erwin P. van der Poel ◽  
Rodolfo Ostilla-Monico ◽  
Chao Sun ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Double Diffusive Convection ◽  
Parallel Plates ◽  
Salt Fingers ◽  
Diffusive Convection ◽  
Double Diffusive
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