Differential diffusion in double-diffusive stratified turbulence

2008 ◽  
pp. 615-617 ◽  
Author(s):  
Hideshi Hanazaki ◽  
Kazuhiro Konishi
Keyword(s):  
Stratified Turbulence ◽  
Differential Diffusion ◽  
Double Diffusive

scholarly journals Differential Diffusivity Effects in Reactive Convective Dissolution

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 83 ◽  
Author(s):  
V. Loodts ◽  
H. Saghou ◽  
B. Knaepen ◽  
L. Rongy ◽  
A. De Wit
Keyword(s):  
Diffusion Coefficients ◽  
Reaction Rate ◽  
Chemical Species ◽  
Mixing Zone ◽  
Simultaneous Presence ◽  
Dynamic Effects ◽  
Density Profiles ◽  
Differential Diffusion ◽  
Different Types ◽  
Double Diffusive

When a solute A dissolves into a host fluid containing a reactant B, an A + B → C reaction can influence the convection developing because of unstable density gradients in the gravity field. When A increases density and all three chemical species A, B and C diffuse at the same rate, the reactive case can lead to two different types of density profiles, i.e., a monotonically decreasing one from the interface to the bulk and a non-monotonic profile with a minimum. We study numerically here the nonlinear reactive convective dissolution dynamics in the more general case where the three solutes can diffuse at different rates. We show that differential diffusion can add new dynamic effects like the simultaneous presence of two different convection zones in the host phase when a non-monotonic profile with both a minimum and a maximum develops. Double diffusive instabilities can moreover affect the morphology of the convective fingers. Analysis of the mixing zone, the reaction rate, the total amount of stored A and the dissolution flux further shows that varying the diffusion coefficients of the various species has a quantitative effect on convection.

Direct Numerical Simulation of Differential Scalar Diffusion in Three-Dimensional Stratified Turbulence

2003 ◽  
Vol 33 (8) ◽  
pp. 1758-1782 ◽  
Author(s):  
Ann E. Gargett ◽  
William J. Merryfield ◽  
Greg Holloway
Keyword(s):  
Molecular Diffusion ◽  
Turbulent Transport ◽  
Spectral Characteristics ◽  
Three Dimensional ◽  
Initial Energy ◽  
Stratified Medium ◽  
Stratified Turbulence ◽  
Differential Diffusion ◽  
Molecular Diffusivity ◽  
Parameter Ranges

Abstract The potential for differential turbulent transport of oceanic temperature (T) and salinity (𝒮) is explored using three-dimensional direct numerical simulations of decaying stratified turbulence. The simulations employ a realistic molecular diffusion coefficient for T, and one for a “salt” scalar S that is 10 times smaller. Initially, a uniformly stratified medium is disturbed by a turbulent burst whose initial energy is assigned a range of values. In each instance, transports of T integrated over the subsequent decay of the burst exceed those of S. The more energetic cases occupy parameter ranges similar to, and exhibit spectral characteristics that are essentially indistinguishable from, those of direct observations of turbulence in the stratified ocean interior. In these cases, the turbulent diffusivity of T exceeds that of S by 6%–22%. These simulations underestimate the degree of differential diffusion between T and salinity 𝒮 (which has a molecular diffusivity 100 times less than T); thus at the Reynolds numbers attained by the simulations these results constitute lower bounds for differential diffusion associated with sporadic turbulence in the ocean. The simulation results are consistent with previous laboratory and two-dimensional numerical experiments and suggest that the assumption of equal turbulent diffusivities for T and 𝒮, commonly used in circulation modeling and in interpreting oceanic mixing measurements, should be reconsidered.

scholarly journals Theory for differential transport of scalars in sheared stratified turbulence

2009 ◽  
Vol 621 ◽  
pp. 1-21 ◽  
Author(s):  
P. RYAN JACKSON ◽  
CHRIS R. REHMANN
Keyword(s):  
Schmidt Number ◽  
Density Ratio ◽  
Computational Cost ◽  
Lewis Number ◽  
Stratified Turbulence ◽  
Viscous Effects ◽  
Grashof Number ◽  
Differential Diffusion ◽  
Schmidt Numbers ◽  
High Computational Cost

Scalars with different molecular diffusivities can be transported at different rates in a strongly stratified, weakly turbulent flow. Rapid distortion theory (RDT) is used to examine the mechanisms responsible for differential diffusion of scalars in a sheared stratified flow. The theory, which applies when the flow is strongly stratified, predicts upgradient flux and its wavenumber dependence, which previous direct numerical simulations have shown to be important in differential diffusion. The net effect of shear on differential diffusion depends on the Grashof number, or the relative importance of buoyancy and viscous effects. RDT also allows the effects of the density ratio, Schmidt number, Lewis number, scalar activity and mean shear to be examined without the high computational cost of direct numerical simulation. RDT predicts that differential diffusion will increase with increasing density ratio, but only at low Grashof number. When the Lewis number is fixed, the Grashof number below which differential diffusion occurs decreases with increasing Schmidt number, and when one of the Schmidt numbers is fixed, differential diffusion decreases with increasing Lewis number. Also, differential transport of passive scalars increases when the Schmidt number of the scalar stratifying the flow increases.

Control of chemically-driven convective dissolution by differential diffusion effects

2021 ◽  
Author(s):  
Mamta Jotkar ◽  
Laurence Rongy ◽  
Anne De Wit
Keyword(s):  
Chemical Reaction ◽  
Reaction Front ◽  
Critical Threshold ◽  
Differential Diffusion ◽  
Solution Density ◽  
Diffusion Effects ◽  
Rayleigh Taylor Instability ◽  
The Difference ◽  
Diffusive Layer ◽  
Double Diffusive

<p>We numerically study the effect of differential diffusion in chemically-driven convective dissolution that can occur upon the reaction of a dissolving species A in a host phase when the chemical reaction destabilizes an otherwise stable density stratification. For example, an A+B→C reaction is known to trigger such convection when, upon dissolution into the host solution, A reacts with B present in the solution to produce C if the difference between C and B in the contribution to the solution density is above a critical threshold. We show that differential diffusivities impact the convective dynamics substantially giving rise to additional convective effects below the reaction front, where C is generated. More specifically, we show that below the reaction front either double-diffusive or diffusive-layer convection can arise, modifying the local Rayleigh-Taylor instability. When B diffuses faster than C, a double-diffusive instability can develop below the reaction front, accelerating the convective dynamics and conversely, when B diffuses slower than C, diffusive-layer convection modes stabilize the dynamics compared to the equal diffusivity case. Our results are relevant for various geological applications or engineering set-ups that involve non-reactive stable density stratifications where transport can be enhanced by reaction-induced convection.</p>

Sign in / Sign up

Export Citation Format

Share Document