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 $0.54\pm 0.10$.

scholarly journals Salinity transfer in bounded double diffusive convection

2015 ◽  
Vol 768 ◽  
pp. 476-491 ◽  
Author(s):  
Yantao Yang ◽  
Erwin P. van der Poel ◽  
Rodolfo Ostilla-Mónico ◽  
Chao Sun ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Rayleigh Number ◽  
Double Diffusive Convection ◽  
Parallel Plates ◽  
Salt Fingers ◽  
Diffusive Convection ◽  
Entire Height ◽  
Salinity Difference ◽  
A Minor ◽  
Rayleigh Benard ◽  
Double Diffusive

The double diffusive convection between two parallel plates is numerically studied for a series of parameters. The flow is driven by the salinity difference and stabilised by the thermal field. Our simulations are directly compared with experiments by Hage & Tilgner (Phys. Fluids, vol. 22, 2010, 076603) for several sets of parameters and reasonable agreement is found. This, in particular, holds for the salinity flux and its dependence on the salinity Rayleigh number. Salt fingers are present in all simulations and extend through the entire height. The thermal Rayleigh number seems to have a minor influence on the salinity flux but affects the Reynolds number and the morphology of the flow. In addition to the numerical calculation, we apply the Grossmann–Lohse theory for Rayleigh–Bénard flow to the present problem without introducing any new coefficients. The theory successfully predicts the salinity flux both with respect to the scaling and even with respect to the absolute value for the numerical and experimental results.

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.

scholarly journals Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

2016 ◽  
Vol 46 (8) ◽  
pp. 2553-2569 ◽  
Author(s):  
Magnus Hieronymus ◽  
Jeffrey R. Carpenter
Keyword(s):  
Heat Flux ◽  
Numerical Simulations ◽  
Scaling Laws ◽  
State Energy ◽  
Diffusive Regime ◽  
Diffusive Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard ◽  
Double Diffusive

AbstractThe steady-state energy and thermal variance budgets form the basis for most current methods for evaluating turbulent fluxes of buoyancy, heat, and salinity. This study derives these budgets for a double-diffusive staircase and quantifies them using direct numerical simulations; 10 runs with different Rayleigh numbers are considered. The energy budget is found to be well approximated by a simple three-term balance, while the thermal variance budget consists of only two terms. The two budgets are also combined to give an expression for the ratio of the heat and salt fluxes. The heat flux scaling is also studied and found to agree well with earlier estimates based on laboratory experiments and numerical simulations at high Rayleigh numbers. At low Rayleigh numbers, however, the authors find large deviations from earlier scaling laws. Last, the scaling theory of Grossman and Lohse, which was developed for Rayleigh–Bénard convection and is based on the partitioning of the kinetic energy and tracer variance dissipation, is adapted to the diffusive regime of double-diffusive convection. The predicted heat flux scalings are compared to the results from the numerical simulations and earlier estimates.

Numerical Study of the Onset of Double-Diffusive Cellular Convection Due to a Uniform Lateral Heat Flux

1982 ◽  
Vol 104 (4) ◽  
pp. 649-655 ◽  
Author(s):  
S. Takao ◽  
M. Tsuchiya ◽  
U. Narusawa
Keyword(s):  
Heat Flux ◽  
Numerical Study ◽  
Vertical Wall ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Physical Experiments ◽  
Diffusive Convection ◽  
The Stability ◽  
Double Diffusive ◽  
Lateral Heat

When a fluid with a vertical solute gradient of (−dS/dy)0 is heated laterally, roll cells start to form at the boundary, developing into a series of convective layers. Numerical experiments were performed to investigate the onset of the abovementioned double-diffusive convection under the application of a uniform lateral heat flux. The paper reports the results and discussion of the following aspects of the stability of double-diffusive convection; (i) the relationship between the critical value, (Ra/Rs)c, above which convection cells form along the vertical wall and the nondimensional slot width, (d/L), (ii) the effect of the Lewis number on (Ra/Rs)c. It was also confirmed that values of (Ra/Rs)c as well as H/L (the nondimensional vertical size of incipient cells) obtained in this numerical experiment for wide slot widths (d/L>∼30), agreed well with those obtained previously by physical experiments.

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

Double diffusion, shear instabilities, and heat impacts of a Pacific Summer Water intrusion in the Beaufort Sea

2021 ◽  
Author(s):  
Jennifer A. MacKinnon ◽  
Matthew H. Alford ◽  
Leo Middleton ◽  
John Taylor ◽  
John B. Mickett ◽  
...  
Keyword(s):  
Density Ratio ◽  
Arctic Basin ◽  
Heat Fluxes ◽  
Double Diffusive Convection ◽  
Thermohaline Structure ◽  
Water Intrusion ◽  
Diffusive Convection ◽  
Vertical Heat ◽  
Pacific Summer Water ◽  
Double Diffusive

Abstract Pacific Summer Water eddies and intrusions transport heat and salt from boundary regions into the western Arctic basin. Here we examine concurrent effects of lateral stirring and vertical mixing using microstructure data collected within a Pacific Summer Water intrusion with a length scale of ∼20 km. This intrusion was characterized by complex thermohaline structure in which warm Pacific Summer Water interleaved in alternating layers of O(1 m) thickness with cooler water, due to lateral stirring and intrusive processes. Along interfaces between warm/salty and cold/fresh water masses, the density ratio was favorable to double-diffusive processes. The rate of dissipation of turbulent kinetic energy (ε) was elevated along the interleaving surfaces, with values up to 3×10−8 W kg−1 compared to background ε of less than 10−9 W kg−1. Based on the distribution of ε as a function of density ratio Rρ , we conclude that double-diffusive convection is largely responsible for the elevated ε observed over the survey. The lateral processes that created the layered thermohaline structure resulted in vertical thermohaline gradients susceptible to double-diffusive convection, resulting in upward vertical heat fluxes. Bulk vertical heat fluxes above the intrusion are estimated in the range of 0.2-1 W m−2, with the localized flux above the uppermost warm layer elevated to 2- 10 W m−2. Lateral fluxes are much larger, estimated between 1000-5000 W m−2, and set an overall decay rate for the intrusion of 1-5 years.

Oscillatory double-diffusive instabilities in a vertical slot

2001 ◽  
Vol 426 ◽  
pp. 347-354 ◽  
Author(s):  
OLIVER S. KERR
Keyword(s):  
Prandtl Number ◽  
Linear Stability ◽  
Salinity Gradient ◽  
Double Diffusive Convection ◽  
Salinity Gradients ◽  
Vertical Slot ◽  
Diffusive Convection ◽  
Prandtl Numbers ◽  
Double Diffusive ◽  
Oscillatory Instabilities

Recent linear stability analyses of double-diffusive convection in a laterally heated vertical slot containing water have shown that for very weak (or no) vertical salinity gradient the initial instabilities are steady, but as the salinity gradient is increased there is a transition to oscillatory instabilities. For higher Prandtl number fluids the initial instabilities in a slot with no stratification can be oscillatory or wave-like. We show that the oscillatory instabilities in water are linked to these higher Prandtl number oscillatory instabilities. The salinity gradient has a destabilizing effect on these oscillations, making them appear for Prandtl numbers where oscillatory instabilities are not possible in the absence of salinity gradients. We derive an asymptotic description for this mode of instability.

Double-diffusive convection in an inclined fluid layer

1982 ◽  
Vol 116 ◽  
pp. 363-378 ◽  
Author(s):  
Sivagnanam Thangam ◽  
Abdelfattah Zebib ◽  
C. F. Chen
Keyword(s):  
Fluid Layer ◽  
Single Cells ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Parallel Plates ◽  
Heat System ◽  
Diffusive Convection ◽  
Short Period ◽  
Positive Angle ◽  
Double Diffusive

The nonlinear double-diffusive convection in a Boussinesq fluid with stable constant vertical solute gradient, and bound by two differentially heated rigid inclined parallel plates is considered. The analysis was carried out by a Galerkin method for the cases when the angle of inclination was 0°, −45° and +45° (positive angle denotes heating from below, and negative angle denotes heating from above). The counter-rotating cells predicted by the linear theory merge into single cells with the same sense of rotation within a very short period of time even under slightly supercritical conditions. This is consistent with the experimental observations. Furthermore, as observed in the experiments, the evolution of instability is more rapid when heating is from above than when heating is from below. Our results for a salt-heat system are in excellent agreement with those based on the limiting case of Lewis number → 0 and Schmidt number → ∞.

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