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.

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 $.

Frontogenesis and frontal arrest of a dense filament in the oceanic surface boundary layer

2017 ◽  
Vol 837 ◽  
pp. 341-380 ◽  
Author(s):  
Peter P. Sullivan ◽  
James C. McWilliams
Keyword(s):  
Boundary Layer ◽  
Turbulent Mixing ◽  
Shear Instability ◽  
Upper Ocean ◽  
Surface Boundary ◽  
Horizontal Shear ◽  
Boundary Layer Turbulence ◽  
Filament Axis ◽  
Small Width ◽  
The Cross

The evolution of upper ocean currents involves a set of complex, poorly understood interactions between submesoscale turbulence (e.g. density fronts and filaments and coherent vortices) and smaller-scale boundary-layer turbulence. Here we simulate the lifecycle of a cold (dense) filament undergoing frontogenesis in the presence of turbulence generated by surface stress and/or buoyancy loss. This phenomenon is examined in large-eddy simulations with resolved turbulent motions in large horizontal domains using${\sim}10^{10}$grid points. Steady winds are oriented in directions perpendicular or parallel to the filament axis. Due to turbulent vertical momentum mixing, cold filaments generate a potent two-celled secondary circulation in the cross-filament plane that is frontogenetic, sharpens the cross-filament buoyancy and horizontal velocity gradients and blocks Ekman buoyancy flux across the cold filament core towards the warm filament edge. Within less than a day, the frontogenesis is arrested at a small width,${\approx}100~\text{m}$, primarily by an enhancement of the turbulence through a small submesoscale, horizontal shear instability of the sharpened filament, followed by a subsequent slow decay of the filament by further turbulent mixing. The boundary-layer turbulence is inhomogeneous and non-stationary in relation to the evolving submesoscale currents and density stratification. The occurrence of frontogenesis and arrest are qualitatively similar with varying stress direction or with convective cooling, but the detailed evolution and flow structure differ among the cases. Thus submesoscale filament frontogenesis caused by boundary-layer turbulence, frontal arrest by frontal instability and frontal decay by forward energy cascade, and turbulent mixing are generic processes in the upper ocean.

Effects of Ambient Turbulence on Interleaving at a Baroclinic Front

2010 ◽  
Vol 40 (4) ◽  
pp. 685-712 ◽  
Author(s):  
William D. Smyth ◽  
Barry Ruddick
Keyword(s):  
Schmidt Number ◽  
Turbulence Models ◽  
Underlying Mechanism ◽  
Vertical Scale ◽  
Salt Fingers ◽  
Calculation Results ◽  
Frontal Zones ◽  
Turbulent Momentum ◽  
Salt Fingering ◽  
Ambient Turbulence

Abstract In this paper the authors investigate the action of ambient turbulence on thermohaline interleaving using both theory and numerical calculations in combination with observations from Meddy Sharon and the Faroe Front. The highly simplified models of ambient turbulence used previously are improved upon by allowing turbulent diffusivities of momentum, heat, and salt to depend on background gradients and to evolve as the instability grows. Previous studies have shown that ambient turbulence, at typical ocean levels, can quench the thermohaline interleaving instability on baroclinic fronts. These findings conflict with the observation that interleaving is common in baroclinic frontal zones despite ambient turbulence. Another challenge to the existing theory comes from numerical experiments showing that the Schmidt number for sheared salt fingers is much smaller than previously assumed. Use of the revised value in an interleaving calculation results in interleaving layers that are both weaker and thinner than those observed. This study aims to resolve those paradoxes. The authors show that, when turbulence has a Prandtl number greater than unity, turbulent momentum fluxes can compensate for the reduced Schmidt number of salt fingering. Thus, ambient turbulence determines the vertical scale of interleaving. In typical oceanic interleaving structures, the observed property gradients are insufficient to predict interleaving growth at an observable level, even when improved turbulence models are used. The deficiency is small, though: gradients sharper by a few tens of percent are sufficient to support instability. The authors suggest that this is due to the efficiency of interleaving in erasing those property gradients. A new class of mechanisms for interleaving, driven by flow-dependent fluctuations in turbulent diffusivities, is identified. The underlying mechanism is similar to the well-known Phillips layering instability; however, because of Coriolis effects, it has a well-defined vertical scale and also a tilt angle opposite to that of finger-driven interleaving.

scholarly journals Experimental study into the Rayleigh–Taylor turbulent mixing zone heterogeneous structure

2003 ◽  
Vol 21 (3) ◽  
pp. 375-379 ◽  
Author(s):  
Yu.A. KUCHERENKO ◽  
A.P. PYLAEV ◽  
V.D. MURZAKOV ◽  
A.V. BELOMESTNIH ◽  
V.N. POPOV ◽  
...  
Keyword(s):  
Turbulent Mixing ◽  
Measurement Errors ◽  
Density Ratio ◽  
Mixing Layer ◽  
Light Sheet ◽  
Immiscible Fluids ◽  
Heterogeneous Structure ◽  
Layer System ◽  
Glycerin Solution ◽  
Refractive Index Matching

Experiments conducted on the SOM facility at the Russian Federal Nuclear Center–VNIITF, concerning the turbulent mixing induced by the Rayleigh–Taylor instability in a three-layer system of immiscible liquids are described. The fluids are contained in a small tank 6.4 cm × 5.4 cm × 12 cm, which is accelerated vertically downward by a gas gun. The mixing layer evolution was imaged by seeding one of the fluids with particles and using a bidirectional light sheet method (refractive index matching was used to minimize measurement errors). Experiments were performed for two different accelerations (g = 350 g0 and g = 100 g0, where g0 = 980 cm/s2, and the acceleration decreases with distance traveled), and with aqueous solutions of glycerin and benzene (with density ratio 1.6). The lower, middle, and upper layers were a sodium hyposulfite–glycerin solution, a water–glycerin solution, and benzene, respectively. The glycerin solution was seeded with particles. The principal objective of the experiments was to obtain the distribution of fluid particle sizes arising from the mixing of the immiscible fluids.

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 A note about density staircases in the Gulf of Naples : 20 years of persistent weak salt-fingering layers in a coastal area

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
Florian Kokoszka ◽  
Daniele Iudicone ◽  
Adriana Zingone ◽  
Vincenzo Saggiomo ◽  
Maurizio Ribera D'Alcalá ◽  
...  
Keyword(s):  
Mixed Layer Depth ◽  
Density Ratio ◽  
Eddy Diffusivity ◽  
Tyrrhenian Sea ◽  
Biological Communities ◽  
Gulf Of Naples ◽  
Critical Range ◽  
Decadal Modulation ◽  
Deep Layers ◽  
Salt Fingering

This is a short communication about the inter-annual recurring presence at the coastal site in the Gulf of Naples of density staircases visible below the mixed surface layer of the water-column, from the end of summer to the beginning of winter, each year during nearly two decades of survey (2001 to 2020). We repetitively observe sequences from 1 to 4 small vertical staircases structures (~ 3 m thick) in the density profiles (~ Δ0.2 kg.m-3), located between 10 m to 50 m deep below the seasonal mixed layer depth. We interpret these vertical structures as the result of double diffusive processes that could host salt-fingering regime (SF) due to warm salty water parcels overlying on relatively fresher and colder layers. This common feature of the Mediterranean basin (i.e., the thermohaline staircases of the Tyrrhenian sea) may sign here for the lateral intrusions of nearshore water masses. These stably stratified layers are characterized by density ratio Rρ 5.0 to 10.0, slightly higher than the critical range (1.0 - 3.0) generally expected for fully developed salt-fingers. SF mixing, such as parameterized (Zhang et al., 1998), appears to inhibit weakly the effective eddy diffusivity with negative averaged value (~ - 1e-8 m2.s-1). A quasi 5-year cycle is visible in the inter-annual variability of the eddy diffusivity associated to SF, suggesting a decadal modulation of the parameters regulating the SF regime. Even contributing weakly to the turbulent mixing of the area, we hypothesis that SF could influence the seasonal stratification by intensifying the density of deep layers. Downward transfer of salt could have an impact on the nutrient supply for the biological communities, that remains to be determined.

Dynamics of vorticity defects in stratified shear flow

2012 ◽  
Vol 694 ◽  
pp. 292-331 ◽  
Author(s):  
N. J. Balmforth ◽  
A. Roy ◽  
C. P. Caulfield
Keyword(s):  
Linear Instability ◽  
Shear Instability ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Stratified Shear Flow ◽  
Prandtl Numbers ◽  
High Reynolds ◽  
Efficient Exploration ◽  
Secondary Instabilities ◽  
Sharp Interfaces

AbstractWe consider the linear stability and nonlinear evolution of two-dimensional shear flows that take the form of an unstratified plane Couette flow that is seeded with a localized ‘defect’ containing sharp density and vorticity variations. For such flows, matched asymptotic expansions furnish a reduced model that allows a straightforward and computationally efficient exploration of flows at sufficiently high Reynolds and Péclet numbers that sharp density and vorticity gradients persist throughout the onset, growth and saturation of instability. We are thereby able to study the linear and nonlinear dynamics of three canonical variants of stratified shear instability: Kelvin–Helmholtz instability, the Holmboe instability, and the lesser-considered Taylor instability, all of which are often interpreted in terms of the interactions of waves riding on sharp interfaces of density and vorticity. The dynamics near onset is catalogued; if the interfaces are sufficiently sharp, the onset of instability is subcritical, with a nonlinear state existing below the linear instability threshold. Beyond onset, both Holmboe and Taylor instabilities are susceptible to inherently two-dimensional secondary instabilities that lead to wave mergers and wavelength coarsening. Additional two-dimensional secondary instabilities are also found to appear for higher Prandtl numbers that take the form of parasitic Holmboe-like waves.

scholarly journals Shear Instability Wave along a Snowband: Instability Structure, Evolution, and Energetics Derived from Dual-Doppler Radar Data

2005 ◽  
Vol 62 (2) ◽  
pp. 351-370 ◽  
Author(s):  
Masayuki Kawashima ◽  
Yasushi Fujiyoshi
Keyword(s):  
Linear Growth ◽  
Doppler Radar ◽  
Growth Period ◽  
Radar Data ◽  
Shear Instability ◽  
Instability Wave ◽  
Horizontal Shear ◽  
Pressure Work ◽  
Doppler Radar Data ◽  
Dual Doppler Radar

Abstract This article presents a detailed analysis of a meso-γ-scale (∼17 km wavelength) shear instability wave along a snowband using a series of dual-Doppler radar data. The wave developed along a low-level shear line that formed under the strain wind field caused by an adjacent mesoscale vortex. The horizontal wind shear across the line was largest at lower levels, and the eddy-component horizontal winds and the retrieved pressure anomaly showed a bottom-intensified structure as well. The resultant vertical pressure gradient force was found to be responsible for the enhancement of alternating updrafts and downdrafts that were subsequently related to the formation of the reflectivity core/gap structure of the wave. Eddy kinetic energy (EKE) budgets of the evolving disturbance were investigated using time series of retrieved kinematic and thermodynamic data. The wave grew at an approximately constant growth rate for about 40 min from its onset. The EKE in this quasi-linear growth period was primarily generated by the horizontal shear that decreased with height. The pressure work was found to remove about two-thirds of this generation in the layer below 1 km, while in the upper layer it was constructive to EKE generation and comparable to the generation of EKE by horizontal shear. These results indicate that the source of EKE was basically located at low levels and the energy was transported upward mainly by the pressure work. After the quasi-linear growth period, horizontal shear generation rapidly decreased and EKE peaked. The buoyancy generation of EKE was small but positive in the quasi-linear growth period, then became negative because of the development of thermally indirect circulations.

scholarly journals Rayleigh–Taylor turbulent mixing evolution under a shock influence

2000 ◽  
Vol 18 (2) ◽  
pp. 155-161 ◽  
Author(s):  
Yu.A. KUCHERENKO ◽  
A.P. PYLAEV ◽  
V.D. MURZAKOV ◽  
V.N. POPOV ◽  
V.E. SAVEL'EV ◽  
...  
Keyword(s):  
Experimental Study ◽  
Solid Surface ◽  
Turbulent Mixing ◽  
Initial Perturbation ◽  
Density Ratio ◽  
Internal Working ◽  
Metal Plates ◽  
Impulse Duration ◽  
Rayleigh Taylor Instability ◽  
The Impact

At the installation SOM, the experimental study of the impulse acceleration influence on the behavior of the turbulized layer obtained as a result of Rayleigh–Taylor instability (RTI) action on the system of two different density liquids with the density ratio n = 3, has been performed. After application of impulse acceleration the systems were moving according to inertia, and by using the light method the coordinates of penetration of the heavier liquid into the lighter one and vice versa were determined. The liquids studied were placed inside the ampoule that had internal working sizes (54 × 64 × 120) mm3. There were initial accidental perturbations like a rough solid surface at the interface and the width of the initial perturbation zone was L0 = 2.3 mm. The moving ampoule blow against metal plates created the impulse acceleration. The relative impulse acceleration was δg/g11 = 22.2–66.6 where g11 is the ampoule acceleration before the impact, the impulse duration was varied from 0.27 ms to 0.096 ms. The results concerned with the turbulized layer extension after the impulse acceleration action were obtained.

scholarly journals Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics

2014 ◽  
Vol 748 ◽  
pp. 113-142 ◽  
Author(s):  
M. Lombardini ◽  
D. I. Pullin ◽  
D. I. Meiron
Keyword(s):  
Turbulent Mixing ◽  
Spherical Surface ◽  
Density Ratio ◽  
Mixing Layer ◽  
Inertial Subrange ◽  
Planar Geometry ◽  
Late Time ◽  
Mean Flow ◽  
Turbulence Statistics ◽  
Decaying Turbulence

AbstractWe present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number $\approx $1.2, the density ratio (precisely $|A_0|\approx 0.67$) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85–112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios $\approx $2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter $\varTheta $ and the effective Atwood ratio $A_e$, which reach similar late time values in both light–heavy and heavy–light configurations. The Taylor-scale Reynolds numbers attained at late times are estimated at approximately 2000 in the light–heavy case and 1000 in the heavy–light case. An analysis of the density self-correlation $b$, a fundamental quantity in the study of variable-density turbulence, shows asymmetries in the mixing layer and non-Boussinesq effects generally observed in high-Reynolds-number Rayleigh–Taylor (RT) turbulence. These traits are more pronounced in the light–heavy mixing layer, as a result of its flow history, in particular because of RT-unstable phases (see Part 1). Another measure distinguishing light–heavy from heavy–light mixing is the velocity-to-scalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavy–light case. The late-time mixing displays the traits some of the traits of the decaying turbulence observed in planar Richtmyer–Meshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorov-like $-5/3$ power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixing-layer curvature.

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