Finescale Instabilities of the Double-Diffusive Shear Flow*

2011 ◽  
Vol 41 (3) ◽  
pp. 571-585 ◽  
Author(s):  
Timour Radko ◽  
Melvin E. Stern
Keyword(s):  
Stability Analysis ◽  
Shear Flow ◽  
Velocity Profile ◽  
Turbulent Mixing ◽  
Richardson Number ◽  
Floquet Theory ◽  
Double Diffusion ◽  
Diffusive Processes ◽  
Main Thermocline ◽  
Double Diffusive

Abstract This study examines dynamics of finescale instabilities in thermohaline–shear flows. It is shown that the presence of the background diapycnal temperature and salinity fluxes due to double diffusion has a destabilizing effect on the basic current. Using linear stability analysis based on the Floquet theory for the sinusoidal basic velocity profile, the authors demonstrate that the well-known Richardson number criterion (Ri < ¼) cannot be directly applied to doubly diffusive fluids. Rigorous instabilities are predicted to occur for Richardson numbers as high as—or even exceeding—unity. The inferences from the linear theory are supported by the fully nonlinear numerical simulations. Since the Richardson number in the main thermocline rarely drops below ¼, whereas the observations of turbulent patches are common, the authors hypothesize that some turbulent mixing events can be attributed to the finescale instabilities associated with double-diffusive processes.

scholarly journals Double diffusion in meromictic lakes of the temperate climate zone

2009 ◽  
Vol 6 (6) ◽  
pp. 7483-7501 ◽  
Author(s):  
C. von Rohden ◽  
B. Boehrer ◽  
J. Ilmberger
Keyword(s):  
Double Diffusion ◽  
Heat Fluxes ◽  
Temperate Climate ◽  
Seasonal Temperature ◽  
Meromictic Lakes ◽  
Temperature Changes ◽  
Convective Mixing ◽  
Lake Bottom ◽  
Diffusive Processes ◽  
Double Diffusive

Abstract. Meromictic lakes are characterized by strong stable density stratification in and below the chemocline, which separates the oxic mixolimnion from the mostly anoxic monimolimnion. Stable density gradients involve slow vertical exchange, especially in the chemocline, where vertical transport can be as low as molecular. Typically, destabilizing temperature gradients establish in the monimolimnion as a consequence of seasonal changing heat fluxes. At the same time, gradients of solutes extending to the lake bottom stabilize the overall stratification. Double diffusive processes may create local instabilities and subsequently cause convective mixing when the destabilization due to heat gradients exceeds the stabilization by solutes (diffusive regime). This configuration can annually occur in the upper part of the monimolimnion, if seasonal temperature changes in the mixolimnion reach the top of the monimolimnion. We present CTD-measurements from two meromictic mining lakes in Germany, which document the seasonal occurrence of convective mixing in discrete horizontal homogeneous layers within the monimolimnion which can be identified by the characteristic step-like structure. In the deeper layers, the steps emerge with a time delay which is determined by the progression of the mixolimnetic temperature changes into the monimolimnion. Interestingly, the chemocline interface is not degraded by these processes. However, double diffusive convection is essential for the redistribution in the inner parts of the monimolimnion at longer time scales, which is crucial for the assessment of the ecologic development of such lakes.

The impact of thermohaline staircases: estimates from a global analysis of Argo floats

2020 ◽  
Author(s):  
Carine van der Boog ◽  
Julie D Pietrzak ◽  
Henk A Dijkstra ◽  
Caroline A Katsman
Keyword(s):  
Heat Transfer ◽  
Indian Ocean ◽  
Atlantic Ocean ◽  
Water Mass ◽  
Double Diffusion ◽  
The Indian Ocean ◽  
Diffusive Processes ◽  
The Impact ◽  
Double Diffusive ◽  
Water Mass Transformation

<p>Thermohaline staircases are stepped structures in the temperature and salinity stratification that result from double diffusive processes. In the open ocean, double diffusive processes enhance the downgradient diapycnal heat transfer compared to turbulent mixing. However, in combination with salinity effects, the resulting buoyancy flux within the thermohaline staircases is counter gradient. This vertical density transport strengthens the stratification and, consequently, affects the density of the water masses above and below the staircase layer. Although 44 percent of the world’s oceans is susceptible to double diffusion and thermohaline staircases are ubiquitous in these regions, the impact of double diffusion on diapycnal heat transfer and on water mass transformation has not been quantified yet. Here, we analyse a dataset of Argo float profiles to obtain a global overview of the occurrence of thermohaline staircases and to estimate their impact on diapycnal heat transfer and water mass transformation. Several regions with a high staircase occurrence are identified. Besides the well-known regions in the Caribbean Sea, the Mediterranean Sea and the subtropical Atlantic Ocean, our analysis reveals a new staircase region in the Indian Ocean. Using this global overview, we estimate, for the first time, the contribution of downgradient diapycnal heat transfer by the staircases. It appears that this contribution is very low compared to the dissipation required to maintain the observed temperature stratification. However, each staircase region can potentially impact the global circulation by affecting the density of the water masses above and below. In particular, the staircase region in the Indian Ocean overlies the waters of the Tasman Leakage. These waters flow westward from Australia towards the Agulhas region and affect the properties of waters entering the Atlantic Ocean. This implies that the vertical flux of salt into the Tasman Leakage waters induced by the presence of thermohaline staircases above can impact the salt transport into the Atlantic Ocean, which in turn is expected to impact the Atlantic Meridional Overturning Circulation. </p>

scholarly journals Double-diffusive mixing makes a small contribution to the global ocean circulation

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Carine G. van der Boog ◽  
Henk A. Dijkstra ◽  
Julie D. Pietrzak ◽  
Caroline A. Katsman
Keyword(s):  
Ocean Circulation ◽  
Mechanical Energy ◽  
Global Ocean ◽  
Small Contribution ◽  
Global Ocean Circulation ◽  
Diffusive Fluxes ◽  
Diffusive Mixing ◽  
Diffusive Processes ◽  
Flowing Waters ◽  
Double Diffusive

AbstractDouble-diffusive processes enhance diapycnal mixing of heat and salt in the open ocean. However, observationally based evidence of the effects of double-diffusive mixing on the global ocean circulation is lacking. Here we analyze the occurrence of double-diffusive thermohaline staircases in a dataset containing over 480,000 temperature and salinity profiles from Argo floats and Ice-Tethered Profilers. We show that about 14% of all profiles contains thermohaline staircases that appear clustered in specific regions, with one hitherto unknown cluster overlying the westward flowing waters of the Tasman Leakage. We estimate the combined contribution of double-diffusive fluxes in all thermohaline staircases to the global ocean’s mechanical energy budget as 7.5 GW [0.1 GW; 32.8 GW]. This is small compared to the estimated energy required to maintain the observed ocean stratification of roughly 2 TW. Nevertheless, we suggest that the regional effects, for example near Australia, could be pronounced.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

scholarly journals The lift on a small sphere in a slow shear flow

1965 ◽  
Vol 22 (2) ◽  
pp. 385-400 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Kinematic Viscosity ◽  
Lift Force ◽  
Flow Direction ◽  
Functional Dependence ◽  
Small Sphere ◽  
Translation Velocity ◽  
Parabolic Velocity Profile ◽  
Direction Opposite

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

Modification of the k-epsilon scheme and its application for describing turbulence in inland water bodies

2021 ◽  
Author(s):  
Irina Soustova ◽  
Yuliya Troitskaya ◽  
Daria Gladskikh
Keyword(s):  
Prandtl Number ◽  
Turbulent Mixing ◽  
Richardson Number ◽  
Three Dimensional ◽  
Water Bodies ◽  
Inland Water ◽  
Dependent Relation ◽  
Vertical Distributions ◽  
Computing Center ◽  
Inland Water Bodies

&lt;p&gt;A parameterization of the Prandtl number as a function of the gradient Richardson number is proposed in order to correctly take into account stratification when calculating the thermohydrodynamic regime of inland water bodies. This parameterization allows the existence of turbulence at any values &amp;#8203;&amp;#8203;of the Richardson number.&lt;/p&gt;&lt;p&gt;The proposed function is used to calculate the turbulent thermal conductivity coefficient in a k-epsilon mixing scheme. Modification is implemented in the three-dimensional hydrostatic model developed at the Research Computing Center of Moscow State University.&lt;/p&gt;&lt;p&gt;It is demonstrated that the proposed modification (in contrast to the standard scheme with a constant Prandtl number) leads to smoothing all sharp changes in vertical distributions of turbulent mixing parameters (turbulent kinetic energy, temperature and thickness of the shock layer) and imposes a Richardson number-dependent relation on the empirical constants of k-epsilon turbulent mixing scheme.&lt;/p&gt;&lt;p&gt;The work was supported by grants of the RF President&amp;#8217;s Grant for Young Scientists (MK-1867.2020.5) and by the RFBR (19-05-00249, 20-05-00776).&amp;#160;&lt;/p&gt;

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