scholarly journals Entrainment and mixed layer dynamics of a surface-stress-driven stratified fluid

2015 ◽  
Vol 765 ◽  
pp. 653-667 ◽  
Author(s):  
G. E. Manucharyan ◽  
C. P. Caulfield
Keyword(s):  
Potential Energy ◽  
Mixed Layer ◽  
Surface Stress ◽  
Stratified Fluid ◽  
Balance Model ◽  
Buoyancy Frequency ◽  
Characteristic Velocity ◽  
Rate Of Increase ◽  
Mixed Layers ◽  
Entrainment Mixing

AbstractWe consider experimentally an initially quiescent and linearly stratified fluid with buoyancy frequency $N_{Q}$ in a cylinder subject to surface-stress forcing from a disc of radius $R$ spinning at a constant angular velocity ${\rm\Omega}$. We observe the growth of the disc-adjacent turbulent mixed layer bounded by a sharp primary interface with a constant characteristic thickness $l_{I}$. To a good approximation the depth of the forced mixed layer scales as $h_{F}/R\sim (N_{Q}/{\rm\Omega})^{-2/3}({\rm\Omega}t)^{2/9}$. Generalising the previous arguments and observations of Shravat et al. (J. Fluid Mech., vol. 691, 2012, pp. 498–517), we show that such a deepening rate is consistent with three central assumptions that allow us to develop a phenomenological energy balance model for the entrainment dynamics. First, the total kinetic energy of the deepening mixed layer $\mathscr{E}_{KF}\propto h_{F}u_{F}^{2}$, where $u_{F}$ is a characteristic velocity scale of the turbulent motions within the forced layer, is essentially independent of time and the buoyancy frequency $N_{Q}$. Second, the scaled entrainment parameter $E={\dot{h}}_{F}/u_{F}$ depends only on the local interfacial Richardson number $Ri_{I}=(N_{Q}^{2}h_{F}l_{I})/(2u_{F}^{2})$. Third, the potential energy increase (due to entrainment, mixing and homogenisation throughout the deepening mixed layer) is driven by the local energy input at the interface, and hence is proportional to the third power of the characteristic velocity $u_{F}$. We establish that internal consistency between these assumptions implies that the rate of increase of the potential energy (and hence the local mass flux across the primary interface) decreases with $Ri_{I}$. This observation suggests, as originally argued by Phillips (Deep-Sea Res., vol. 19, 1972, pp. 79–81), that the mixing in the vicinity of the primary interface leads to the spontaneous appearance of secondary partially mixed layers, and we observe experimentally such secondary layers below the primary interface.

The growth of a turbulent patch in a stratified fluid

1988 ◽  
Vol 190 ◽  
pp. 55-70 ◽  
Author(s):  
Harindra J. S. Fernando
Keyword(s):  
Energy Source ◽  
Mixed Layer ◽  
Turbulent Mixing ◽  
Interfacial Layer ◽  
Patch Size ◽  
Stratified Fluid ◽  
Buoyancy Frequency ◽  
External Energy ◽  
External Energy Source ◽  
Vertical Size

The behaviour of a turbulent region generated within a linearly-stratified fluid by an external energy source has been studied experimentally. A monoplanar grid that generated small-amplitude oscillations was used as the energy source. The results show that the mixed layer initially grows rapidly, as in an unstratified fluid, but when its physical vertical size becomes rf ∼ (K1/N)½, at a time tf ≈ 4.0 N−1, where N is the buoyancy frequency and K1 is the ‘action’ of the grid, the buoyancy forces become dominant and drastically reduce further vertical growth of the patch. While the patch size remains at rf, a well-defined density interfacial layer is formed at the entrainment interface. An important feature of the interfacial layer is the presence of internal waves, excited by the mixed-layer turbulence. If the grid oscillations are continuously maintained, the interfacial waves break and cause turbulent mixing, thereby increasing the size of the patch beyond rf at a very slow rate. Theoretical estimates are made for the growth characteristics and are compared with the experimental results.

The deepening of a mixed layer in a stratified fluid

1975 ◽  
Vol 71 (2) ◽  
pp. 385-405 ◽  
Author(s):  
P. F. Linden
Keyword(s):  
Potential Energy ◽  
Internal Waves ◽  
Mixed Layer ◽  
Turbulent Energy ◽  
Stratified Fluid ◽  
Homogeneous Field ◽  
Constant Density ◽  
Simple Relationship ◽  
Mean Flow ◽  
Mixing Rate

In this paper two aspects of the deepening of a mixed layer in a stratified fluid are examined in the laboratory. The first is the deepening of a layer into a region of constant density gradient. Turbulence is produced by an oscillating grid which generates a horizontally homogeneous field of motion with no significant mean flow. It is found that the rate at which the potential energy of the basic stratification is increased by the mixing does not bear a simple relationship to the rate of energy input by the grid. On the other hand, when allowance is made for the decay of turbulent energy away from the grid and only that portion to reach the bottom of the mixed layer is considered, the rate of potential energy increase is found to be proportional to this available energy. The second aspect to be discussed is the effect of energy radiation by internal waves in the region below the mixed layer. Estimates are made of the possible loss of energy to these waves, which reduces the amount available to deepen the layer. An experimental demonstration of up to 50 % reduction in the mixing rate due to the presence of internal waves is given. Finally, the implications of these results are discussed in the light of current theoretical models of the deepening process.

Entrainment and mixing dynamics of surface-stress-driven stratified flow in a cylinder

2012 ◽  
Vol 691 ◽  
pp. 498-517 ◽  
Author(s):  
A. Shravat ◽  
C. Cenedese ◽  
C. P. Caulfield
Keyword(s):  
Surface Stress ◽  
High Frequency ◽  
Rotating Disk ◽  
Disk Drive ◽  
Time Dependent ◽  
Characteristic Velocity ◽  
Cylindrical Tank ◽  
Rate Of Increase ◽  
Mixing Dynamics ◽  
Probe Measurements

AbstractWe extend previous work of Boyer, Davies & Guo (Fluid Dyn. Res., vol. 21, 1997, pp. 381–401) to consider the evolution of an initially two-layer stratified fluid in a cylindrical tank which is driven by a horizontal rotating disk. The turbulent motions induced by the disk drive entrainment at the interface, and similarly to the results of Boyeret al. (1997), the layer nearer to the disk deepens. Through high-frequency conductivity probe measurements, we establish that the deepening layer is very well-mixed, and the thickness of the interface between the two evolving layers appears to be approximately constant. Under certain circumstances, we find that the rate of increase in depth of the deepening layer decreases with time, at variance with the results of Boyeret al. (1997), and implying that the characteristic velocity in the deepening layer decreases as the upper layer deepens. We propose that such time-dependent deepening, and the associated weakening of the upper-layer velocities, occurs naturally because of the combined power requirements of entrainment and layer homogenization which inhibit, when the stratification is very strong, the characteristic velocities of the deepening layer approaching the (constant) velocities of the driving disk, as assumed by Boyeret al. (1997).

scholarly journals Turbulent mixing in stratified fluids: layer formation and energetics

1994 ◽  
Vol 279 ◽  
pp. 279-311 ◽  
Author(s):  
Young-Gyu Park ◽  
J. A. Whitehead ◽  
Anand Gnanadeskian
Keyword(s):  
Equilibrium State ◽  
Mixed Layer ◽  
Richardson Number ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Density Structure ◽  
Initial State ◽  
Instability Theory ◽  
Critical Richardson Number ◽  
Mixed Layers

Water with constant initial salt stratification was mixed with a horizontally moving vertical rod. The initially linear density profile turned into a series of steps when mixing was weak, in agreement with instability theory by Phillips (1972) and Posmentier (1977). For stronger mixing no steps formed. However, in all cases mixed layers formed next to the top and bottom boundaries and expanded into the interior due to the no-flux condition at the horizontal boundaries. The critical Richardson number Rie, dividing experiments with steps and ones without, increases with Reynolds number Re as Rie ≈ exp(Re/900). Steps evolved over time, with small ones forming first and larger ones appearing later. The interior seemed to reach an equilibrium state with a collection of stationary steps. The boundary mixed layers continued to penetrate into the interior. They finally formed two mixed layers separated by a step, and ultimately acquired the same densities so the fluid became homogeneous. The length scale of the equilibrium steps, ls, is a linear function of U/Ni, where U is the speed of the stirring rod and Ni is the buoyancy frequency of the initial stratification. The mixing efficiency Rf also evolved in relation to the evolution of the density structure. During the initiation of the steps, Rf showed two completely different modes of evolution depending on the overall Richardson number of the initial state, Rio. For Rio [Gt ] Rie, Rf increased initially. However for Rio near Rie, Rf decreased. Then the steps reached an equilibrium state where Rf was constant at a value that depended on the initial stratification. The density flux was measured to be uniform in the layered interior irrespective of the interior density gradient during the equilibrium state. Thus, the density (salt) was transported from the bottom boundary mixed layer through the layered interior to the top boundary mixed layer without changing the interior density structure. The relationship between Ril and Rf was found for Ril > 1, where Ril is the Richardson number based on the thickness of the interface between the mixed layers. Rf decreases as Ril increases, consistent with the most crucial assumption of the instability theory of Phillips/Posmentier.

scholarly journals Parameterization of Eddy Effects on Mixed Layers and Tracer Transport: A Linearized Eddy Perspective

2005 ◽  
Vol 35 (10) ◽  
pp. 1717-1725 ◽  
Author(s):  
Peter D. Killworth
Keyword(s):  
Ocean Circulation ◽  
Mixed Layer ◽  
Eddy Diffusion ◽  
Stratified Fluid ◽  
Neutral Stability ◽  
Tracer Transport ◽  
Layer Density ◽  
Passive Tracers ◽  
Mixed Layers

Abstract Two aspects of the effects of eddies on ocean circulation have proven difficult to parameterize: eddy effects in regions of neutrally stable (or convecting) fluid and the mixing of passive tracers. The effects of linearized eddies, although a restrictive parameter regime, can be straightforwardly computed in these cases. The eddy effects in areas of neutral stability—for example, mixed layers—blend naturally into those in the stably stratified water below, although losing the concept of bolus velocity. Instead, the mixed layer density is advected by an extra overturning velocity and is diffused laterally by a diffusion that is the same as the eddy diffusion at the top of the stably stratified fluid. Passive tracers are advected by the bolus velocity and mixed by the same diffusivity as is used to compute the bolus velocity at that location, so that two different diffusivities are not needed.

Variations in mixed-layer illite/smectite diagenesis in the rift and post-rift sediments of the Jeanne d'Arc Basin, Grand Banks offshore Newfoundland, Canada

2004 ◽  
Vol 41 (4) ◽  
pp. 401-429 ◽  
Author(s):  
Iftikhar A Abid ◽  
Reinhard Hesse ◽  
John D Harper
Keyword(s):  
Mixed Layer ◽  
Fine Fraction ◽  
Upper Jurassic ◽  
Grand Banks ◽  
Depth Profiles ◽  
Jeanne D'arc Basin ◽  
Central Ridge ◽  
Jeanne D'arc ◽  
Layer I ◽  
Mixed Layers

Mixed-layer illite/smectite (I/S) clays were analyzed from 22 deep exploration wells from the Jeanne d'Arc Basin on the Grand Banks offshore Newfoundland, the host of large commercial hydrocarbon accumulations discovered in the last two and a half decades. The fine fraction of the clays (<0.1 µm) consists mainly of mixed-layer I/S with minor amounts of kaolinite, illite, and chlorite. Smectite and (or) smectite-rich I/S clays were supplied to the Jeanne d'Arc Basin from Upper Jurassic to Tertiary times. Smectite-rich I/S clays occur only in shallow samples irrespective of geologic age. The proportion of illite in I/S mixed-layers, as well as the degree of ordering, increase with depth and temperature indicating that smectite-rich I/S clays have been progressively illitized in both rift and post-rift sediments of the Jeanne d'Arc Basin during burial. The transition from random to R1-ordered I/S occurs between subsurface depths of 1940 and 3720 m and crosses major stratigraphic boundaries. The transition from R1- to R3-ordered I/S generally occurs below 4000 m depth. Variable shapes of I/S depth profiles reflect the influence of temperature, fluid migration, subsidence history, basin structure, lithology, and salt diapirism on I/S diagenesis. Based on these variations, the basin can be subdivided into 4 regions with different illitization gradients. In the Southern Jeanne d'Ac Basin, advanced I/S diagenesis probably reflects uplift and denudation and (or) higher paleogeothermal gradients. Rapid increase of percent illite in I/S with depth in the Trans-Basinal Fault area is most likely controlled by upward flow of hot, K+-bearing fluids along faults. The migration of hydrocarbons probably followed the same pathways as the illitizing fluids. Delayed illitization in the Northern Jeanne d'Arc Basin and Central Ridge area reflects insufficient K+ supply because of a lack of detrital K-feldspar in the host sediment, the absence of faulting, and the presence of thick shale intervals. These findings show that I/S depth profiles may vary within the same sedimentary basin due to a variety of geological factors. Single wells generally cannot be considered representative for the basin as a whole.

Parameterization of Mixed Layer Eddies. Part I: Theory and Diagnosis

2008 ◽  
Vol 38 (6) ◽  
pp. 1145-1165 ◽  
Author(s):  
Baylor Fox-Kemper ◽  
Raffaele Ferrari ◽  
Robert Hallberg
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Baroclinic Instability ◽  
Finite Amplitude ◽  
Climate Impacts ◽  
Surface Mixed Layer ◽  
Rotation Rates ◽  
Wide Range ◽  
Horizontal Density Gradient ◽  
Mixed Layers

Abstract Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

scholarly journals Ultramicrosensors based on transition metal hexacyanoferrates for scanning electrochemical microscopy

2013 ◽  
Vol 4 ◽  
pp. 649-654 ◽  
Author(s):  
Maria A Komkova ◽  
Angelika Holzinger ◽  
Andreas Hartmann ◽  
Alexei R Khokhlov ◽  
Christine Kranz ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Detection Limit ◽  
Transition Metal ◽  
Prussian Blue ◽  
Electrochemical Deposition ◽  
Mixed Layer ◽  
Scanning Electrochemical Microscopy ◽  
The Stability ◽  
Mixed Layers ◽  
Electrochemical Microscopy

We report here a way for improving the stability of ultramicroelectrodes (UME) based on hexacyanoferrate-modified metals for the detection of hydrogen peroxide. The most stable sensors were obtained by electrochemical deposition of six layers of hexacyanoferrates (HCF), more specifically, an alternating pattern of three layers of Prussian Blue and three layers of Ni–HCF. The microelectrodes modified with mixed layers were continuously monitored in 1 mM hydrogen peroxide and proved to be stable for more than 5 h under these conditions. The mixed layer microelectrodes exhibited a stability which is five times as high as the stability of conventional Prussian Blue-modified UMEs. The sensitivity of the mixed layer sensor was 0.32 A·M−1·cm−2, and the detection limit was 10 µM. The mixed layer-based UMEs were used as sensors in scanning electrochemical microscopy (SECM) experiments for imaging of hydrogen peroxide evolution.

Oceanic wave-balanced surface fronts and filaments

2013 ◽  
Vol 730 ◽  
pp. 464-490 ◽  
Author(s):  
James C. McWilliams ◽  
Baylor Fox-Kemper
Keyword(s):  
Mixed Layer ◽  
Stokes Drift ◽  
Surface Gravity Wave ◽  
Initial Flow ◽  
Coriolis Forces ◽  
Flow Perturbation ◽  
Front Shape ◽  
Oceanic Wave ◽  
Mixed Layers ◽  
Layer Deformation

AbstractA geostrophic, hydrostatic, frontal or filamentary flow adjusts conservatively to accommodate a surface gravity wave field with wave-averaged, Stokes-drift vortex and Coriolis forces in an altered balanced state. In this altered state, the wave-balanced perturbations have an opposite cross-front symmetry to the original geostrophic state; e.g. the along-front flow perturbation is odd-symmetric about the frontal centre while the geostrophic flow is even-symmetric. The adjustment tends to make the flow scale closer to the deformation radius, and it induces a cross-front shape displacement in the opposite direction to the overturning effects of wave-aligned down-front and up-front winds. The ageostrophic, non-hydrostatic, adjusted flow may differ from the initial flow substantially, with velocity and buoyancy perturbations that extend over a larger and deeper region than the initial front and Stokes drift. The largest effect occurs for fronts that are wider than the mixed layer deformation radius and that fill about two-thirds of a well-mixed surface layer, with the Stokes drift spanning only the shallowest part of the mixed layer. For even deeper mixed layers, and especially for thinner or absent mixed layers, the wave-balanced adjustments are not as large.

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