scholarly journals Equilibration of Two-Dimensional Double-Diffusive Intrusions

2007 ◽  
Vol 37 (3) ◽  
pp. 625-643 ◽  
Author(s):  
Julian Simeonov ◽  
Melvin E. Stern
Keyword(s):  
Equilibrium State ◽  
Mixed Layer ◽  
Vertical Direction ◽  
Maximum Velocity ◽  
Reynolds Numbers ◽  
Horizontal Gradient ◽  
Two Dimensional ◽  
Salinity Gradients ◽  
Gravity Acceleration ◽  
Mixed Layers

Abstract This paper considers the equilibration of lateral intrusions in a doubly diffusive fluid with uniform unbounded basic-state gradients in temperature and salinity. These are density compensated in the horizontal direction and finger favorable in the vertical direction. Previous nonlinear studies of this effect have qualitative and quantitative limitations because of their fictitious parameterizations of the weak “turbulence” that arises. Here, two-dimensional direct numerical simulations (DNS) that resolve scales from the smallest to the intrusive are used to predict the equilibrium state. This is achieved by numerically tilting the x–z computational box so that the mean intrusion is represented by a mode with no lateral variation, but smaller-scale 2D eddies comparable to the intrusion thickness are resolved. The DNS show that the initial plane wave intrusion evolves to an equilibrium state containing both a salt finger interface and a diffusive interface, surrounded by well-mixed layers. The inversion of the horizontally averaged density in the mixed layer is negligibly small, but the salt finger buoyancy flux produces large transient density inversions that drive the mixed layer convection. For the considered values of horizontal/vertical gradients, the calculations yield small Cox numbers and buoyancy Reynolds numbers [comparable to those measured in staircases during the Caribbean-Sheets and Layers Transects (C-SALT) program]. An important testable result is the time-averaged maximum velocity of the fastest-growing intrusion Umax = 18.0 (Σ*z/Σ*x)+1/2KT(gΘ*z/νKT)1/4. Here Θ*z is the undisturbed vertical temperature gradient in buoyancy units, Σ*z and Σ*x are the corresponding vertical and horizontal salinity gradients, g is the gravity acceleration, and ν and KT are the respective values of the molecular viscosity and heat diffusivity. The paradoxical inverse dependence on the horizontal gradient results from the assumption that the latter is unbounded.

Interferometric study of stable salinity gradients heated from below or cooled from above

1982 ◽  
Vol 116 ◽  
pp. 411-430 ◽  
Author(s):  
W. T. Lewis ◽  
F. P. Incropera ◽  
R. Viskanta
Keyword(s):  
Mixed Layer ◽  
Mixing Layer ◽  
Density Distributions ◽  
Salinity Gradients ◽  
Isothermal Boundary ◽  
Secondary Layer ◽  
Constant Heating ◽  
Mixed Layers ◽  
Layer Development ◽  
Heating From Below

Mixing-layer development is investigated in laboratory experiments of salt-stratified solutions which are cooled from above or heated from below through the imposition of isothermal boundaries. A Mach-Zehnder interferometer is used to infer salt and density distributions within stable regions of the solution and to determine the extent of mixing-layer development. In both heating from below and cooling from above, this development differs significantly from that which has been observed for constant heating from below. Although the formation of a secondary mixed layer is observed, it does not lead to the development of additional mixed layers. Instead, the secondary layer eventually recedes, and the existence of a single mixed layer is restored. This behaviour is due to the isothermal boundary and the effect which it has no decreasing the heat transfer to or from the solution with increasing time. Once the condition of a single mixed layer is restored, extremely large (stable) density gradients develop in the boundary layer separating the mixed and stable regions, and subsequent growth of the mixed layer is slow. In cooling from above, mixing-layer development depends strongly on whether the isothermal boundary is in direct contact with the solution or separated by an air space.

An experimental investigation of the instability of a two-dimensional jet at low Reynolds numbers

1964 ◽  
Vol 20 (2) ◽  
pp. 337-352 ◽  
Author(s):  
Hiroshi Sato ◽  
Fujihiko Sakao
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Maximum Velocity ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Low Reynolds Numbers ◽  
Laminar Jet ◽  
Artificial Disturbance ◽  
Low Reynolds ◽  
The Stability

An experimental investigation was made of the stability of a two-dimensional jet at low Reynolds numbers with extremely small residual disturbances both in and around the jet. The velocity distribution of a laminar jet is in agreement with Bickley's theoretical result. The stability and transition of a laminar jet are characterized by the Reynolds number based on the slit width and the maximum velocity of the jet. When the Reynolds number is less than 10, the whole jet is laminar. When the Reynolds number is between 10 and around 50, periodic velocity fluctuations are found in the jet. They die out as they travel downstream without developing into irregular fluctuations. When the Reynolds number exceeds about 50, periodic fluctuations develop into irregular, turbulent fluctuations. The frequency of the periodic fluctuation is roughly proportional to the square of the jet velocity.The stability of the jet against an artificially imposed disturbance was also investigated. Sound was used as an artificial disturbance. The disturbance is either amplified or damped in the jet depending on its frequency. The conventional stability theory was modified by considering the streamwise increase of Reynolds number. The experimental results are in agreement with the theoretical results.

scholarly journals Global Estimates of Lateral Springtime Restratification

2016 ◽  
Vol 46 (5) ◽  
pp. 1555-1573 ◽  
Author(s):  
Leah Johnson ◽  
Craig M. Lee ◽  
Eric A. D’Asaro
Keyword(s):  
Mixed Layer ◽  
Upper Ocean ◽  
Density Gradients ◽  
Leading Order ◽  
Layer Model ◽  
One Dimensional ◽  
Salinity Gradients ◽  
Frontal Dynamics ◽  
Global Estimates ◽  
Mixed Layers

AbstractSubmesoscale frontal dynamics are thought to be of leading-order importance for stratifying the upper ocean by slumping horizontal density gradients to produce vertical stratification. Presented here is an investigation of submesoscale instabilities in the mixed layer—mixed layer eddies (MLEs)—as a potential mechanism of frontal slumping that stratifies the upper ocean during the transition from winter to spring, when wintertime forcings weaken but prior to the onset of net solar warming. Observations from the global Argo float program are compared to predictions from a one-dimensional mixed layer model to assess where in the world’s oceans lateral processes influence mixed layer evolution. The model underestimates spring stratification for ~75% ± 25% of the world’s oceans. Relationships between vertical and horizontal temperature and salinity gradients are used to suggest that in 30% ± 20% of the oceans this excess stratification can be attributed to the slumping of horizontal density fronts. Finally, 60% ± 10% of the frontal enhanced stratification is consistent with MLE theory, suggesting that MLEs may be responsible for enhanced stratification in 25% ± 15% of the world’s oceans. Enhanced stratification from frontal tilting occurs in regions of strong horizontal density gradients (e.g., midlatitude subtropical gyres), with a small fraction occurring in regions of deep mixed layers (e.g., high latitudes). Stratification driven by MLEs appears to constrain the coexistence of sharp lateral gradients and deep wintertime mixed layers, limiting mixed layer depths in regions of large lateral density gradients, with an estimated wintertime restratification flux of order 100 W m−2.

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.

Shear instability in a stratified fluid when shear and stratification are not aligned

2011 ◽  
Vol 685 ◽  
pp. 191-201 ◽  
Author(s):  
Julien Candelier ◽  
Stéphane Le Dizès ◽  
Christophe Millet
Keyword(s):  
Froude Number ◽  
Unstable Mode ◽  
Vertical Direction ◽  
Maximum Velocity ◽  
Stratified Fluid ◽  
Shear Instability ◽  
Two Dimensional ◽  
Horizontal Length ◽  
The Stability ◽  
Vertical Jet

AbstractThe effect of an inclination angle of the shear with respect to the stratification on the linear properties of the shear instability is examined in the work. For this purpose, we consider a two-dimensional plane Bickley jet of width $L$ and maximum velocity ${U}_{0} $ in a stably stratified fluid of constant Brunt–Väisälä frequency $N$ in an inviscid and Boussinesq framework. The plane of the jet is assumed to be inclined with an angle $\theta $ with respect to the vertical direction of stratification. The stability analysis is performed using both numerical and theoretical methods for all the values of $\theta $ and Froude number $F= {U}_{0} / (LN)$. We first obtain that the most unstable mode is always a two-dimensional Kelvin–Helmholtz (KH) sinuous mode. The condition of stability based on the Richardson number $Ri\gt 1/ 4$, which reads here $F\lt 3 \sqrt{3} / 2$, is recovered for $\theta = 0$. But when $\theta \not = 0$, that is, when the directions of shear and stratification are not perfectly aligned, the Bickley jet is found to be unstable for all Froude numbers. We show that two modes are involved in the stability properties. We demonstrate that when $F$ is decreased below $3 \sqrt{3} / 2$, there is a ‘jump’ from one two-dimensional sinuous mode to another. For small Froude numbers, we show that the shear instability of the inclined jet is similar to that of a horizontal jet but with a ‘horizontal’ length scale ${L}_{h} = L/ \sin \theta $. In this regime, the characteristics (oscillation frequency, growth rate, wavenumber) of the most unstable mode are found to be proportional to $\sin \theta $. For large Froude numbers, the shear instability of the inclined jet is similar to that of a vertical jet with the same scales but with a different Froude number, ${F}_{v} = F/ \hspace *{-.1pc}\cos \theta $. It is argued that these results could be valid for any type of shear flow.

scholarly journals Two-dimensional flow field distribution characteristics of flocking drainage pipes in tunnel

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 139-148
Author(s):  
Shiyang Liu ◽  
Xuefu Zhang ◽  
Feng Gao ◽  
Liangwen Wei ◽  
Qiang Liu ◽  
...  
Keyword(s):  
Flow Field ◽  
Field Distribution ◽  
Rapid Development ◽  
Maximum Velocity ◽  
Distribution Characteristics ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Laboratory Test Results ◽  
Transverse Distance ◽  
Two Dimensional Flow

AbstractWith the rapid development of traffic infrastructure in China, the problem of crystal plugging of tunnel drainage pipes becomes increasingly salient. In order to build a mechanism that is resilient to the crystal plugging of flocking drainage pipes, the present study used the numerical simulation to analyze the two-dimensional flow field distribution characteristics of flocking drainage pipes under different flocking spacings. Then, the results were compared with the laboratory test results. According to the results, the maximum velocity distribution in the flow field of flocking drainage pipes is closely related to the transverse distance h of the fluff, while the longitudinal distance h of the fluff causes little effect; when the transverse distance h of the fluff is less than 6.25D (D refers to the diameter of the fluff), the velocity between the adjacent transverse fluffs will be increased by more than 10%. Moreover, the velocity of the upstream and downstream fluffs will be decreased by 90% compared with that of the inlet; the crystal distribution can be more obvious in the place with larger velocity while it is less at the lower flow rate. The results can provide theoretical support for building a mechanism to deal with and remove the crystallization of flocking drainage pipes.

Effects of shoulder translation on lumbar moment for two dimensional modeling strategies during lifting

1998 ◽  
Vol 1 (3) ◽  
pp. 173-187
Author(s):  
Wayne J. Albert ◽  
Joan M. Stevenson ◽  
Geneviève A. Dumas ◽  
Roger W. Wheeler
Keyword(s):  
Sagittal Plane ◽  
Tracking System ◽  
Vertical Direction ◽  
Two Dimensional ◽  
Model Type ◽  
Trunk Acceleration ◽  
Analysis System ◽  
Trunk Orientation ◽  
Shoulder Position ◽  
Dynamic Link

The objectives of this study were to: 1) develop a dynamic 2D link segment model for lifting using the constraints of four sensors from an electromagnetic motion analysis system; 2) evaluate the magnitude of shoulder movement in the sagittal plane during lifting; and 3) investigate the effect of shoulder translation on trunk acceleration and lumbar moments calculated by the developed model and comparing it with two separate 2D dynamic link segment models. Six women and six men lifted loads of 2 kg, 7 kg, 12 kg and 2 kg, 12 kg, 22 kg respectively, under stoop, squat and freestyle conditions. Trunk orientation and position, as well as shoulder position were monitored during all lifts using the Polhemus FASTRAK\trdmk. Results indicated that average range of motion was 0.05 ± 0.02 m in the horizontal direction and 0.03 ± 0.02 m in the vertical direction. Shoulder position relative to T1 was located 0.07 ± 0.02 m anteriorly, and 0.02 ± 0.04 m superiorly (0.06 and 0.00 m for males and 0.08 and 0.04 m for females, respectively). To estimate the effect of shoulder motion on trunk acceleration and L5/S1 moments, three two-dimensional dynamic link segment models were developed within the constraints of the electromagnetic tracking system and compared. Trunk segment endpoints were defined as L5/S1 and either T1 or shoulder depending on model type. For trunk accelerations, average differences between models were greater than 40 deg/s² in 70.4% trunk accelerations did not translate into significantly different moment calculations between models. Average peak dynamic L5/S1 moment differences between models were smaller than 4 Nm for all lifting conditions which failed to be statistically significant (p>0.05). The model type did not have a statistically significant effect on peak L5/S1 moments. Therefore, despite important shoulder joint translations, peak L5/S1 moments were not significantly affected.

Lamellar Porous Vermiculite Membranes for Boosting Nanofluidic Osmotic Energy Conversion

2021 ◽  
Author(s):  
Li Cao ◽  
Hong Wu ◽  
Chunyang Fan ◽  
Zhiming Zhang ◽  
Benbing Shi ◽  
...  
Keyword(s):  
Energy Conversion ◽  
Power Density ◽  
Great Promise ◽  
Two Dimensional ◽  
Nanofluidic Channels ◽  
Salinity Gradients ◽  
Transmembrane Resistance

Lamellar membranes with two-dimensional nanofluidic channels hold great promise in harvesting osmotic energy from salinity gradients. However, the power density is often limited by the high transmembrane resistance primarily caused...

scholarly journals GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO

2011 ◽  
Vol 21 (03) ◽  
pp. 421-457 ◽  
Author(s):  
RAPHAËL DANCHIN ◽  
MARIUS PAICU
Keyword(s):  
Global Existence ◽  
Turbulent Flows ◽  
Vertical Direction ◽  
Boussinesq System ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Incompressible Euler Equation ◽  
Navier Stokes Equation ◽  
Transport Diffusion ◽  
Anisotropic Viscosity

Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq system with horizontal viscosity in only one equation. In this paper, we focus on the global existence issue for possibly large initial data. We first examine the case where the Navier–Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transport–diffusion equation with diffusion in the horizontal direction only. For both systems, we construct global weak solutions à la Leray and strong unique solutions for more regular data. Our results rest on the fact that the diffusion acts perpendicularly to the buoyancy force.

scholarly journals Effects of Diurnal Variations on Tropical Equilibrium States: A Two-Dimensional Cloud-Resolving Modeling Study

2007 ◽  
Vol 64 (2) ◽  
pp. 656-664 ◽  
Author(s):  
Shouting Gao ◽  
Yushu Zhou ◽  
Xiaofan Li
Keyword(s):  
Equilibrium State ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Zenith Angle ◽  
Solar Zenith Angle ◽  
Diurnal Variations ◽  
Equilibrium States ◽  
Sea Surface ◽  
Two Dimensional ◽  
Time Invariant

Abstract Effects of diurnal variations on tropical heat and water vapor equilibrium states are investigated based on hourly data from two-dimensional cloud-resolving simulations. The model is integrated for 40 days and the simulations reach equilibrium states in all experiments. The simulation with a time-invariant solar zenith angle produces a colder and drier equilibrium state than does the simulation with a diurnally varied solar zenith angle. The simulation with a diurnally varied sea surface temperature generates a colder equilibrium state than does the simulation with a time-invariant sea surface temperature. Mass-weighted mean temperature and precipitable water budgets are analyzed to explain the thermodynamic differences. The simulation with the time-invariant solar zenith angle produces less solar heating, more condensation, and consumes more moisture than the simulation with the diurnally varied solar zenith angle. The simulation with the diurnally varied sea surface temperature produces a colder temperature through less latent heating and more IR cooling than the simulation with the time-invariant sea surface temperature.

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