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Journal articles on the topic 'Stratified flow'

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Published: 4 June 2021

Last updated: 1 April 2023

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1

Moiseev, K. V. "Stratified flow with natural convection weakly stratified fluid." Proceedings of the Mavlyutov Institute of Mechanics 11, no. 1 (2016): 88–93. http://dx.doi.org/10.21662/uim2016.1.013.

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In work on the basis of a mathematical model based on a linear approximation, we study the formation of the layered flows with natural convection, poorly stratified inhomogeneous liquid. The regions of the parameters under which a layered structure of the flow-cell in a side heating.

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2

Cisneros-Aguirre, Jesús, J. L. Pelegrí, and P. Sangrà. "Experiments on layer formation in stratified shear flow." Scientia Marina 65, S1 (July 30, 2001): 117–26. http://dx.doi.org/10.3989/scimar.2001.65s1117.

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3

BALMFORTH, NEIL J., and YUAN-NAN YOUNG. "Stratified Kolmogorov flow." Journal of Fluid Mechanics 450 (January 9, 2002): 131–67. http://dx.doi.org/10.1017/s0022111002006371.

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In this study we investigate the Kolmogorov flow (a shear flow with a sinusoidal velocity profile) in a weakly stratified, two-dimensional fluid. We derive amplitude equations for this system in the neighbourhood of the initial bifurcation to instability for both low and high Péclet numbers (strong and weak thermal diffusion, respectively). We solve amplitude equations numerically and find that, for low Péclet number, the stratification halts the cascade of energy from small to large scales at an intermediate wavenumber. For high Péclet number, we discover diffusively spreading, thermal boundary layers in which the stratification temporarily impedes, but does not saturate, the growth of the instability; the instability eventually mixes the temperature inside the boundary layers, so releasing itself from the stabilizing stratification there, and thereby grows more quickly. We solve the governing fluid equations numerically to compare with the asymptotic results, and to extend the exploration well beyond onset. We find that the arrest of the inverse cascade by stratification is a robust feature of the system, occurring at higher Reynolds, Richards and Péclet numbers – the flow patterns are invariably smaller than the domain size. At higher Péclet number, though the system creates slender regions in which the temperature gradient is concentrated within a more homogeneous background, there are no signs of the horizontally mixed layers separated by diffusive interfaces familiar from doubly diffusive systems.

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4

Ng, T. S., C. J. Lawrence, and G. F. Hewitt. "Laminar stratified pipe flow." International Journal of Multiphase Flow 28, no. 6 (June 2002): 963–96. http://dx.doi.org/10.1016/s0301-9322(02)00004-6.

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5

Fan, Jiahua. "Stratified flow through outlets." Journal of Hydro-environment Research 2, no. 1 (September 2008): 3–18. http://dx.doi.org/10.1016/j.jher.2008.04.001.

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6

Shogo, Shakouchi, and Uchiyama Tomomi. "1097 MIXING PHENOMENA OF DENSITY STRATIFIED FLUID WITH JET FLOW." Proceedings of the International Conference on Jets, Wakes and Separated Flows (ICJWSF) 2013.4 (2013): _1097–1_—_1097–4_. http://dx.doi.org/10.1299/jsmeicjwsf.2013.4._1097-1_.

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7

BALMFORTH, N. J., and Y. N. YOUNG. "Stratified Kolmogorov flow. Part 2." Journal of Fluid Mechanics 528 (April 10, 2005): 23–42. http://dx.doi.org/10.1017/s002211200400271x.

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8

Castro, I. P., and W. H. Snyder. "Upstream motions in stratified flow." Journal of Fluid Mechanics 187 (February 1988): 487–506. http://dx.doi.org/10.1017/s0022112088000539.

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In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

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9

Lin, Q., W. R. Lindberg, D. L. Boyer, and H. J. S. Fernando. "Stratified flow past a sphere." Journal of Fluid Mechanics 240, no. -1 (July 1992): 315. http://dx.doi.org/10.1017/s0022112092000119.

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10

Govindarajan, Rama, and Kirti Chandra Sahu. "Instabilities in Viscosity-Stratified Flow." Annual Review of Fluid Mechanics 46, no. 1 (January 3, 2014): 331–53. http://dx.doi.org/10.1146/annurev-fluid-010313-141351.

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11

Soo, S. L., and R. W. Lyczkowski. "Analysis of Stratified Flow Mixing." Nuclear Science and Engineering 91, no. 3 (November 1985): 349–58. http://dx.doi.org/10.13182/nse85-a17310.

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12

Valentine, Greg A. "Stratified flow in pyroclastic surges." Bulletin of Volcanology 49, no. 4 (August 1987): 616–30. http://dx.doi.org/10.1007/bf01079967.

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13

Korbel, A., and W. Bochniak. "Stratified plastic flow in metals." International Journal of Mechanical Sciences 128-129 (August 2017): 269–76. http://dx.doi.org/10.1016/j.ijmecsci.2017.04.006.

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14

Barnard, Richard C., and Peter R. Wolenski. "Flow Invariance on Stratified Domains." Set-Valued and Variational Analysis 21, no. 2 (February 14, 2013): 377–403. http://dx.doi.org/10.1007/s11228-013-0230-y.

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15

Dewey, Richard, David Richmond, and Chris Garrett. "Stratified Tidal Flow over a Bump." Journal of Physical Oceanography 35, no. 10 (October 1, 2005): 1911–27. http://dx.doi.org/10.1175/jpo2799.1.

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Abstract The interaction of a stratified flow with an isolated topographic feature can introduce numerous disturbances into the flow, including turbulent wakes, internal waves, and eddies. Measurements made near a “bump” east of Race Rocks, Vancouver Island, reveal a wide range of phenomena associated with the variable flow speeds and directions introduced by the local tides. Upstream and downstream flows were observed by placing two acoustic Doppler current profilers (ADCPs) on one flank of the bump. Simultaneous shipboard ADCP surveys corroborated some of the more striking features. Froude number conditions varied from subcritical to supercritical as the tidal velocities varied from 0.2 to 1.5 m s−1. During the strong ebb, when the moored ADCPs were located on the lee side, a persistent full-water-depth lee wave was detected in one of the moored ADCPs and the shipboard ADCP. However, the placement of the moorings would suggest that, by the time it appears in the moored ADCP beams, the lee wave has been swept downstream or has separated from the bump. Raw ADCP beam velocities suggest enhanced turbulence during various phases of the tide. Many of the three-dimensional flow characteristics are in good agreement with laboratory studies, and some characteristics, such as shear in the bottom boundary layer, are not.

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16

Vlachos, N. A. "Studies of Wavy Stratified and Stratified/Atomization Gas-Liquid Flow." Journal of Energy Resources Technology 125, no. 2 (June 1, 2003): 131–36. http://dx.doi.org/10.1115/1.1576265.

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Studies of wavy stratified and stratified/atomization two-phase flow in horizontal pipes are outlined. Notable features of this flow regime include the appearance of disturbance waves, the atomization onset and the drastic change of the gas/liquid interface profile from flat to “concave.” Liquid-to-wall shear stress tends to decrease circumferentially. A computational procedure for predicting main flow characteristics, which takes into account the above results in its design relations, is first assessed with detailed experimental data and is then combined with a CFD code, aiming at enhancing the predictive capability.

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17

Boubnov, B. M., E. B. Gledzer, and E. J. Hopfinger. "Stratified circular Couette flow: instability and flow regimes." Journal of Fluid Mechanics 292 (June 10, 1995): 333–58. http://dx.doi.org/10.1017/s0022112095001558.

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The stability conditions of the flow between two concentric cylinders with the inner one rotating (circular Couette flow) have been investigated experimentally and theoretically for a fluid with axial, stable linear density stratification. The behaviour of the flow, therefore, depends on the Froude number Fr = Ω/N (where Ω is the angular velocity of the inner cylinder and N is the buoyancy frequency of the fluid) in addition to the Reynolds number and the non-dimensional gap width ε, here equal to 0.275.Experiments show that stratification has a stabilizing effect on the flow with the critical Reynolds number depending on N, in agreement with linear stability theory. The selected, most amplified, vertical wavelength at onset of instability is reduced by the stratification effect and is for the geometry considered only about half the gap width. Furthermore, the observed instability is non-axisymmetric. The resulting vortex motion causes some mixing and this leads to layer formation, clearly visible on shadowgraph images, with the height of the layer being determined by the vertical vortex size. This regime of vertically reduced vortex size is referred to as the S-regime.For larger Reynolds and Froude numbers the role of stratification decreases and the most amplified vertical wavelength is determined by the gap width, giving rise to the usual Taylor vortices (we call this the T-regime). The layers which emerge are determined by these vortices. For relatively small Reynolds number when Fr ≈ 1 the Taylor vortices are stable and the layers have a height h equal to the gap width; for larger Reynolds number or Fr ≈ 2 the Taylor vortices interact in pairs (compacted Taylor vortices, regime CT) and layers of twice the gap width are predominant. Stratification inhibits the azimuthal wavy vortex flow observed in homogeneous fluid. By further increasing the Reynolds number, turbulent motions appear with Taylor vortices superimposed like in non-stratified fluid.The theoretical analysis is based on a linear stability consideration of the axisymmetric problem. This gives bounds of instability in the parameter space (Ω, N) for given vertical and radial wavenumbers. These bounds are in qualitative agreement with experiments. The possibility of oscillatory-type instability (overstability) observed experimentally is also discussed.

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18

Boubnov, B. "Stratified circular Couette flow: instability and flow regimes." International Journal of Multiphase Flow 22 (December 1996): 127. http://dx.doi.org/10.1016/s0301-9322(97)88413-3.

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19

Al-Sarkhi, A., E. Pereyra, I. Mantilla, and C. Avila. "Dimensionless oil-water stratified to non-stratified flow pattern transition." Journal of Petroleum Science and Engineering 151 (March 2017): 284–91. http://dx.doi.org/10.1016/j.petrol.2017.01.016.

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20

Nouri, Saliha, Zouhaier Hafsia, Salah Mahmoud Boulaaras, Ali Allahem, Salem Alkhalaf, and Baowei Feng. "Numerical Analysis of Stratified and Slug Flows." Mathematical Problems in Engineering 2021 (October 19, 2021): 1–9. http://dx.doi.org/10.1155/2021/8418008.

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The main purpose of this study is to compare two-dimensional (2D) and three-dimensional (3D) two-phase models for both stratified and slug flows. These two flow regimes interest mainly the petroleum and chemical industries. The volume of fluid (VOF) approach is used to predict the interface between the two-phase flows. The stratified turbulent flow corresponds to the oil-water phases through a cylindrical pipe. To simulate the turbulent stratified flow, the k − ω turbulence model is used. The slug laminar flow concerns the kerosene-water phases through a rectangular microchannel. The simulated results are validated using the previous experimental results available in the literature. For the stratified flow, the axial velocity and the water volume fraction profiles obtained by 2D and 3D models approximate the measurement profiles at the same test section. Also, the T-junction in a 2D model affects only the inlet vicinity. For downstream, the 2D and 3D models lead to the same axial velocity and water volume distribution. For the slug flow, the simulated results show that the 3D model predicts the thin film wall contrary to the 2D model. Moreover, the 2D model underestimates the slug length.

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21

Zhang, Tao, Bin Chen, Kun Sun, and Wenjie Chang. "Study on the Law of Diesel Oil Carrying Water in Lanzhou–Chengdu–Chongqing Product Oil Pipeline Based on Large Eddy Simulation." Processes 8, no. 9 (August 27, 2020): 1049. http://dx.doi.org/10.3390/pr8091049.

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Water accumulation at the bottom of the product oil pipeline will lead to corrosion damage to the pipeline. The study on water carrying laws of refined oil could provide a reference for the safe operation of the pipeline. In this paper, the actual size of Lanzhou–Jiangyou section of Lanzhou–Chengdu–Chongqing pipeline was taken as the pipeline size. The volume of fluid (VOF) model of oil-water two-phase flow based on large eddy simulation (LES) was established. The numerical simulation of the water-carrying behavior of the product oil in the inclined pipeline was carried out. The LES-based two-phase flow model can capture the characteristics of stratified flow, wavy stratified flow, and dispersed flow under various operating conditions. The model was applied to simulate the water carrying process under various oil inlet velocities and the inclined pipe angles. The results show that as the pipeline inclined angle is 10~20° and the oil inlet velocity is 0.66 m/s, the flow patterns in the pipeline mainly include stratified flow and wavy stratified flow. As the oil inlet velocity is 0.88~1.55 m/s, the flow patterns in the pipe are mainly stratified flow, wavy stratified flow, and dispersed flow. As the inclined angle of the pipeline is 30~40°, the flow patterns in the pipeline mainly include stratified flows, wavy stratified flows, and dispersed flows. Finally, with the increase of flow time, water can be carried completely from the pipeline through the oil. With the increase of oil inlet velocity, the water carrying capacity of oil gradually increases. With the increase of pipeline inclination, the water carrying capacity of oil firstly increases and then decreases.

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22

FUKUSHIMA, Chiharu, Suketsugu NAKANISHI, and Hideo OSAKA. "321 Stratified flow induced by an impulsively started rotating cylinder : Patterns of stratified circular flow." Proceedings of Conference of Chugoku-Shikoku Branch 2006.44 (2006): 123–24. http://dx.doi.org/10.1299/jsmecs.2006.44.123.

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23

BAINES, PETER G. "Two-dimensional plumes in stratified environments." Journal of Fluid Mechanics 471 (November 5, 2002): 315–37. http://dx.doi.org/10.1017/s0022112002002215.

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Laboratory experiments on the flow of negatively buoyant two-dimensional plumes adjacent to a wall in a density-stratified environment are described. The flow passes through several stages, from an inertial jet to a buoyant plume, to a neutrally buoyant jet, and then a negatively buoyant plume when it overshoots its equilibrium density. This fluid then ‘springs back’ and eventually occupies an intermediate range of heights. The flow is primarily characterized by the initial value of the buoyancy number, B0 = Q0N3/g′02, where Q0 is the initial volume flux per unit width, g′0 is the initial buoyancy and N is the buoyancy frequency of the environment. Scaled with the initial equilibrium depth D of the in flowing fluid, the maximum depth of penetration increases with B0, as does the width of the initial down flow, which is observed to increase very slowly with distance downward. Observations are made of the profiles of flow into and away from the plume as a function of height. Various properties of the flow are compared with predictions from the ‘standard’ two-dimensional entraining plume model, and this shows generally consistent agreement, although there are differences in magnitudes and in details. This flow constrasts with flows down gentle slopes into stratified environments, where two-way exchange of fluid occurs.

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24

Xu, X., C. Yi, and E. Kutter. "Stably stratified canopy flow in complex terrain." Atmospheric Chemistry and Physics 15, no. 13 (July 10, 2015): 7457–70. http://dx.doi.org/10.5194/acp-15-7457-2015.

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Abstract. Stably stratified canopy flow in complex terrain has been considered a difficult condition for measuring net ecosystem–atmosphere exchanges of carbon, water vapor, and energy. A long-standing advection error in eddy-flux measurements is caused by stably stratified canopy flow. Such a condition with strong thermal gradient and less turbulent air is also difficult for modeling. To understand the challenging atmospheric condition for eddy-flux measurements, we use the renormalized group (RNG) k–&varepsilon; turbulence model to investigate the main characteristics of stably stratified canopy flows in complex terrain. In this two-dimensional simulation, we imposed persistent constant heat flux at ground surface and linearly increasing cooling rate in the upper-canopy layer, vertically varying dissipative force from canopy drag elements, buoyancy forcing induced from thermal stratification and the hill terrain. These strong boundary effects keep nonlinearity in the two-dimensional Navier–Stokes equations high enough to generate turbulent behavior. The fundamental characteristics of nighttime canopy flow over complex terrain measured by the small number of available multi-tower advection experiments can be reproduced by this numerical simulation, such as (1) unstable layer in the canopy and super-stable layers associated with flow decoupling in deep canopy and near the top of canopy; (2) sub-canopy drainage flow and drainage flow near the top of canopy in calm night; (3) upward momentum transfer in canopy, downward heat transfer in upper canopy and upward heat transfer in deep canopy; and (4) large buoyancy suppression and weak shear production in strong stability.

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25

Heravi, Pooyan, Li-An Chu, and Da-Jeng Yao. "Effects of inlet junctions on horizontally stratified flows." AIP Advances 13, no. 1 (January 1, 2023): 015125. http://dx.doi.org/10.1063/5.0136279.

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Horizontally stratified flows can be seen in a wide variety of micro-scale engineering problems. Recent studies have shown that diffusion at the interface between two liquids leads to a lateral flow, causing the fluid to rotate around the central axis of the channel. This lateral flow has the potential to disrupt the intended mechanism of the device or can be exploited for new device designs. The present investigation presents numerical and experimental results that provide important insights into the effects of the inlet junction on the flow field throughout the microfluidic device. The effects of four different archetypal inlet junctions—an idealized single inlet, counter-flow T junction, perpendicular flow T junction, and Y junction are considered. The results show that counter-flow T junction results in the least amount of lateral flow, while the straight channel results in the highest. The Y channel induces the second least rotation, and the perpendicular T junction creates slightly stronger lateral flows. Furthermore, based on lateral streamlines, it is suggested that the reason for the difference between these junctions can be explained by the interaction of the Dean vortices formed by the rotation of the fluid at the junction and the interaction of the Dean flow with the diffusion-induced vortices. To test this hypothesis, a less common junction (Y junction with angles higher than 180°) is modeled and has shown to reduce the lateral flow even further. Understanding the differences between the junctions would allow for more efficient microfluidic designs for various applications.

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26

CASTRO, IAN P. "Weakly stratified laminar flow past normal flat plates." Journal of Fluid Mechanics 454 (March 10, 2002): 21–46. http://dx.doi.org/10.1017/s0022112001007248.

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Numerical computations of the steady, two-dimensional, incompressible, uniform velocity but stably stratified flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the stratification is weak enough to avoid occurrence of the gravity wave motions familiar in more strongly stratified flows over obstacles. The nature of the flow is explored for channel half-widths, H, in the range 5 [les ] H [les ] 100, for Reynolds numbers, Re, (based on body half-width and the upstream velocity, U) up to 600 and for stratification levels between zero (i.e. neutral flow) and the limit set by the first appearance of waves. The fourth parameter governing the flow is the Schmidt number, Sc, the ratio of the molecular diffusion of the agent providing the stratification to the molecular viscosity. For cases of very large (in the limit, infinite) Sc a novel technique is used, which avoids solving the density equation explicitly. Results are compared with the implications of the asymptotic theory of Chernyshenko & Castro (1996) and with earlier computations of neutral flows over both flat plates and circular cylinders. The qualitative behaviour in the various flow regimes identified by the theory is demonstrated, but it is also shown that in some cases a flow zone additional to those identified by the theory appears and that, in any case, precise agreement would, for most regimes, require very much higher Re and/or H. Some examples of multiple (i.e. non-unique) solutions are shown and we discuss the likelihood of these being genuine, rather than an artefact of the numerical scheme.

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27

Liu, Zhiyu, S. A. Thorpe, and W. D. Smyth. "Instability and hydraulics of turbulent stratified shear flows." Journal of Fluid Mechanics 695 (February 20, 2012): 235–56. http://dx.doi.org/10.1017/jfm.2012.13.

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AbstractThe Taylor–Goldstein (T–G) equation is extended to include the effects of small-scale turbulence represented by non-uniform vertical and horizontal eddy viscosity and diffusion coefficients. The vertical coefficients of viscosity and diffusion, ${A}_{V} $ and ${K}_{V} $, respectively, are assumed to be equal and are expressed in terms of the buoyancy frequency of the flow, $N$, and the dissipation rate of turbulent kinetic energy per unit mass, $\varepsilon $, quantities that can be measured in the sea. The horizontal eddy coefficients, ${A}_{H} $ and ${K}_{H} $, are taken to be proportional to the dimensionally correct form, ${\varepsilon }^{1/ 3} {l}^{4/ 3} $, found appropriate in the description of horizontal dispersion of a field of passive markers of scale $l$. The extended T–G equation is applied to examine the stability and greatest growth rates in a turbulent shear flow in stratified waters near a sill, that at the entrance to the Clyde Sea in the west of Scotland. Here the main effect of turbulence is a tendency towards stabilizing the flow; the greatest growth rates of small unstable disturbances decrease, and in some cases flows that are unstable in the absence of turbulence are stabilized when its effects are included. It is conjectured that stabilization of a flow by turbulence may lead to a repeating cycle in which a flow with low levels of turbulence becomes unstable, increasing the turbulent dissipation rate and so stabilizing the flow. The collapse of turbulence then leads to a condition in which the flow may again become unstable, the cycle repeating. Two parameters are used to describe the ‘marginality’ of the observed flows. One is based on the proximity of the minimum flow Richardson number to the critical Richardson number, the other on the change in dissipation rate required to stabilize or destabilize an observed flow. The latter is related to the change needed in the flow Reynolds number to achieve zero growth rate. The unstable flows, typical of the Clyde Sea site, are relatively further from neutral stability in Reynolds number than in Richardson number. The effects of turbulence on the hydraulic state of the flow are assessed by examining the speed and propagation direction of long waves in the Clyde Sea. Results are compared to those obtained using the T–G equation without turbulent viscosity or diffusivity. Turbulence may change the state of a flow from subcritical to supercritical.

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28

Dentz, Marco, and Jesus Carrera. "Mixing and spreading in stratified flow." Physics of Fluids 19, no. 1 (January 2007): 017107. http://dx.doi.org/10.1063/1.2427089.

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29

Rouseff, Daniel, Kraig B. Winters, and Peter Kaczkowski. "Tomographic reconstruction of stratified fluid flow." Journal of the Acoustical Society of America 89, no. 4B (April 1991): 1875. http://dx.doi.org/10.1121/1.2029346.

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30

Bala, Manju. "Stability of Stratified Compressible Shear Flow." International Journal of Mathematics Trends and Technology 46, no. 2 (June 25, 2017): 53–61. http://dx.doi.org/10.14445/22315373/ijmtt-v46p511.

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31

Jacobitz, F. G., M. M. Rogers, and J. H. Ferziger. "Waves in stably stratified turbulent flow." Journal of Turbulence 6 (January 2005): N32. http://dx.doi.org/10.1080/14685240500462069.

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32

Winters, K. B., and D. Rouseff. "Tomographic reconstruction of stratified fluid flow." IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 40, no. 1 (January 1993): 26–33. http://dx.doi.org/10.1109/58.184995.

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33

Torres, C. R., and J. E. Castillo. "Stratified rotating flow over complex terrain." Applied Numerical Mathematics 47, no. 3-4 (December 2003): 531–41. http://dx.doi.org/10.1016/s0168-9274(03)00085-0.

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34

Chernyshenko, S. "Stratified Sadovskii flow in a channel." Journal of Fluid Mechanics 250 (May 1993): 423–31. http://dx.doi.org/10.1017/s002211209300151x.

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Stably stratified and non-stratified flows past a touching pair of vortices with continuous velocity are considered. An asymptotic solution for the very long eddies is determined. Numerical results cover the whole range of subcritical stratification and eddy length.

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35

Kadri, Y., P. Bonneton, J. M. Chomaz, and M. Perrier. "Stratified flow over three-dimensional topography." Dynamics of Atmospheres and Oceans 23, no. 1-4 (January 1996): 321–34. http://dx.doi.org/10.1016/0377-0265(95)00433-5.

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36

Taitel, Y. "Stratified three phase flow in pipes." International Journal of Multiphase Flow 22 (December 1996): 118. http://dx.doi.org/10.1016/s0301-9322(97)88338-3.

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37

Kuru, W. "Linear stability of stratified channel flow." International Journal of Multiphase Flow 22 (December 1996): 122. http://dx.doi.org/10.1016/s0301-9322(97)88369-3.

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38

Strack, Otto D. L. "Vertically integrated flow in stratified aquifers." Journal of Hydrology 548 (May 2017): 794–800. http://dx.doi.org/10.1016/j.jhydrol.2017.01.039.

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39

Hunt, Bruce, and Martin Gribble. "Stratified Flow Approximation for Sloping Aquifers." Journal of Hydrologic Engineering 2, no. 2 (April 1997): 50–55. http://dx.doi.org/10.1061/(asce)1084-0699(1997)2:2(50).

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40

Mahrt, L., and N. Gamage. "Observations of Turbulence in Stratified Flow." Journal of the Atmospheric Sciences 44, no. 7 (April 1987): 1106–21. http://dx.doi.org/10.1175/1520-0469(1987)044<1106:ootisf>2.0.co;2.

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41

Vladimirov, I. Yu, N. N. Korchagin, A. S. Savin, and E. O. Savina. "Stratified unbounded flow past of obstacles." Oceanology 51, no. 6 (December 2011): 916–24. http://dx.doi.org/10.1134/s000143701106021x.

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42

Killworth, Peter D. "Flow Properties in Rotating, Stratified Hydraulics." Journal of Physical Oceanography 22, no. 9 (September 1992): 997–1017. http://dx.doi.org/10.1175/1520-0485(1992)022<0997:fpirsh>2.0.co;2.

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43

Allen, J. S., and P. A. Newberger. "On Intermediate Models for Stratified Flow." Journal of Physical Oceanography 23, no. 11 (November 1993): 2462–86. http://dx.doi.org/10.1175/1520-0485(1993)023<2462:oimfsf>2.0.co;2.

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44

Taitel, Y., D. Barnea, and J. P. Brill. "Stratified three phase flow in pipes." International Journal of Multiphase Flow 21, no. 1 (January 1995): 53–60. http://dx.doi.org/10.1016/0301-9322(94)00058-r.

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45

Kuru, W. C., M. Sangalli, D. D. Uphold, and M. J. McCready. "Linear stability of stratified channel flow." International Journal of Multiphase Flow 21, no. 5 (September 1995): 733–53. http://dx.doi.org/10.1016/0301-9322(95)00015-p.

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Ponetti, G., M. Sammartino, and V. Sciacca. "Transitions in a stratified Kolmogorov flow." Ricerche di Matematica 66, no. 1 (June 22, 2016): 189–99. http://dx.doi.org/10.1007/s11587-016-0296-6.

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Denier, James P., and Jillian A. K. Stott. "Wave-Mean Flow Interactions in Thermally Stratified Poiseuille Flow." Studies in Applied Mathematics 102, no. 2 (February 1999): 121–36. http://dx.doi.org/10.1111/1467-9590.00106.

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Xu, X., C. Yi, and E. Kutter. "Stably stratified canopy flow in complex terrain." Atmospheric Chemistry and Physics Discussions 14, no. 21 (November 17, 2014): 28483–522. http://dx.doi.org/10.5194/acpd-14-28483-2014.

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Abstract. The characteristics of stably stratified canopy flows in complex terrain are investigated by employing the Renormalized Group (RNG) k-ε turbulence model. In this two-dimensional simulation, we imposed persistent constant heat flux at ground surface and linearly increasing cooling rate in the upper canopy layer, vertically varying dissipative force from canopy drag elements, buoyancy forcing induced from thermal stratification and the hill terrain. These strong boundary effects keep nonlinearity in the two-dimensional Navier–Stokes equations high enough to generate turbulent behavior. The fundamental characteristics of nighttime canopy flow over complex terrain measured by a few multi-tower advection experiments can be produced by this numerical simulation, such as: (1) unstable layer in the canopy, (2) super-stable layer associated with flow decoupling in deep canopy and near the top of canopy, (3) upward momentum transfer in canopy, and (4) large buoyancy suppression and weak shear production in strong stability.

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Mkhinini, Nadia, Thomas Dubos, and Philippe Drobinski. "On the nonlinear destabilization of stably stratified shear flow." Journal of Fluid Mechanics 731 (August 15, 2013): 443–60. http://dx.doi.org/10.1017/jfm.2013.374.

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AbstractA weakly nonlinear analysis of the bifurcation of the stratified Ekman boundary-layer flow near a critical bulk Richardson number is conducted and compared to a similar analysis of a continuously stratified parallel shear flow subject to Kelvin–Helmholtz instability. Previous work based on asymptotic expansions and predicting supercritical bifurcation at Prandtl number $Pr\lt 1$ and subcritical bifurcation at $Pr\gt 1$ for the parallel base flow is confirmed numerically and through fully nonlinear temporal simulations. When applied to the non-parallel Ekman flow, weakly nonlinear analysis and fully nonlinear calculations confirm that the nature of the bifurcation is dominantly controlled by $Pr$, although a sharp threshold at $Pr= 1$ is not found. In both flows the underlying physical mechanism is that the mean flow adjusts so as to induce a viscous (respectively diffusive) flux of momentum (respectively buoyancy) that balances the vertical flux induced by the developing instability, leading to a weakening of the mean shear and mean stratification. The competition between the former nonlinear feedback, which tends to be stabilizing, and the latter, which is destabilizing and strongly amplified as $Pr$ increases, determines the supercritical or subcritical character of the bifurcation. That essentially the same competition is at play in both the parallel shear flow and the Ekman flow suggests that the underlying mechanism is valid for complex, non-parallel stratified shear flows.

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MERRYFIELD, WILLIAM J., and GREG HOLLOWAY. "Eddy fluxes and topography in stratified quasi-geostrophic models." Journal of Fluid Mechanics 380 (February 10, 1999): 59–80. http://dx.doi.org/10.1017/s0022112098003656.

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Turbulent stratified flow over topography is studied using layered quasi-geostrophic models. Mean flows develop under random forcing, with lower-layer mean stream-function positively correlated with topography. When friction is sufficiently small, upper-layer mean flow is weaker than, but otherwise resembles, lower-layer mean flow. When lower-layer friction is larger, upper-layer mean flow reverses and can exceed lower-layer mean flow in strength. The mean interface between layers is domed over topographic elevations. Eddy fluxes of potential vorticity and layer thickness act in the sense of driving the flow toward higher entropy. Such behaviour contradicts usual eddy parameterizations, to which modifications are suggested.

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