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1

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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2

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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3

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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4

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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5

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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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

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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16

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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17

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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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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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31

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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32

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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33

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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34

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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35

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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36

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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37

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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38

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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39

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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40

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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41

Imberger, J., and G. N. Ivey. "Boundary mixing in stratified reservoirs." Journal of Fluid Mechanics 248 (March 1993): 477–91. http://dx.doi.org/10.1017/s0022112093000850.

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We consider the steady flow driven by turbulent mixing in a benthic boundary layer along a sloping boundary in the general case of a non-uniform background density gradient. The velocity and density fields are decomposed into barotropic and baroclinic components, and a solution is obtained by taking an expansion in the small parameter A, the aspect ratio of the boundary layer defined as the thickness divided by the alongslope length. The flow in the boundary layer is governed by a balance between alongslope baroclinic and barotropic density fluxes. A number of flow regimes can exist, and we show that in the regimes relevant to lakes and reservoirs, the barotropic flow is divergent and drives an exchange flow between the boundary layer and the interior. This leads to changes in the interior density gradient which are significant when compared to field observations.
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42

Takagi, Norimasa, Toshifumi Noma, Masaaki Sakuta, Junpei Nakamura, and Hitoshi Imamura. "Flow visualization around an artificial upwelling structure in stratified flow." Journal of the Visualization Society of Japan 10, no. 1Supplement (1990): 115–18. http://dx.doi.org/10.3154/jvs.10.1supplement_115.

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43

Louay Abd Al-Azez Mahdi, Hasanain Adnan Abdul Wahhab, and Miqdam Tariq Chaichan. "The Change of Flow Pattern from Stratified to Stratified-Wavy for Condensation in Wire on Tube Heat Exchangers." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 117, no. 2 (June 1, 2024): 105–15. http://dx.doi.org/10.37934/arfmts.117.2.105115.

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Flow patterns inside wire-on-tube condensers with different refrigerant mass flow rates were studied in a theoretical study. In this study, tubes with diameters of 3.25 mm (3/16"), 4.83 mm (1/4") and 6.29 mm (5/16") were used. R-134a and R-600a cooling fluids were used at condensing temperatures of 54.4°C, 45°C, and 35°C. The results of this study were obtained using Equal Equation Solver (EES) software. The proposed model was able to predict the type of refrigerant flow pattern based on the limitations reported in previous studies. It was possible to distinguish four kinds of flow patterns: laminar, wavy laminar, plugged, and spiral. The first variation in flow pattern from laminar to wavy laminar flow found between 0.8 and 0.39, and a second variation in flow pattern found from wavy laminar flow to plug or slug flow between 0.15 and 0.05. For the refrigerant conditions, the condensation temperature did not affect the flow pattern. When using R-134a, the inner tube diameter had no effect on the flow pattern. Change occurs with R-600a as inner diameter was increased.
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44

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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45

Spalding, Dudley Brian. "NUMERICAL BENCHMARK TEST NO. 2.7: STRATIFIED FLOW." Multiphase Science and Technology 3, no. 1-4 (1987): 483–84. http://dx.doi.org/10.1615/multscientechn.v3.i1-4.340.

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46

Hwang, Jong-Yeon, Kyung-Soo Yang, and Dong-Woo Kim. "Numerical Simulation of Stratified Taylor-Couette Flow." Transactions of the Korean Society of Mechanical Engineers B 30, no. 7 (July 1, 2006): 630–37. http://dx.doi.org/10.3795/ksme-b.2006.30.7.630.

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47

Ali, Imad Taher, Imran Afgan, and Ilyas Khurshid. "Stratified Two-Phase Turbulent Pipe Flow Simulations." International Journal on Advanced Science, Engineering and Information Technology 12, no. 4 (August 6, 2022): 1301. http://dx.doi.org/10.18517/ijaseit.12.4.16361.

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48

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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49

Zhang, Bing, Jing Lv, Peng Huo, and Shao Xiong Zhang. "Application of EFDC to Density Stratified Flow." Applied Mechanics and Materials 256-259 (December 2012): 2486–89. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.2486.

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Environmental Fluid Dynamics Code (EFDC) was developed by Hamrick at Virginia Institute of Marine Science for estuarine and coastal applications. EFDC is a general-purpose modeling package for simulating three-dimensional flow, transport, and biogeochemical processes in surface water systems such as rivers, lakes, reservoirs, estuaries, wetlands and coastal regions. Use the 3-D numerical model EFDC simulated the density stratified flow in a slut. Compared the simulation and experimental data, the results showed that EFDC could accurately simulated the density stratified flow.
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50

Stetsyuk, I. "Calculation of stratified flow behind underwater obstacle." Transactions of the Krylov State Research Centre 3, no. 393 (August 25, 2020): 97–102. http://dx.doi.org/10.24937/2542-2324-2020-3-393-97-102.

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