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Journal articles on the topic 'Stratified boundary layer'

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Author: Grafiati

Published: 14 March 2023

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1

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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2

Chimonas, George. "Substructure layers and modes in the stratified boundary layer." Dynamics of Atmospheres and Oceans 27, no. 1-4 (January 1998): 187–200. http://dx.doi.org/10.1016/s0377-0265(97)00008-0.

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3

RAHM, LARS, and URBAN SVENSSON. "Dispersion in a stratified benthic boundary layer." Tellus A 41A, no. 2 (March 1989): 148–61. http://dx.doi.org/10.1111/j.1600-0870.1989.tb00372.x.

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4

Dzhaugashtin, K. E., and A. Zh Naimanova. "Wall boundary layer in a stratified medium." Journal of Engineering Physics and Thermophysics 72, no. 2 (March 1999): 273–80. http://dx.doi.org/10.1007/bf02699150.

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5

Rahm, Lars, and Urban Svensson. "Dispersion in a stratified benthic boundary layer." Tellus A: Dynamic Meteorology and Oceanography 41, no. 2 (January 1989): 148–61. http://dx.doi.org/10.3402/tellusa.v41i2.11827.

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6

McWilliams, James C., Edward Huckle, and Alexander F. Shchepetkin. "Buoyancy Effects in a Stratified Ekman Layer." Journal of Physical Oceanography 39, no. 10 (October 1, 2009): 2581–99. http://dx.doi.org/10.1175/2009jpo4130.1.

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Abstract The K-profile parameterization scheme is used to investigate the stratified Ekman layer in a “fair weather” regime of weak mean surface heating, persistently stable density stratification, diurnal solar cycle, and broadband fluctuations in the surface stress and buoyancy flux. In the case of steady forcing, the boundary layer depth typically scales as h ∼ u*/Nf, where u* is the friction velocity, f is the Coriolis frequency, and N is the interior buoyancy frequency that confirms empirical fits. The diurnal cycle of solar forcing acts to deepen the boundary layer because of net interior absorption and compensating surface cooling. Parameterized mesoscale and submesoscale eddy-induced restratification flux compresses the boundary layer. With transient forcing, the mean boundary layer profiles are altered; that is, rectification occurs with a variety of causes and manifestations, including changes in h and in the Ekman profile u(z). Overall, stress fluctuations tend to deepen the mean boundary layer, especially near the inertial frequency. Low- and high-frequency surface buoyancy-flux fluctuations have net shallowing and deepening effects, respectively. Eddy-induced interior profile fluctuations are relatively ineffective as a source of boundary layer rectification. Rectification effects in their various combinations lead to a range of mean velocity and buoyancy profiles. In particular, they lead to a “rotated” effective eddy-viscosity profile with misalignment between the mean turbulent stress and mean shear and to a “flattening” of the velocity profile with a larger vertical scale for the current veering than the speed decay; both of these effects from rectification are consistent with previous measurements.

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7

THOMAS, LEIF N., and PETER B. RHINES. "Nonlinear stratified spin-up." Journal of Fluid Mechanics 473 (December 10, 2002): 211–44. http://dx.doi.org/10.1017/s0022112002002367.

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Both a weakly nonlinear analytic theory and direct numerical simulation are used to document processes involved during the spin-up of a rotating stratified fluid driven by wind-stress forcing for time periods less than a homogeneous spin-up time. The strength of the wind forcing, characterized by the Rossby number ε, is small enough (i.e. ε[Lt ]1) that a regular perturbation expansion in ε can be performed yet large enough (more specifically, ε∝E1/2, where E is the Ekman number) that higher-order effects of vertical diffusion and horizontal advection of momentum/density are comparable in magnitude. Cases of strong stratification, where the Burger number S is equal to one, with zero heat flux at the upper boundary are considered. The Ekman transport calculated to O(ε) decreases with increasing absolute vorticity. In contrast to nonlinear barotropic spin-up, vortex stretching in the interior is predominantly linear, as vertical advection negates stretching of interior relative vorticity, yet is driven by Ekman pumping modified by nonlinearity. As vertical vorticity is generated during the spin-up of the fluid, the vertical vorticity feeds back on the Ekman pumping/suction, enhancing pumping and vortex squashing while reducing suction and vortex stretching. This feedback mechanism causes anticyclonic vorticity to grow more rapidly than cyclonic vorticity. Strict application of the zero-heat-flux boundary condition leads to the growth of a diffusive thermal boundary layer E−1/4 times thicker than the Ekman layer embedded within it. In the Ekman layer, vertical diffusion of heat balances horizontal advection of temperature by extracting heat from the thermal boundary layer beneath. The flux of heat extracted from the top of the thermal boundary layer by this mechanism is proportional to the product of the Ekman transport and the horizontal gradient of the temperature at the surface. The cooling caused by this heat flux generates density inversions and intensifies lateral density gradients where the wind-stress curl is negative. These thermal gradients make the potential vorticity strongly negative, conditioning the fluid for ensuing symmetric instability which greatly modifies the spin-up process.

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8

Hunt, J. C. R. "Diffusion in the Stably Stratified Atmospheric Boundary Layer." Journal of Climate and Applied Meteorology 24, no. 11 (November 1985): 1187–95. http://dx.doi.org/10.1175/1520-0450(1985)024<1187:ditssa>2.0.co;2.

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9

Kranenburg, C. "Boundary-induced entrainment in two-layer stratified flow." Journal of Geophysical Research 92, no. C5 (1987): 5417. http://dx.doi.org/10.1029/jc092ic05p05417.

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10

Scotti, Alberto, and Brian White. "The Mixing Efficiency of Stratified Turbulent Boundary Layers." Journal of Physical Oceanography 46, no. 10 (October 2016): 3181–91. http://dx.doi.org/10.1175/jpo-d-16-0095.1.

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AbstractThe mixing efficiency observed in stratified turbulent boundary layers is considered within the framework of the Monin–Obukhov similarity theory. It is shown that the efficiency within the layer increases with distance from the boundary. Near the boundary, the efficiency is proportional to the distance from the boundary scaled with the Monin–Obukhov length. Far from the boundary, the efficiency relaxes to a value that depends on the overall thickness of the layer relative to the Monin–Obukhov layer. This value approaches 1/6 when the thickness is larger than 1/2 of the Monin–Obukhov length. The same analysis shows that the buoyancy Reynolds number cannot be used to unequivocally predict the efficiency. The −1/2 scaling between the efficiency and buoyancy Reynolds number that has been observed in field measurements and experiments is shown to depend on an extra dimensional scale and thus is not universal.

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11

Daniels, P. G., and R. J. Gargaro. "Buoyancy effects in stably stratified horizontal boundary-layer flow." Journal of Fluid Mechanics 250 (May 1993): 233–51. http://dx.doi.org/10.1017/s0022112093001442.

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This paper describes numerical and asymptotic solutions of the steady two-dimensional boundary-layer equations governing buoyant flow on a horizontal, thermally insulated surface. The class of flows considered is one for which there is a uniform external stream at constant temperature but for which conditions upstream lead to a statically stable temperature field within the boundary layer. This has the effect of generating an adverse pressure gradient which, if sufficiently strong, causes the boundary-layer solution to terminate in a singularity. Results are obtained for a range of Prandtl numbers.

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12

Reznik, G. M. "Wave boundary layers in a stably-neutrally stratified ocean." Океанология 59, no. 2 (June 9, 2019): 201–7. http://dx.doi.org/10.31857/s0030-1574592201-207.

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The theory of wave boundary layers developed in [7], is generalized to the case of stably-neutrally stratified ocean consisting of upper homogeneous and lower stratified layers. In this configuration, in addition to the boundary layers near the ocean bottom and/or surface, a wave boundary layer develops near the interface between the layers in the lower stratified part of basin. Each the boundary layer is a narrow domain characterized by sharp, growing in time, vertical gradients of buoyancy and horizontal velocity. As in [7], the near interface boundary layer arises as a result of free linear evolution of rather general initial fields. An asymptotic solution describing the long-term evolution is presented and compared to exact solution; the asymptotic solution approximates the exact one fairly well even on not very large times.

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13

Christodoulou, George C., and George D. Economou. "BOUNDARY CONDITIONS IN FINITE ELEMENT MODELING OF STRATIFIED COASTAL CIRCULATION." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 190. http://dx.doi.org/10.9753/icce.v21.190.

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The effect of boundary conditions on numerical computations of stratified flow in coastal waters is examined. Clamped, free radiation and sponge layer conditions are implemented in a two-layer finite element model and the results of simple tests in a two-layer stratified basin are presented.

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14

Hewitt, Richard E., Peter W. Duck, Michael R. Foster, and Peter A. Davies. "Nonlinear Spin-Up of a Rotating Stratified Fluid: Theory." Journal of Fluids Engineering 120, no. 4 (December 1, 1998): 662–66. http://dx.doi.org/10.1115/1.2820719.

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We consider the boundary layer that forms on the wall of a rotating container of stratified fluid when altered from an initial state of rigid body rotation. The container is taken to have a simple axisymmetric form with sloping walls. The introduction of a non-normal component of buoyancy into the velocity boundary-layer is shown to have a considerable effect for certain geometries. We introduce a similarity-type solution and solve the resulting unsteady boundary-layer equations numerically for three distinct classes of container geometry. Computational and asymptotic results are presented for a number of parameter values. By mapping the parameter space we show that the system may evolve to either a steady state, a double-structured growing boundary-layer, or a finite-time breakdown depending on the container type, rotation change and stratification. In addition to extending the results of Duck et al. (1997) to a more general container shape, we present evidence of a new finite-time breakdown associated with higher Schmidt numbers.

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15

Einaudi, F., and J. J. Finnigan. "Wave-Turbulence Dynamics in the Stably Stratified Boundary Layer." Journal of the Atmospheric Sciences 50, no. 13 (July 1993): 1841–64. http://dx.doi.org/10.1175/1520-0469(1993)050<1841:wtdits>2.0.co;2.

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16

Andrén, Anders, and Chin-Hoh Moeng. "Single-Point Closures in a Neutrally Stratified Boundary Layer." Journal of the Atmospheric Sciences 50, no. 20 (October 1993): 3366–79. http://dx.doi.org/10.1175/1520-0469(1993)050<3366:spcian>2.0.co;2.

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17

Weng, W., L. Chan, P. A. Taylor, and D. Xu. "Modelling stably stratified boundary-layer flow over low hills." Quarterly Journal of the Royal Meteorological Society 123, no. 543 (October 1997): 1841–66. http://dx.doi.org/10.1002/qj.49712354304.

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18

Xie, Ming-liang, and Jian-zhong Lin. "Stability of Density Stratified Flow in the Boundary Layer." Journal of Hydrodynamics 18, no. 5 (October 2006): 505–11. http://dx.doi.org/10.1016/s1001-6058(06)60127-3.

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19

Lenschow, Donald H., Xing Sheng Li, Cui Juan Zhu, and B. Boba Stankov. "The stably stratified boundary layer over the great plains." Boundary-Layer Meteorology 42, no. 1-2 (January 1988): 95–121. http://dx.doi.org/10.1007/bf00119877.

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20

Lenschow, Donald H., Shi F. Zhang, and B. Boba Stankov. "The stably stratified boundary layer over the great plains." Boundary-Layer Meteorology 42, no. 1-2 (January 1988): 123–35. http://dx.doi.org/10.1007/bf00119878.

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21

De Baas, Anne F., and A. G. M. Driedonks. "Internal gravity waves in a stably stratified boundary layer." Boundary-Layer Meteorology 31, no. 3 (March 1985): 303–23. http://dx.doi.org/10.1007/bf00120898.

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22

Sorbjan, Zbigniew, and Ben B. Balsley. "Microstructure of Turbulence in the Stably Stratified Boundary Layer." Boundary-Layer Meteorology 129, no. 2 (September 19, 2008): 191–210. http://dx.doi.org/10.1007/s10546-008-9310-1.

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23

Lozovatsky, I., S. U. P. Jinadasa, H. J. S. Fernando, J. H. Lee, and Chang Su Hong. "The wall-layer dynamics in a weakly stratified tidal bottom boundary layer." Journal of Marine Research 73, no. 6 (November 1, 2015): 207–32. http://dx.doi.org/10.1357/002224015817391276.

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24

Pedlosky, Joseph. "The Response of a Weakly Stratified Layer to Buoyancy Forcing." Journal of Physical Oceanography 39, no. 4 (April 1, 2009): 1060–68. http://dx.doi.org/10.1175/2008jpo3996.1.

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Abstract The response of a weakly stratified layer of fluid to a surface cooling distribution is investigated with linear theory in an attempt to clarify recent numerical results concerning the sinking of cooled water in polar ocean boundary currents. A channel of fluid is forced at the surface by a cooling distribution that varies in the down-channel as well as the cross-channel directions. The resulting geostrophic flow in the central region of the channel impinges on its boundaries, and regions of strong downwelling are observed. For the parameters of the problem investigated, the downwelling occurs in a classical Stewartson layer but the forcing of the layer leads to an unusual relation with the interior flow, which is forced to satisfy the thermal condition on the boundary while the geostrophic normal flow in the interior is brought to rest in the boundary layer. As a consequence of the layer’s dynamics, the resulting long-channel flow exhibits a nonmonotonic approach to the interior flow, and the strongest vertical velocities are limited to the boundary layer whose scale is so small that numerical models resolve the region only with great difficulty. The analytical model presented here is able to reproduce key features of the previous nonlinear numerical calculations.

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25

Pearson, Brodie C., Alan L. M. Grant, Jeff A. Polton, and Stephen E. Belcher. "Langmuir Turbulence and Surface Heating in the Ocean Surface Boundary Layer." Journal of Physical Oceanography 45, no. 12 (December 2015): 2897–911. http://dx.doi.org/10.1175/jpo-d-15-0018.1.

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AbstractThis study uses large-eddy simulation to investigate the structure of the ocean surface boundary layer (OSBL) in the presence of Langmuir turbulence and stabilizing surface heat fluxes. The OSBL consists of a weakly stratified layer, despite a surface heat flux, above a stratified thermocline. The weakly stratified (mixed) layer is maintained by a combination of a turbulent heat flux produced by the wave-driven Stokes drift and downgradient turbulent diffusion. The scaling of turbulence statistics, such as dissipation and vertical velocity variance, is only affected by the surface heat flux through changes in the mixed layer depth. Diagnostic models are proposed for the equilibrium boundary layer and mixed layer depths in the presence of surface heating. The models are a function of the initial mixed layer depth before heating is imposed and the Langmuir stability length. In the presence of radiative heating, the models are extended to account for the depth profile of the heating.

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26

HEWITT, R. E., P. A. DAVIES, P. W. DUCK, and M. R. FOSTER. "Spin-up of stratified rotating flows at large Schmidt number: experiment and theory." Journal of Fluid Mechanics 389 (June 25, 1999): 169–207. http://dx.doi.org/10.1017/s0022112099004905.

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We consider the nonlinear spin-up/down of a rotating stratified fluid in a conical container. An analysis of axisymmetric similarity-type solutions to the relevant boundary-layer problem, Duck, Foster & Hewitt (1997), has revealed three types of behaviour for this geometry. In general, the boundary layer evolves to either a steady state, or a gradually thickening boundary layer, or a finite-time singularity depending on the Schmidt number, the ratio of initial to final rotation rates, and the relative importance of rotation and stratification.In this paper we emphasize the experimental aspects of an investigation into the initial readjustment process. We make comparisons with the previously presented boundary-layer theory, showing good quantitative agreement for positive changes in the rotation rate of the container (relative to the initial rotation sense). The boundary-layer analysis is shown to be less successful in predicting the flow evolution for nonlinear decelerations of the container. We discuss the qualitative features of the spin-down experiments, which, in general, are dominated by non-axisymmetric effects. The experiments are conducted using salt-stratified solutions, which have a Schmidt number of approximately 700.The latter sections of the paper present some stability results for the steady boundary-layer states. A high degree of non-uniqueness is possible for the system of steady governing equations; however the experimental results are repeatable and stability calculations suggest that ‘higher branch’ solutions are, in general, unstable. The eigenvalue spectrum arising from the linear stability analysis is shown to have both continuous and discrete components. Some analytical results concerning the continuous spectrum are presented in an appendix.A brief appendix completes the previous analysis of Duck, Foster & Hewitt (1997), presenting numerical evidence of a different form of finite-time singularity available for a more general boundary-layer problem.

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27

Banyte, D., D. A. Smeed, and M. Morales Maqueda. "The Weakly Stratified Bottom Boundary Layer of the Global Ocean." Journal of Geophysical Research: Oceans 123, no. 8 (August 2018): 5587–98. http://dx.doi.org/10.1029/2018jc013754.

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28

OHYA, YUJI, DAVID E. NEFF, and ROBERT N. MERONEY. "TURBULENCE STRUCTURE IN A STRATIFIED BOUNDARY LAYER UNDER STABLE CONDITIONS." Boundary-Layer Meteorology 83, no. 1 (April 1997): 139–62. http://dx.doi.org/10.1023/a:1000205523873.

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29

Saiki, Eileen M., Chin-Hoh Moeng, and Peter P. Sullivan. "Large-Eddy Simulation Of The Stably Stratified Planetary Boundary Layer." Boundary-Layer Meteorology 95, no. 1 (April 2000): 1–30. http://dx.doi.org/10.1023/a:1002428223156.

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30

Denier, James P., and Eunice W. Mureithi. "Weakly nonlinear wave motions in a thermally stratified boundary layer." Journal of Fluid Mechanics 315 (May 25, 1996): 293–316. http://dx.doi.org/10.1017/s0022112096002431.

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We consider weakly nonlinear wave motions in a thermally stratified boundary layer. Attention is focused on the upper branch of the neutral stability curve, corresponding to small wavelengths and large Reynolds number. In this limit the motion is governed by a first harmonic/mean flow interaction theory in which the wave-induced mean flow is of the same order of magnitude as the wave component of the flow. We show that the flow is governed by a system of three coupled partial differential equations which admit finite-amplitude periodic solutions bifurcating from the linear, neutral points.

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31

Schatzmann, M., J. Donat, S. Hendel, and G. Krishan. "Design of a low-cost stratified boundary-layer wind tunnel." Journal of Wind Engineering and Industrial Aerodynamics 54-55 (February 1995): 483–91. http://dx.doi.org/10.1016/0167-6105(94)00061-h.

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32

Michalcová, Vladimíra, Lenka Lausová, Iveta Skotnicová, and Stanislav Pospíšil. "Numerical and Experimental Models of the Thermally Stratified Boundary Layer." Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series. 16, no. 2 (December 1, 2016): 135–40. http://dx.doi.org/10.1515/tvsb-2016-0024.

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Abstract The article describes a change of selected turbulent variables in the surroundings of a flow around thermally loaded object. The problem is solved numerically in the software Ansys Fluent using a Transition SST model that is able to take into account the difference between high and low turbulence at the interface between the wake behind an obstacle and the free stream. The results are verified with experimental measurements in the wind tunnel.

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33

Li, Dong, Kun Luo, and Jianren Fan. "Buoyancy effects in an unstably stratified turbulent boundary layer flow." Physics of Fluids 29, no. 1 (January 2017): 015104. http://dx.doi.org/10.1063/1.4973667.

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34

Mason, P. J., and S. H. Derbyshire. "Large-Eddy Simulation of the stably-stratified atmospheric boundary layer." Boundary-Layer Meteorology 53, no. 1-2 (October 1990): 117–62. http://dx.doi.org/10.1007/bf00122467.

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35

Holleman, R. C., W. R. Geyer, and D. K. Ralston. "Stratified Turbulence and Mixing Efficiency in a Salt Wedge Estuary." Journal of Physical Oceanography 46, no. 6 (June 2016): 1769–83. http://dx.doi.org/10.1175/jpo-d-15-0193.1.

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AbstractHigh-resolution observations of velocity, salinity, and turbulence quantities were collected in a salt wedge estuary to quantify the efficiency of stratified mixing in a high-energy environment. During the ebb tide, a midwater column layer of strong shear and stratification developed, exhibiting near-critical gradient Richardson numbers and turbulent kinetic energy (TKE) dissipation rates greater than 10−4 m2 s−3, based on inertial subrange spectra. Collocated estimates of scalar variance dissipation from microconductivity sensors were used to estimate buoyancy flux and the flux Richardson number Rif. The majority of the samples were outside the boundary layer, based on the ratio of Ozmidov and boundary length scales, and had a mean Rif = 0.23 ± 0.01 (dissipation flux coefficient Γ = 0.30 ± 0.02) and a median gradient Richardson number Rig = 0.25. The boundary-influenced subset of the data had decreased efficiency, with Rif = 0.17 ± 0.02 (Γ = 0.20 ± 0.03) and median Rig = 0.16. The relationship between Rif and Rig was consistent with a turbulent Prandtl number of 1. Acoustic backscatter imagery revealed coherent braids in the mixing layer during the early ebb and a transition to more homogeneous turbulence in the midebb. A temporal trend in efficiency was also visible, with higher efficiency in the early ebb and lower efficiency in the late ebb when the bottom boundary layer had greater influence on the flow. These findings show that mixing efficiency of turbulence in a continuously forced, energetic, free shear layer can be significantly greater than the broadly cited upper bound from Osborn of 0.15–0.17.

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36

Brink, K. H., and S. J. Lentz. "Buoyancy Arrest and Bottom Ekman Transport. Part II: Oscillating Flow." Journal of Physical Oceanography 40, no. 4 (April 1, 2010): 636–55. http://dx.doi.org/10.1175/2009jpo4267.1.

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Abstract The effects of a sloping bottom and stratification on a turbulent bottom boundary layer are investigated for cases where the interior flow oscillates monochromatically with frequency ω. At higher frequencies, or small slope Burger numbers s = αN/f (where α is the bottom slope, N is the interior buoyancy frequency, and f is the Coriolis parameter), the bottom boundary layer is well mixed and the bottom stress is nearly what it would be over a flat bottom. For lower frequencies, or larger slope Burger number, the bottom boundary layer consists of a thick, weakly stratified outer layer and a thinner, more strongly stratified inner layer. Approximate expressions are derived for the different boundary layer thicknesses as functions of s and σ = ω/f. Further, buoyancy arrest causes the amplitude of the fluctuating bottom stress to decrease with decreasing σ (the s dependence, although important, is more complicated). For typical oceanic parameters, arrest is unimportant for fluctuation periods shorter than a few days. Substantial positive (toward the right when looking toward deeper water in the Northern Hemisphere) time-mean flows develop within the well-mixed boundary layer, and negative mean flows exist in the weakly stratified outer boundary layer for lower frequencies and larger s. If the interior flow is realistically broad band in frequency, the numerical model predicts stress reduction over all frequencies because of the nonlinearity associated with a quadratic bottom stress. It appears that the present one-dimensional model is reliable only for time scales less than the advective time scale that governs interior stratification.

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37

Hewitt, Richard E., Peter A. Davies, Peter W. Duck, Michael R. Foster, and Fraser W. Smith. "Nonlinear Spin-Up of a Rotating Stratified Fluid: Experimental Method and Preliminary Results." Journal of Fluids Engineering 120, no. 4 (December 1, 1998): 667–71. http://dx.doi.org/10.1115/1.2820720.

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We consider the nonlinear spin-up of a rotating stratified fluid in a conical container. An analysis of similarity-type solutions to the relevant boundary-layer problem (Duck et al, 1997) has revealed three types of behavior for this geometry. In general, the boundary-layer evolves to either a steady state, a growing boundary-layer, or a finite-time singularity depending on the initial to final rotation rate ratio, and a “modified Burger number.” We emphasize the experimental aspects of our continuing spin-up investigations and make some preliminary comparisons with the boundary-layer theory, showing good agreement. The experimental data presented is obtained through particle tracking velocimetry. We briefly discuss the qualitative features of the spin-down experiments which, in general, are dominated by nonaxisymmetric effects. The experiments are performed using a conical container filled with a linearly stratified fluid, the generation of which is nontrivial. We present a general method for creating a linear density profile in containers with sloping boundaries.

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38

LEVY, M. A., and H. J. S. FERNANDO. "Turbulent thermal convection in a rotating stratified fluid." Journal of Fluid Mechanics 467 (September 24, 2002): 19–40. http://dx.doi.org/10.1017/s0022112002001350.

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Turbulent convection induced by heating the bottom boundary of a horizontally homogeneous, linearly (temperature) stratified, rotating fluid layer is studied using a series of laboratory experiments. It is shown that the growth of the convective mixed layer is dynamically affected by background rotation (or Coriolis forces) when the parameter R = (h2Ω3/q0)2/3 exceeds a critical value of Rc ≈ 275. Here h is the depth of the convective layer, Ω is the rate of rotation, and q0 is the buoyancy flux at the bottom boundary. At larger R, the buoyancy gradient in the mixed layer appears to scale as (db/dz)ml = CΩ2, where C ≈ 0.02. Conversely, when R < Rc, the buoyancy gradient is independent of Ω and approaches that of the non-rotating case. The entrainment velocity, ue, for R > Rc was found to be dependent on Ω according to E = [Ri(1 + CΩ2/N2)]−1, where E is the entrainment coefficient based on the convective velocity w∗ = (q0h)1/3, E = ue/w∗, Ri is the Richardson number Ri = N2h2/w2∗, and N is the buoyancy frequency of the overlying stratified layer. The results indicate that entrainment in this case is dominated by non-penetrative convection, although the convective plumes can penetrate the interface in the form of lenticular protrusions.

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39

Foster, M. R. "Rotating stratified flow past a steep-sided obstacle: incipient separation." Journal of Fluid Mechanics 206 (September 1989): 47–73. http://dx.doi.org/10.1017/s0022112089002223.

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Many of the most interesting phenomena observed to occur in the flow of rotating and stratified fluids past obstacles, for example eddy shedding and wake unsteadiness, are due to separation of the boundary layer on the obstacle or its Taylor column. If the Rossby number of the flow lies between E½ and E (E is the Ekman number) and the Burger number is small, the structure of a viscous shear layer of width E⅙ on the circumscribing cylinder of an axisymmetric obstacle controls the inviscid flow. The surface boundary layer is not an Ekman layer, but a Prandtl layer, even at small Rossby numbers. As the slope of the obstacle at its base increases, the nature of the inviscid motion is altered substantially, in the rotation-dominated regime. We show that, for sufficiently large slopes, the flow develops a small region of non-uniqueness external to the column, simultaneously with the separation of the narrow band of fluid flowing round the base of the object.

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40

GAYEN, BISHAKHDATTA, SUTANU SARKAR, and JOHN R. TAYLOR. "Large eddy simulation of a stratified boundary layer under an oscillatory current." Journal of Fluid Mechanics 643 (December 17, 2009): 233–66. http://dx.doi.org/10.1017/s002211200999200x.

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A numerical study based on large eddy simulation is performed to investigate a bottom boundary layer under an oscillating tidal current. The focus is on the boundary layer response to an external stratification. The thermal field shows a mixed layer that is separated from the external stratified fluid by a thermocline. The mixed layer grows slowly in time with an oscillatory modulation by the tidal flow. Stratification strongly affects the mean velocity profiles, boundary layer thickness and turbulence levels in the outer region although the effect on the near-bottom unstratified fluid is relatively mild. The turbulence is asymmetric between the accelerating and decelerating stages. The asymmetry is more pronounced with increasing stratification. There is an overshoot of the mean velocity in the outer layer; this jet is linked to the phase asymmetry of the Reynolds shear stress gradient by using the simulation data to examine the mean momentum equation. Depending on the height above the bottom, there is a lag of the maximum turbulent kinetic energy, dissipation and production with respect to the peak external velocity and the value of the lag is found to be influenced by the stratification. Flow instabilities and turbulence in the bottom boundary layer excite internal gravity waves that propagate away into the ambient. Unlike the steady case, the phase lines of the internal waves change direction during the tidal cycle and also from near to far field. The frequency spectrum of the propagating wave field is analysed and found to span a narrow band of frequencies clustered around 45°.

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41

Holmes, R. M., and Trevor J. McDougall. "Diapycnal Transport near a Sloping Bottom Boundary." Journal of Physical Oceanography 50, no. 11 (November 1, 2020): 3253–66. http://dx.doi.org/10.1175/jpo-d-20-0066.1.

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AbstractThe diapycnal motion in the stratified ocean near a sloping bottom boundary is studied using analytical solutions from one-dimensional boundary layer theory. Bottom-intensification of the diapycnal mixing intensity ensures that in the stratified mixing layer (SML), where isopycnals are relatively flat, the diapycnal motion is downward toward denser fluid. In contrast, convergence of the diffusive buoyancy flux near the seafloor drives diapycnal upwelling in what we define as the bottom boundary layer (BBL). Much of the one-dimensional BBL is characterized by a stratification only slightly reduced from that in the SML because the maximum in the buoyancy flux at the top of the BBL, where the diapycnal velocity changes sign, must occur in well-stratified fluid. The diapycnal upwelling in the BBL is determined by variations not only in the magnitude of the buoyancy gradient but also in the curvature of isopycnals. The net diapycnal upwelling is concentrated in the bottom half of the BBL where the magnitude of the buoyancy gradient changes most rapidly. The curvature effect drives upwelling near the seafloor that only makes a significant contribution to the net upwelling for steep slopes. The structure of the diapycnal velocity in this stratified BBL differs from the case of a turbulent well-mixed BBL that has been assumed in some recent theoretical studies on bottom-intensified mixing. This work therefore extends recent theories in a way that should be more applicable to abyssal ocean observations where well-mixed BBLs are not common.

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42

Gurski, K. F., and R. L. Pego. "Normal modes for a stratified viscous fluid layer." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 3 (June 2002): 611–25. http://dx.doi.org/10.1017/s0308210500001803.

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We consider internal gravity waves in a stratified fluid layer with rigid horizontal boundaries and periodic boundary conditions on the sides at constant temperature with a small constant viscosity, modelled using the incompressible Navier-Stokes equations. Using operator-theoretic methods to study the damping rates of internal waves we prove there are non-oscillatory wave modes with arbitrarily small damping rates. We provide an asymptotic approximation for these non-oscillatory modes. Additionally, we find that the eigenvalues for damped oscillations are in an explicitly describable half-ring.

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43

Candelier, Julien, Stéphane Le Dizès, and Christophe Millet. "Inviscid instability of a stably stratified compressible boundary layer on an inclined surface." Journal of Fluid Mechanics 694 (February 2, 2012): 524–39. http://dx.doi.org/10.1017/jfm.2012.7.

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AbstractThe three-dimensional stability of an inflection-free boundary layer flow of length scale$L$and maximum velocity${U}_{0} $in a stably stratified and compressible fluid of constant Brunt–Väisälä frequency$N$, sound speed${c}_{s} $and stratification length$H$is examined in an inviscid framework. The shear plane of the boundary layer is assumed to be inclined at an angle$\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)$. When non-Boussinesq and compressible effects are negligible ($L/ H\ll 1$and${U}_{0} / {c}_{s} \ll 1$), the boundary layer flow is found to be unstable for any$F$as soon as$\theta \not = 0$. Compressible and non-Boussinesq effects are considered in the strongly stratified limit: they are shown to have no influence on the stability properties of an inclined boundary layer (when$F/ \sin \theta \ll 1$). In this limit, the instability is associated with the emission of internal-acoustic waves.

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JAVAM, A., and S. W. ARMFIELD. "Stability and transition of stratified natural convection flow in open cavities." Journal of Fluid Mechanics 445 (October 16, 2001): 285–303. http://dx.doi.org/10.1017/s0022112001005614.

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In this study we have investigated the behaviour of natural convection flow in open cavities, with both homogeneous and thermally stratified ambient, using direct numerical simulation. The cavity is insulated at the top and bottom boundaries, heated from the left-hand side boundary and open at the right-hand side. A wide range of Rayleigh numbers were considered (5 × 106 to 1 × 1010) with Pr = 0.7 for all cases. It was found that the homogeneous flow is steady for all Rayleigh numbers considered, whereas the stratified flow with a high enough Rayleigh number exhibits low- and high-frequency signals of the same type as are observed for closed cavity flow. The thermal boundary layer is examined in detail and it is shown that both low- and high-frequency signals are located predominantly in the upper region of the heated plate and are associated with a reverse-S-flow formed by the boundary layer exit jet interacting with the stratified interior. The low-frequency signal is associated with standing waves in the boundary layer, whereas the high-frequency signal is associated with travelling waves. The high-frequency signal occurs initially as a harmonic of the base low-frequency signal. A corner jet with the same inlet characteristics as the natural convection boundary layer exit jet is also examined and shown to exhibit a similar bifurcation, but with the low frequency always dominant. It is suggested that the generation mechanism for the bifurcation of the natural convection flow is the same as that for the corner jet.

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45

Brink, K. H., and S. J. Lentz. "Buoyancy Arrest and Bottom Ekman Transport. Part I: Steady Flow." Journal of Physical Oceanography 40, no. 4 (April 1, 2010): 621–35. http://dx.doi.org/10.1175/2009jpo4266.1.

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Abstract It is well known that along-isobath flow above a sloping bottom gives rise to cross-isobath Ekman transport and therefore sets up horizontal density gradients if the ocean is stratified. These transports in turn eventually bring the along-isobath bottom velocity, hence bottom stress, to rest (“buoyancy arrest”) simply by means of the thermal wind shear. This problem is revisited here. A modified expression for Ekman transport is rationalized, and general expressions for buoyancy arrest time scales are presented. Theory and numerical calculations are used to define a new formula for boundary layer thickness for the case of downslope Ekman transport, where a thick, weakly stratified arrested boundary layer results. For upslope Ekman transport, where advection leads to enhanced stability, expressions are derived for both the weakly sloping (in the sense of slope Burger number s = αN/f, where α is the bottom slope, N is the interior buoyancy frequency, and f is the Coriolis parameter) case where a capped boundary layer evolves and the larger s case where a nearly linearly stratified boundary layer joins smoothly to the interior density profile. Consistent estimates for the buoyancy arrest time scale are found for each case.

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Tjernström, Michael. "Is There a Diurnal Cycle in the Summer Cloud-Capped Arctic Boundary Layer?" Journal of the Atmospheric Sciences 64, no. 11 (November 1, 2007): 3970–86. http://dx.doi.org/10.1175/2007jas2257.1.

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Abstract Data from the Arctic Ocean Experiment 2001 (AOE-2001) are used to study the vertical structure and diurnal cycle of the summertime central Arctic cloud-capped boundary layer. Mean conditions show a shallow stratocumulus-capped boundary layer, with a nearly moist neutrally stratified cloud layer, although cloud tops often penetrated into the stable inversion. The subcloud layer was more often stably stratified. Conditions near the surface were relatively steady, with a strong control on temperature and moisture by the melting ice surface. A statistically significant diurnal cycle was found in many parameters, although weak in near-surface temperature and moisture. Near-surface wind speed and direction and friction velocity had a pronounced cycle, while turbulent kinetic energy showed no significant diurnal variability. The cloud layer had the most pronounced diurnal variability, with lowest cloud-base height midday followed by enhanced drizzle and temporarily higher cloud-top heights in the afternoon. This is opposite to the cycle found in midlatitude or subtropical marine stratocumulus. The cloud layer was warmest (coolest) and more (less) stably stratified midafternoon (midmorning), coinciding with the coolest (warmest) but least (most) stably stratified capping inversion layer. It is speculated that drizzle is important in regulating the diurnal variability in the cloud layer, facilitated by enhanced midday mixing due to a differential diurnal variability in cloud and subcloud layer stability. Changing the Arctic aerosol climate could change these clouds to a more typical “marine stratocumulus structure,” which could act as a negative feedback on Arctic warming.

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47

Frehlich, Rod, Yannick Meillier, and Michael L. Jensen. "Measurements of Boundary Layer Profiles with In Situ Sensors and Doppler Lidar." Journal of Atmospheric and Oceanic Technology 25, no. 8 (August 1, 2008): 1328–40. http://dx.doi.org/10.1175/2007jtecha963.1.

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Abstract A new in situ measurement system and lidar processing algorithms were developed for improved measurements of boundary layer profiles. The first comparisons of simultaneous Doppler lidar–derived profiles of the key turbulence statistics of the two orthogonal horizontal velocity components (longitudinal and transverse) are presented. The instrument requirements for accurate observations of stably stratified turbulence were determined. A region of stably stratified low turbulence with constant gradients of temperature and velocity was observed above the nocturnal boundary layer using high-rate sensors. The important turbulence parameters were estimated, and turbulence spectra were consistent with new theoretical descriptions of stratified turbulence. The impact of removing the larger-scale velocity features in Doppler lidar estimates of turbulent velocity variance and length scales was investigated. The Doppler lidar–derived estimates of energy dissipation rate ε were found to be insensitive to spatial filtering of the large-scale atmospheric processes. The in situ and lidar-derived profiles were compared for the stable boundary layer in a suburban environment.

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48

Park, Young-Gyu, J. A. Whitehead, and Anand Gnanadeskian. "Turbulent mixing in stratified fluids: layer formation and energetics." Journal of Fluid Mechanics 279 (November 25, 1994): 279–311. http://dx.doi.org/10.1017/s0022112094003915.

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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.

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Lott, François, Bruno Deremble, and Clément Soufflet. "Mountain Waves Produced by a Stratified Boundary Layer Flow. Part I: Hydrostatic Case." Journal of the Atmospheric Sciences 77, no. 5 (April 23, 2020): 1683–97. http://dx.doi.org/10.1175/jas-d-19-0257.1.

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Abstract A hydrostatic theory for mountain waves with a boundary layer of constant eddy viscosity is presented. It predicts that dissipation impacts the dynamics over an inner layer whose depth is controlled by the inner-layer scale δ of viscous critical-level theory. The theory applies when the mountain height is smaller or near δ and is validated with a fully nonlinear model. In this case the pressure drag and the wave Reynolds stress can be predicted by inviscid theory, if one takes for the incident wind its value around the inner-layer scale. In contrast with the inviscid theory and for small mountains the wave drag is compensated by an acceleration of the flow in the inner layer rather than of the solid earth. Still for small mountains and when stability increases, the emitted waves have smaller vertical scale and are more dissipated when traveling through the inner layer: a fraction of the wave drag is deposited around the top of the inner layer before reaching the outer regions. When the mountain height becomes comparable to the inner-layer scale, nonseparated upstream blocking and downslope winds develop. Theory and the model show that (i) the downslope winds penetrate well into the inner layer and (ii) upstream blocking and downslope winds are favored when the static stability is strong and (iii) are not associated with upper-level wave breaking.

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50

Ali, N., G. Cortina, N. Hamilton, M. Calaf, and R. B. Cal. "Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition." Journal of Fluid Mechanics 828 (August 31, 2017): 175–95. http://dx.doi.org/10.1017/jfm.2017.492.

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A large eddy simulation framework is used to explore the structure of the turbulent flow in a thermally stratified wind turbine array boundary layer. The flow field is driven by a constant geostrophic wind with time-varying surface boundary conditions obtained from a selected period of the CASES-99 field experiment. Proper orthogonal decomposition is used to extract coherent structures of the turbulent flow under the considered thermal stratification regimes. The flow structure is discussed in the context of three-dimensional representations of key modes, which demonstrate features ranging in size from the wind turbine wakes to the atmospheric boundary layer. Results demonstrate that structures related to the atmospheric boundary layer flow dominate over those introduced by the wind farm for the unstable and neutrally stratified regimes; large structures in atmospheric turbulence are beneficial for the wake recovery, and consequently the presence of the turbulent wind turbine wakes is diminished. Contrarily, the flow in the stably stratified case is fully dominated by the presence of the turbines and highly influenced by the Coriolis force. A comparative analysis of the test cases indicates that during the stable regime, higher-order modes contribute less to the overall character of the flow. Under neutral and unstable stratification, important turbulence dynamics are distributed over a larger range of basis functions. The influence of the wind turbines on the structure of the atmospheric boundary layer is mainly quantified via the turbulence kinetic energy of the first ten modes. Linking the new insights into structure of the wind turbine/atmospheric boundary layer and their interaction addressed here will benefit the formulation of new simplified models for commercial application.

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