We conduct a parametric study of diapycnal mixing using one-dimensional-turbulence (ODT) simulations. Homogeneous sheared stratified turbulence is considered. ODT simulations reproduce the intermediate and energetic regimes of mixing, in agreement with previous work, but do not capture important physics of the diffusive regime. ODT indicates for the intermediate regime, and for the energetic regime and limit of near-zero stratification. Here is the turbulent diffusivity for mass, the dissipation rate, N the buoyancy frequency, and h the computational domain height, where h is relevant mainly in simulations with jump-periodic vertical boundary conditions. These scaling relationships suggest that is independent of the molecular diffusivity. ODT results for a wide range of parameters show that cannot be parametrized solely with the turbulent intensity parameter , in contrast with the previous studies, but it is well predicted by correlations using the Ellison length scale.
REFERENCES
1.
W. G.
Large
, J. C.
McWilliams
, and S. C.
Doney
, “Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization
,” Rev. Geophys.
32
, 363
, doi:10.1029/94RG01872 (1994
).2.
S. A.
Thorpe
, “Recent developments in the study of ocean turbulence
,” Annu. Rev. Earth Planet Sci.
32
, 91
(2004
).3.
J. S.
Turner
, Buoyancy Effects in Fluids
(Cambridge University Press
Cambridge
, 1979
).4.
H. J. S.
Fernando
, “Turbulent mixing in stratified fluids
,” Annu. Rev. Fluid Mech.
23
, 455
(1991
).5.
G. N.
Ivey
, K. B.
Winters
, and J. R.
Koseff
, “Density stratification, turbulence, but how much mixing?
,” Annu. Rev. Fluid Mech.
40
, 169
(2008
).6.
C.
Wunsch
and R.
Ferrari
, “Vertical mixing, energy, and the general circulation of the oceans
,” Annu. Rev. Fluid Mech.
36
, 281
(2004
).7.
M. E.
Barry
, G. N.
Ivey
, K. B.
Winters
, and J.
Imberger
, “Measurements of diapycnal diffusivities in stratified fluids
,” J. Fluid Mech.
442
, 267
(2001
).8.
C. R.
Rehmann
and J. R.
Koseff
, “Mean potential energy change in stratified grid turbulence
,” Dyn. Atmos. Oceans
37
, 271
(2004
).9.
L. H.
Shih
, J. R.
Koseff
, G. N.
Ivey
, and J. H.
Ferziger
, “Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations
,” J. Fluid Mech.
525
, 193
(2005
).10.
T. R.
Osborn
, “Estimates of the local rate of vertical diffusion from dissipation measurements
,” J. Phys. Oceanogr.
10
, 83
(1980
).11.
D. D.
Stretch
and S. K.
Venayagamoorthy
, “Diapycnal diffusivities in homogeneous stratified turbulence
,” Geophys. Res. Lett.
37
, L02602
, doi:10.1029/2009GL041514 (2010
).12.
S. B.
Pope
, Turbulent Flows
(Cambridge University Press
Cambridge
, 2000
).13.
S. K.
Venayagamoorthy
and D. D.
Stretch
, “Lagrangian mixing in decaying stably stratified turbulence
,” J. Fluid Mech.
564
, 197
(2006
).14.
S. K.
Venayagamoorthy
and D. D.
Stretch
, “On the turbulent Prandtl number in homogeneous stably stratified turbulence
,” J. Fluid Mech.
644
, 359
(2010
).15.
T.
Gerz
, U.
Schumann
, and S. E.
Elghobashi
, “Direct numerical simulation of stratified homogeneous turbulent shear flows
,” J. Fluid Mech.
200
, 563
(1989
).16.
S. E.
Holt
, J. R.
Koseff
, and J. H.
Ferziger
, “A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence
,” J. Fluid Mech.
237
, 499
(1992
).17.
L. H.
Shih
, J. R.
Koseff
, J. H.
Ferziger
, and C. R.
Rehmann
, “Scaling and parameterization of stratified homogeneous turbulent shear flow
,” J. Fluid Mech.
412
, 1
(2000
).18.
A. R.
Kerstein
, “One-dimensional turbulence: Model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows
,” J. Fluid Mech.
392
, 277
(1999a
).19.
A. R.
Kerstein
and S.
Wunsch
, “Simulation of a stably stratified atmospheric boundary layer using one-dimensional turbulence
,” Boundary-Layer Meteorol.
118
, 325
(2006
).20.
E. D.
Gonzalez
-Juez, A. R.
Kerstein
, and D. O.
Lignell
, “Fluxes across double-diffusive interfaces: A one-dimensional-turbulence study
,” J. Fluid Mech.
(to be published).21.
A. R.
Kerstein
, “One-dimensional turbulence: Part 2. Staircases in double-diffusive convection
,” Dyn. Atmos. Oceans
30
, 25
(1999b).22.
T. D.
Dreeben
and A. R.
Kerstein
, “Simulation of vertical slot convection using one-dimensional turbulence
,” Int. J. Heat Mass Transfer
43
, 3823
(2000
).23.
A. R.
Kerstein
, W. T.
Ashurst
, S.
Wunsch
, and V.
Nilsen
, “One-dimensional turbulence: Vector formulation and application to free shear flows
,” J. Fluid Mech.
447
, 85
(2001
).24.
T.
Echekki
, A. R.
Kerstein
, T. D.
Dreeben
, and J. Y.
Chen
, “One-dimensional turbulence simulation of turbulent jet diffusion flames: Model formulation and illustrative applications
,” Combust. Flame
125
, 1083
(2001
).25.
S.
Wunsch
and A. R.
Kerstein
, “A model for layer formation in stably stratified turbulence
,” Phys. Fluids
13
, 702
(2001
).26.
S.
Wunsch
and A. R.
Kerstein
, “A stochastic model for high-Rayleigh-number convection
,” J. Fluid Mech.
528
, 173
(2005
).27.
W. T.
Ashurst
and A. R.
Kerstein
, “One-dimensional turbulence: Variable-density formulation and application to mixing layers
,” Phys. Fluids
17
, 025107
(2005
).28.
S.
Wunsch
, “Scaling laws for layer formation in stably-stratified turbulent flows
,” Phys. Fluids
12
, 672
(2000
).29.
K. B.
Winters
, P. N.
Lombard
, J. J.
Riley
, and E. A.
D
’Asaro, “Available potential energy and mixing in density-stratified fluids
,” J. Fluid Mech.
289
, 115
(1995
).30.
K. B.
Winters
and E. A.
D’Asaro
, “Diascalar flux and the rate of fluid mixing
,” J. Fluid Mech.
317
, 179
(1996
).31.
J. W.
Miles
, “On the stability of heterogeneous shear flows
,” J. Fluid Mech.
10
, 496
(1961
).32.
L. N.
Howard
, “Note on a paper of John W. Miles
,” J. Fluid Mech.
10
, 509
(1961
).33.
R. J.
McDermott
, “Toward one-dimensional turbulence subgrid closure for large-eddy simulation
,” Ph.D. thesis, University of Utah
, 2005
.34.
A. M.
Law
and W. D.
Kelton
, Simulation Modeling and Analysis
(McGraw-Hill
, New York
, 2000
).35.
J. J.
Rohr
, E. C.
Itsweire
, K. N.
Helland
, and C. W. V.
Atta
, “Growth and decay of turbulence in a stably stratified shear flow
,” J. Fluid Mech.
195
, 77
(1988
).36.
L. H.
Shih
, “Numerical simulations of stably stratified turbulent flow
,” Ph.D. thesis, Stanford University
, 2003
.37.
J. J.
Riley
and M. P.
Lelong
, “Fluid motions in the presence of strong stable stratification
,” Annu. Rev. Fluid Mech.
32
, 613
(2000
).38.
W. R.
Peltier
and C. P.
Caulfield
, “Mixing efficiency in stratified shear flows
,” Annu. Rev. Fluid Mech.
35
, 135
(2003
).39.
G. N.
Ivey
and J.
Imberger
, “On the nature of turbulence in a stratified fluid. Part I: The energetics of mixing
,” J. Phys. Oceanogr.
21
, 650
(1991
).40.
T. H.
Ellison
, “Turbulent transport of heat and momentum from an infinite rough plane
,” J. Fluid Mech.
2
, 456
(1957
).41.
H.
Tennekes
and J. L.
Lumley
, A First Course in Turbulence
(MIT Cambridge
, MA
, 1972
).42.
J.
Weinstock
, “Vertical turbulent diffusion in a stably stratified fluid
,” J. Atmos. Sci.
35
, 1022
(1978
).43.
J.
Weinstock
, “Vertical diffusivity and overturning length in stably stratified turbulence
,” J. Geophys. Res.
97
, 12653
, doi:10.1029/92JC01099 (1992
).44.
G. T.
Csanady
, “Turbulent diffusion in a stratified fluid
,” J. Atmos. Sci.
21
, 439
(1964
).45.
H. J.
Pearson
, J. S.
Puttock
, and J. C. R.
Hunt
, “A statistical model of fluid-element motions and vertical diffusion in a homogeneous stratified turbulent flow
,” J. Fluid Mech.
129
, 219
(1983
).46.
W. J.
Merryfield
, G.
Holloway
, and A. E.
Gargett
, “Differential vertical transport of heat and salt by weak stratified turbulence
,” Geophys. Res. Lett.
25
, 2773
, doi:10.1029/98GL02210 (1998
).47.
P. R.
Jackson
and C. R.
Rehmann
, “Theory for differential transport of scalars in sheared stratified turbulence
,” J. Fluid Mech.
621
, 1
(2009
).48.
A. R.
Kerstein
, “One-dimensional turbulence: Stochastic simulation of multi-scale dynamics
,” Lect. Notes Phys.
756
, 291
(2009
).49.
R. C.
Schmidt
, A. R.
Kerstein
, and R.
McDermott
, “ODTLES: A multi-scale model for 3D turbulent flow based on one-dimensional turbulence modeling
,” Comput. Methods Appl. Mech. Eng.
199
, 865
(2010
).© 2011 American Institute of Physics.
2011
American Institute of Physics
You do not currently have access to this content.
