Breaking groups of large-amplitude internal gravity waves are simulated numerically and the resulting diapycnal mixing and residual momentum are quantified. The wave frequency strongly affects the mixing, with high- and low-frequency waves doing many times more mixing than intermediate-frequency waves with the same steepness. The total residual momentum remaining in the breaking region after the remnants of the wave group propagates away shows similar frequency dependence as the diapycnal mixing. Additionally, the propagation of the breaking events and the spatial distribution of the mixing are found to agree qualitatively with a kinematic description of breaking internal wave groups.
REFERENCES
1.
J. A.
MacKinnon
and K. B.
Winters
, “Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.9°
,” Geophys. Res. Lett.
32
, L15605
, doi: (2005
).2.
F. P.
Bretherton
, “The propagation of internal gravity waves in a shear flow
,” Q. J. R. Meteorol. Soc.
92
, 466
(1966
).3.
R. H. J.
Grimshaw
, “The modulation of an internal gravity-wave packet, and the resonance with the mean motion
,” Stud. Appl. Math.
56
, 241
(1977
).4.
K. L.
Polzin
, “Spatial variability of turbulent mixing in the abyssal ocean
,” Science
276
, 93
(1997
).5.
The Hawaiian Ocean Mixing Experiment was a multi-year field program dedicated to studying the internal waves generated by the internal tide flowing over the Hawaiian ridge
. Vol. 36
Issue 6
, 2006
of the Journal of Physical Oceanography is a special issue devoted to the Hawaiian Ocean Mixing Experiment.6.
M.
Alford
, J. A.
MacKinnon
, Z.
Zhao
, R.
Pinkel
, J.
Klymak
, and T.
Peacock
, “Internal waves across the Pacific
,” Geophys. Res. Lett.
34
, L24601
, doi: (2007
).7.
M. C.
Gregg
, E. A.
D’Asaro
, T. J.
Shay
, and N.
Larson
, “Observations of persistent mixing and near-inertial waves
,” J. Phys. Oceanogr.
16
, 856
(1986
).8.
M. H.
Alford
and R.
Pinkel
, “Observations of overturning in the thermocline: The context of mixing
,” J. Phys. Oceanogr.
30
, 805
(2000
).9.
K.
Polzin
and R.
Ferrari
, “Isopycnal dispersion in nature
,” J. Phys. Oceanogr.
34
, 247
(2004
).10.
M.-P.
Lelong
and M. A.
Sundermeyer
, “Geostrophic adjustment of an isolated diapycnal mixing event and its implications for small-scale later dispersion
,” J. Phys. Oceanogr.
35
, 2352
(2005
).11.
M. A.
Sundermeyer
and M.-P.
Lelong
, “Numerical simulations of lateral dispersion by the relaxation of diapycnal mixing events
,” J. Phys. Oceanogr.
35
, 2368
(2005
).12.
L.
Thomas
, A.
Tandon
, and A.
Mahadevan
, “Submesoscale ocean processes and dynamics
,” in Ocean Modeling in Eddying Regimes
(American Geophysical Union
, Washington, DC
, 2008
), pp. 17
–38
.13.
K.
Smith
and R.
Ferrari
, “The production and dissipation of compensated thermohaline variance by mesoscale stirring
,” J. Phys. Oceanogr.
39
, 2477
(2009
).14.
A.
Eliassen
and E.
Palm
, “On the transfer of energy in stationary mountain waves
,” Geofysike Publ.
22
, 1
(1960
).15.
D. C.
Fritts
and T. J.
Dunkerton
, “A quasi-linear study of gravity-wave saturation and self-acceleration
,” J. Atmos. Sci.
41
, 3272
(1984
).16.
D. C.
Fritts
and T. J.
Dunkerton
, “Fluxes of heat and constituents due to convectively unstable gravity waves
,” J. Atmos. Sci.
42
, 549
(1985
).17.
R. P.
Mied
, “The occurrence of parametric instabilities in finite-amplitude internal gravity waves
,” J. Fluid Mech.
78
, 763
(1976
).18.
J.
Klostermeyer
, “On parametric instabilities of finite-amplitude internal gravity waves
,” J. Fluid Mech.
119
, 367
(1982
).19.
B. R.
Sutherland
, “Finite-amplitude internal wavepacket dispersion and breaking
,” J. Fluid Mech.
429
, 343
(2001
).20.
P. K.
Kundu
and I. M.
Cohen
, Fluid Mechanics
, 2nd ed. (Academic
, San Diego, CA
, 2002
).21.
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
).22.
Y.
Tseng
and J. H.
Ferziger
, “Mixing and available potential energy in stratified flows
,” Phys. Fluids
13
, 1281
(2001
).23.
R.
Salmon
, Lectures on Geophysical Fluid Dynamics
(Oxford University Press
, New York
, 1998
).24.
S. A.
Thorpe
, “On internal wave groups
,” J. Phys. Oceanogr.
29
, 1085
(1999
).25.
K. B.
Winters
, J. A.
MacKinnon
, and B.
Mills
, “A spectral model for process studies of rotating, density-stratified flows
,” J. Atmos. Ocean. Technol.
21
, 69
(2004
).26.
G. L.
Brown
, A. B. G.
Bush
, and B. R.
Sutherland
, “Beyond ray tracing for internal waves. II. Finite-amplitude effects
,” Phys. Fluids
20
, 106602
(2008
).27.
J. F.
Scinocca
and T. G.
Shepherd
, “Nonlinear wave-activity conservation laws and hamiltonian structure for the two-dimensional anelastic equations
,” J. Atmos. Sci.
49
, 5
(1992
).28.
B. R.
Sutherland
, “Weakly nonlinear internal gravity wave packets
,” J. Fluid Mech.
569
, 249
(2006
).29.
K. B.
Winters
and E. A.
D’Asaro
, “Three-dimensional wave instability near a critical level
,” J. Fluid Mech.
272
, 255
(1994
).30.
M. L.
Waite
and P.
Bartello
, “Stratified turbulence generated by internal gravity waves
,” J. Fluid Mech.
546
, 313
(2006
).31.
S. A.
Thorpe
, “Turbulence and mixing in a Scottish loch
,” Philos. Trans. R. Soc. London, Ser. A
286
, 125
(1977
).32.
J.
Klostermeyer
, “Two- and three-dimensional parametric instabilities in finite-amplitude internal gravity waves
,” Geophys. Astrophys. Fluid Dyn.
61
, 1
(1991
).33.
P. N.
Lombard
and J. J.
Riley
, “Instability and breakdown of internal gravity waves. I. Linear stability analysis
,” Phys. Fluids
8
, 3271
(1996
).34.
M.-P.
Lelong
and T. J.
Dunkerton
, “Inertia-gravity wave breaking in three dimensions. Part I: Convectively stable waves
,” J. Atmos. Sci.
55
, 2473
(1998
).35.
M.-P.
Lelong
and T. J.
Dunkerton
, “Inertia-gravity wave breaking in three dimensions. Part II: Convectively unstable waves
,” J. Atmos. Sci.
55
, 2489
(1998
).© 2011 American Institute of Physics.
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American Institute of Physics
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