We present the first three-dimensional numerical simulations of the mass transport capabilities of mode-2 waves formed by a lock-release mechanism with both single and double pycnocline stratifications. Single pycnoclines and double pycnoclines with a small spacing between the pycnocline centres were found to exhibit large Lee instabilities which formed during the collapse of the intermediate density region. These instabilities led to the generation of vorticity dipoles across the mid-depth, and thereby contributed to the reduction in the mass transported by the wave. A double pycnocline with a separation of approximately 12% of the depth between the two pycnocline centres was found to transport a passive tracer optimally for the longest time-period. Increasing Schmidt number correlated with increasing mass transport, while decreasing the tracer diffusivity led to increasing mass transport, but only when a trapped core existed. Contrasted two-dimensional simulations reveal that in certain cases, most noticeably the optimal transport case, the mass transport is significantly different from the corresponding three-dimensional simulation.
REFERENCES
1.
K. R.
Helfrich
and W. K.
Melville
, “Long nonlinear internal waves
,” Annu. Rev. Fluid Mech.
38
, 395
–425
(2006
).2.
L. A.
Ostrovsky
and Y. A.
Stepanyants
, “Do internal solitions exist in the ocean?
,” Rev. Geophys.
27
, 293
–310
, doi:10.1029/RG027i003p00293 (1989
).3.
E. L.
Shroyer
, J. N.
Moum
, and J. D.
Nash
, “Mode 2 waves on the continental shelf: Ephemeral components of the nonlinear internal wavefield
,” J. Geophys. Res.: Oceans
115
, C07001
, doi:10.1029/2009JC005605 (2010
).4.
Y. J.
Yang
, Y. C.
Fang
, T. Y.
Tang
, and S. R.
Ramp
, “Convex and concave types of second baroclinic mode internal solitary waves
,” Nonlinear Processes Geophys.
17
, 605
–614
(2010
).5.
S. R.
Ramp
, Y. J.
Yang
, D. B.
Reeder
, and F. L.
Bahr
, “Observations of a mode-2 nonlinear internal wave on the northern Heng-Chun ridge south of Taiwan
,” J. Geophys. Res.: Oceans
117
, C03043
, doi:10.1029/2011JC007662 (2012
).6.
S. R.
Ramp
, Y. J.
Yang
, D. B.
Reeder
, M. C.
Buijsman
, and F. L.
Bahr
, “The evolution of mode-2 nonlinear internal waves over the northern Heng-Chun ridge south of Taiwan
,” Nonlinear Processes Geophys.
2
, 243
–296
(2015
).7.
D. M.
Farmer
and J. D.
Smith
, “Tidal interaction of stratified flow with a sill in Knight Inlet
,” Deep-Sea Res., Part A
27
, 239
–254
(1980
).8.
D. J.
Bogucki
, L. G.
Redekopp
, and J.
Barth
, “Internal solitary waves in the coastal mixing and optics 1996 experiment: Multimodal structure and resuspension
,” J. Geophys. Res.: Oceans
110
, C02024
, doi:10.1029/2003JC002253 (2005
).9.
K.
Konyaev
, K.
Sabinin
, and A.
Serebryany
, “Large-amplitude internal waves at the Mascarene ridge in the Indian ocean
,” Deep Sea Res., Part I
42
, 2075
–2091
(1995
).10.
J.
da Silva
, A.
New
, and J.
Magalhaes
, “On the structure and propagation of internal solitary waves generated at the Mascarene plateau in the Indian ocean
,” Deep Sea Res., Part I
58
, 229
–240
(2011
).11.
M.
Salloum
, O. M.
Knio
, and A.
Brandt
, “Numerical simulation of mass transport in internal solitary waves
,” Phys. Fluids
24
, 016602
(2012
).12.
A.
Brandt
and K. R.
Shipley
, “Laboratory experiments on mass transport by large amplitude mode-2 internal solitary waves
,” Phys. Fluids
26
, 046601
(2014
).13.
A. P.
Stamp
and M.
Jacka
, “Deep-water internal solitary waves
,” J. Fluid Mech.
305
, 347
–371
(1995
).14.
D. E.
Terez
and O. M.
Knio
, “Numerical simulations of large-amplitude internal solitary waves
,” J. Fluid Mech.
362
, 53
–82
(1998
).15.
A. P.
Mehta
, B. R.
Sutherland
, and P. J.
Kyba
, “Interfacial gravity currents. II. Wave excitation
,” Phys. Fluids
14
, 3558
–3569
(2002
).16.
P. T.
Stevick
, L. S.
Incze
, S. D.
Kraus
, S.
Rosen
, N.
Wolff
, and A.
Baukus
, “Trophic relationships and oceanography on and around a small offshore bank
,” Mar. Ecol.: Prog. Ser.
363
, 15
–28
(2008
).17.
C. J.
Subich
, K. G.
Lamb
, and M.
Stastna
, “Simulation of the Navier Stokes equations in three dimensions with a spectral collocation method
,” Int. J. Numer. Methods Fluids
73
, 103
–129
(2013
).18.
P. K.
Kundu
, I. M.
Cohen
, and D. R.
Dowling
, Fluid Mechanics
, 5th ed. (Academic Press
, 2012
).19.
M.
Carr
, P. A.
Davies
, and R. P.
Hoebers
, “Experiments on the structure and stability of mode-2 internal solitary-like waves propagating on an offset pycnocline
,” Phys. Fluids
27
, 046602
(2015
).20.
B. R.
Sutherland
, “Interfacial gravity currents. I. Mixing and entrainment
,” Phys. Fluids
14
, 2244
–2254
(2002
).21.
J.
Olsthoorn
, A.
Baglaenko
, and M.
Stastna
, “Analysis of asymmetries in propagating mode-2 waves
,” Nonlinear Processes Geophys.
20
, 59
–69
(2013
).22.
K. B.
Winters
and J. J.
Riley
, “Instability of internal waves near a critical level
,” Dyn. Atmos. Oceans
16
, 249
–278
(1992
).23.
A. M.
Abdilghanie
and P. J.
Diamessis
, “On the generation and evolution of numerically simulated large-amplitude internal gravity wave packets
,” Theor. Comput. Fluid Dyn.
26
, 205
–224
(2011
).24.
K.
Dohan
and B.
Sutherland
, “Numerical and laboratory generation of internal waves from turbulence
,” Dyn. Atmos. Oceans
40
, 43
–56
(2005
).25.
T. B.
Benjamin
, “Internal waves of permanent form in fluids of great depth
,” J. Fluid Mech.
29
, 559
–592
(1967
).26.
N. P.
Schmidt
, “Generation, propagation and dissipation of second mode internal solitary waves
,” Ph.D. thesis, University of Canterbury
, 1998
.27.
T.
Maxworthy
, “On the formation of nonlinear internal waves from the gravitational collapse of mixed regions in two and three dimensions
,” J. Fluid Mech.
96
, 47
–64
(1980
).28.
O. G.
Derzho
and R.
Grimshaw
, “Solitary waves with a vortex core in a shallow layer of stratified fluid
,” Phys. Fluids
9
, 3378
–3385
(1997
).29.
K. G.
Lamb
, “A numerical investigation of solitary internal waves with trapped cores formed via shoaling
,” J. Fluid Mech.
451
, 109
–144
(2002
).30.
M.
Carr
, S. E.
King
, and D. G.
Dritschel
, “Instability in internal solitary waves with trapped cores
,” Phys. Fluids
24
, 016601
(2012
).31.
P.
Luzzatto-Fegiz
and K. R.
Helfrich
, “Laboratory experiments and simulations for solitary internal waves with trapped cores
,” J. Fluid Mech.
757
, 354
–380
(2014
).32.
M.
Stastna
, J.
Olsthoorn
, A.
Baglaenko
, and A.
Coutino
, “Strong mode-mode interactions in internal solitary-like waves
,” Phys. Fluids
27
, 046604
(2015
).33.
P.
Diamessis
, private communication (2016
).© 2016 Author(s).
2016
Author(s)
You do not currently have access to this content.
