Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T12:05:13.286Z Has data issue: false hasContentIssue false
  • English
  • Français

Internal solitary waves with subsurface cores

Published online by Cambridge University Press:  18 June 2019

Yangxin He Open the ORCID record for Yangxin He [Opens in a new window] ,
Kevin G. Lamb Open the ORCID record for Kevin G. Lamb [Opens in a new window]  and
Ren-Chieh Lien
Yangxin He*
Affiliation:
Department of Applied Math, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Kevin G. Lamb
Affiliation:
Department of Applied Math, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Ren-Chieh Lien
Affiliation:
Applied Physics Laboratory, University of Washington, Seattle, WA, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Large internal solitary waves with subsurface cores have recently been observed in the South China Sea. Here fully nonlinear solutions of the Dubreil–Jacotin–Long equation are used to study the conditions under which such cores exist. We find that the location of the cores, either at the surface or below the surface, is largely determined by the sign of the vorticity of the near-surface background current. The results of a numerical simulation of a two-dimensional shoaling internal solitary wave are presented which illustrate the formation of a subsurface core.

JFM classification

Geophysical and Geological Flows: Internal waves Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Wave breaking
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 1 - 17
Check for updates
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akylas, T. R. & Grimshaw, R. H. J. 1992 Solitary internal waves with oscillatory tails. J. Fluid Mech. 242, 279–298.10.1017/S0022112092002374Google Scholar
Bourgault, D., Galbraith, P. S. & Chavanne, C. 2016 Generation of internal solitary waves by frontally forced intrusions in geophysical flows. Nat. Commun. 7, 13606.10.1038/ncomms13606Google Scholar
Brown, D. J. & Christie, D. R. 1998 Fully nonlinear solitary waves in continuously stratified incompressible Boussinesq fluids. Phys. Fluids 10 (10), 2569–2586.10.1063/1.869771Google Scholar
Carr, M., Fructus, D., Grue, J., Jensen, A. & Davies, P. A. 2008 Convectively induced shear instability in large amplitude internal solitary waves. Phys. Fluids 20 (12), 126601.10.1063/1.3030947Google Scholar
Choi, W. 2006 The effect of a background shear current on large amplitude internal solitary waves. Phys. Fluids 18 (3), 036601.10.1063/1.2180291Google Scholar
Da Silva, J. C. B., New, A. L. & Magalhaes, J. M. 2011 On the structure and propagation of internal solitary waves generated at the mascarene plateau in the Indian Ocean. Deep Sea Res. I 58 (3), 229–240.10.1016/j.dsr.2010.12.003Google Scholar
Davis, R. E. & Acrivos, A. 1967 Solitary internal waves in deep water. J. Fluid Mech. 29 (3), 593–607.10.1017/S0022112067001041Google Scholar
Deepwell, D. & Stastna, M. 2016 Mass transport by mode-2 internal solitary-like waves. Phys. Fluids 28, 056606.10.1063/1.4948544Google Scholar
Derzho, O. G. & Grimshaw, R. 1997 Solitary waves with a vortex core in a shallow layer of stratified fluid. Phys. Fluids 9 (11), 3378–3385.10.1063/1.869450Google Scholar
Grue, J., Jensen, A., Rusas, P. O. & Sveen, J. K. 2000 Breaking and broadening of internal solitary waves. J. Fluid Mech. 413, 181–217.10.1017/S0022112000008648Google Scholar
Hamann, M. M., Alford, M. H. & Mickett, J. B. 2018 Generation and propagation of nonlinear internal waves in sheared currents over the washington continental shelf. J. Geophys. Res. Oceans 123 (4), 2381–2400.10.1002/2017JC013388Google Scholar
Helfrich, K. R. & White, B. L. 2010 A model for large-amplitude internal solitary waves with trapped cores. Nonlinear Process. Geophys. 17, 303–318.10.5194/npg-17-303-2010Google Scholar
Kamachi, M. & Honji, H. 1982 Steady flow patterns of internal solitary bulges in a stratified fluid. Phys. Fluids 25 (7), 1119–1120.10.1063/1.863876Google Scholar
King, S. E., Carr, M. & Dritschel, D. G. 2011 The steady-state form of large-amplitude internal solitary waves. J. Fluid Mech. 666, 477–505.10.1017/S0022112010004301Google Scholar
Klymak, J. M. & Moum, J. N. 2003 Internal solitary waves of elevation advancing on a shoaling shelf. Geophys. Res. Lett. 30 (20), 2045.10.1029/2003GL017706Google Scholar
Lamb, K. G. 2002 A numerical investigation of solitary internal waves with trapped cores formed via shoaling. J. Fluid Mech. 451, 109–144.10.1017/S002211200100636XGoogle Scholar
Lamb, K. G. 2003 Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores. J. Fluid Mech. 478, 81–100.10.1017/S0022112002003269Google Scholar
Lamb, K. G. 2007 Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography. Cont. Shelf Res. 27, 1208–1232.10.1016/j.csr.2007.01.020Google Scholar
Lamb, K. G. 2010 Energetics of internal solitary waves in a background sheared current. Nonl. Processes Geophys. 17, 553–568.10.5194/npg-17-553-2010Google Scholar
Lamb, K. G. & Farmer, D. 2011 Instabilities in an internal solitary-like wave on the Oregon shelf. J. Phys. Oceanogr. 41 (1), 67–87.10.1175/2010JPO4308.1Google Scholar
Lamb, K. G. & Wilkie, K. P. 2004 Conjugate flows for waves with trapped cores. Phys. Fluids 16 (12), 4685–4695.10.1063/1.1811551Google Scholar
Lien, R.-C., D’Asaro, E. A., Henyey, F., Chang, M.-H., Tang, T.-Y. & Yang, Y.-J. 2012 Trapped core formation within a shoaling nonlinear internal wave. J. Phys. Oceanogr. 42 (4), 511–525.10.1175/2011JPO4578.1Google Scholar
Lien, R.-C., Henyey, F., Ma, B. & Yang, Y. J. 2014 Large-amplitude internal solitary waves observed in the Northern South China sea: properties and energetics. J. Phys. Oceanogr. 44 (4), 1095–1115.10.1175/JPO-D-13-088.1Google Scholar
Luzzatto-Fegiz, P. & Helfrich, K. R. 2014 Laboratory experiments and simulations for solitary internal waves with trapped cores. J. Fluid Mech. 757, 354–380.10.1017/jfm.2014.501Google Scholar
Ostrovsky, L. A. & Stepanyants, Y. A. 1989 Do internal solitions exist in the ocean? Rev. Geophys. 27 (3), 293–310.10.1029/RG027i003p00293Google Scholar
Scotti, A. & Pineda, J. 2004 Observation of very large and steep internal waves of elevation near the Massachusetts coast. Geophys. Res. Lett. 31 (22), L22307.10.1029/2004GL021052Google Scholar
Shroyer, E. L., Moum, J. N. & Nash, J. D. 2010 Mode 2 waves on the continental shelf: ephemeral components of the nonlinear internal wavefield. J. Geophys. Res. Oceans 115, C07001.10.1029/2009JC005605Google Scholar
Stamp, A. P. & Jacka, M. 1995 Deep-water internal solitaty waves. J. Fluid Mech. 305, 347–371.10.1017/S0022112095004654Google Scholar
Stastna, M. & Lamb, K. G. 2002 Large fully nonlinear internal solitary waves: the effect of background current. Phys. Fluids 14 (9), 2987–2999.10.1063/1.1496510Google Scholar
Stastna, M. & Walter, R. 2014 Transcritical generation of nonlinear internal waves in the presence of background shear flow. Phys. Fluids 26, 086601.10.1063/1.4891871Google Scholar
Sutherland, B. R. & Nault, J. T. 2007 Intrusive gravity currents propagating along thin and thick interfaces. J. Fluid Mech. 586, 109–118.10.1017/S0022112007007288Google Scholar
Tung, K.-K., Chan, T. F. & Kubota, T. 1982 Large amplitude internal waves of permanent form. Stud. Appl. Maths 66 (1), 1–44.10.1002/sapm19826611Google Scholar
Turkington, B., Eydeland, A. & Wang, S. 1991 A computational method for solitary internal waves in a continuously stratified fluid. Stud. Appl. Maths 85 (2), 93–127.10.1002/sapm199185293Google Scholar
Venayagamoorthy, S. K. & Fringer, O. B. 2007 On the formation and propagation of nonlinear internal boluses across a shelf break. J. Fluid Mech. 577, 137–159.10.1017/S0022112007004624Google Scholar
Walter, R. K., Stastna, M., Woodson, C. B. & Monismith, S. G. 2016 Observations of nonlinear internal waves at a persistent coastal upwelling front. Cont. Shelf Res. 117, 100–117.10.1016/j.csr.2016.02.007Google Scholar
Zhang, S. & Alford, M. H. 2015 Instabilities in nonlinear internal waves on the Washington continental shelf. J. Geophys. Res. Oceans 120 (7), 5272–5283.10.1002/2014JC010638Google Scholar