Skip to main content Accessibility help

Internal solitary waves with subsurface cores

  • Yangxin He (a1), Kevin G. Lamb (a1) and Ren-Chieh Lien (a2)


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.


Corresponding author

Email address for correspondence:


Hide All
Akylas, T. R. & Grimshaw, R. H. J. 1992 Solitary internal waves with oscillatory tails. J. Fluid Mech. 242, 279298.10.1017/S0022112092002374
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/ncomms13606
Brown, D. J. & Christie, D. R. 1998 Fully nonlinear solitary waves in continuously stratified incompressible Boussinesq fluids. Phys. Fluids 10 (10), 25692586.10.1063/1.869771
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), 126601.10.1063/1.3030947
Choi, W. 2006 The effect of a background shear current on large amplitude internal solitary waves. Phys. Fluids 18 (3), 036601.10.1063/1.2180291
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), 229240.10.1016/j.dsr.2010.12.003
Davis, R. E. & Acrivos, A. 1967 Solitary internal waves in deep water. J. Fluid Mech. 29 (3), 593607.10.1017/S0022112067001041
Deepwell, D. & Stastna, M. 2016 Mass transport by mode-2 internal solitary-like waves. Phys. Fluids 28, 056606.10.1063/1.4948544
Derzho, O. G. & Grimshaw, R. 1997 Solitary waves with a vortex core in a shallow layer of stratified fluid. Phys. Fluids 9 (11), 33783385.10.1063/1.869450
Grue, J., Jensen, A., Rusas, P. O. & Sveen, J. K. 2000 Breaking and broadening of internal solitary waves. J. Fluid Mech. 413, 181217.10.1017/S0022112000008648
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), 23812400.10.1002/2017JC013388
Helfrich, K. R. & White, B. L. 2010 A model for large-amplitude internal solitary waves with trapped cores. Nonlinear Process. Geophys. 17, 303318.10.5194/npg-17-303-2010
Kamachi, M. & Honji, H. 1982 Steady flow patterns of internal solitary bulges in a stratified fluid. Phys. Fluids 25 (7), 11191120.10.1063/1.863876
King, S. E., Carr, M. & Dritschel, D. G. 2011 The steady-state form of large-amplitude internal solitary waves. J. Fluid Mech. 666, 477505.10.1017/S0022112010004301
Klymak, J. M. & Moum, J. N. 2003 Internal solitary waves of elevation advancing on a shoaling shelf. Geophys. Res. Lett. 30 (20), 2045.10.1029/2003GL017706
Lamb, K. G. 2002 A numerical investigation of solitary internal waves with trapped cores formed via shoaling. J. Fluid Mech. 451, 109144.10.1017/S002211200100636X
Lamb, K. G. 2003 Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores. J. Fluid Mech. 478, 81100.10.1017/S0022112002003269
Lamb, K. G. 2007 Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography. Cont. Shelf Res. 27, 12081232.10.1016/j.csr.2007.01.020
Lamb, K. G. 2010 Energetics of internal solitary waves in a background sheared current. Nonl. Processes Geophys. 17, 553568.10.5194/npg-17-553-2010
Lamb, K. G. & Farmer, D. 2011 Instabilities in an internal solitary-like wave on the Oregon shelf. J. Phys. Oceanogr. 41 (1), 6787.10.1175/2010JPO4308.1
Lamb, K. G. & Wilkie, K. P. 2004 Conjugate flows for waves with trapped cores. Phys. Fluids 16 (12), 46854695.10.1063/1.1811551
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), 511525.10.1175/2011JPO4578.1
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), 10951115.10.1175/JPO-D-13-088.1
Luzzatto-Fegiz, P. & Helfrich, K. R. 2014 Laboratory experiments and simulations for solitary internal waves with trapped cores. J. Fluid Mech. 757, 354380.10.1017/jfm.2014.501
Ostrovsky, L. A. & Stepanyants, Y. A. 1989 Do internal solitions exist in the ocean? Rev. Geophys. 27 (3), 293310.10.1029/RG027i003p00293
Scotti, A. & Pineda, J. 2004 Observation of very large and steep internal waves of elevation near the Massachusetts coast. Geophys. Res. Lett. 31 (22), L22307.10.1029/2004GL021052
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, C07001.10.1029/2009JC005605
Stamp, A. P. & Jacka, M. 1995 Deep-water internal solitaty waves. J. Fluid Mech. 305, 347371.10.1017/S0022112095004654
Stastna, M. & Lamb, K. G. 2002 Large fully nonlinear internal solitary waves: the effect of background current. Phys. Fluids 14 (9), 29872999.10.1063/1.1496510
Stastna, M. & Walter, R. 2014 Transcritical generation of nonlinear internal waves in the presence of background shear flow. Phys. Fluids 26, 086601.10.1063/1.4891871
Sutherland, B. R. & Nault, J. T. 2007 Intrusive gravity currents propagating along thin and thick interfaces. J. Fluid Mech. 586, 109118.10.1017/S0022112007007288
Tung, K.-K., Chan, T. F. & Kubota, T. 1982 Large amplitude internal waves of permanent form. Stud. Appl. Maths 66 (1), 144.10.1002/sapm19826611
Turkington, B., Eydeland, A. & Wang, S. 1991 A computational method for solitary internal waves in a continuously stratified fluid. Stud. Appl. Maths 85 (2), 93127.10.1002/sapm199185293
Venayagamoorthy, S. K. & Fringer, O. B. 2007 On the formation and propagation of nonlinear internal boluses across a shelf break. J. Fluid Mech. 577, 137159.10.1017/S0022112007004624
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, 100117.10.1016/j.csr.2016.02.007
Zhang, S. & Alford, M. H. 2015 Instabilities in nonlinear internal waves on the Washington continental shelf. J. Geophys. Res. Oceans 120 (7), 52725283.10.1002/2014JC010638
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Internal solitary waves with subsurface cores

  • Yangxin He (a1), Kevin G. Lamb (a1) and Ren-Chieh Lien (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.