World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Energetics of Internal Solitary Waves in a Background Sheared Current : Volume 17, Issue 5 (08/10/2010)

By Lamb, K. G.

Click here to view

Book Id: WPLBN0003984270
Format Type: PDF Article :
File Size: Pages 16
Reproduction Date: 2015

Title: Energetics of Internal Solitary Waves in a Background Sheared Current : Volume 17, Issue 5 (08/10/2010)  
Author: Lamb, K. G.
Volume: Vol. 17, Issue 5
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Lamb, K. G. (2010). Energetics of Internal Solitary Waves in a Background Sheared Current : Volume 17, Issue 5 (08/10/2010). Retrieved from

Description: Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada. The energetics of internal waves in the presence of a background sheared current is explored via numerical simulations for four different situations based on oceanographic conditions: the nonlinear interaction of two internal solitary waves; an internal solitary wave shoaling through a turning point; internal solitary wave reflection from a sloping boundary and a deep-water internal seiche trapped in a deep basin. In the simulations with variable water depth using the Boussinesq approximation the combination of a background sheared current, bathymetry and a rigid lid results in a change in the total energy of the system due to the work done by a pressure change that is established across the domain. A final simulation of the deep-water internal seiche in which the Boussinesq approximation is not invoked and a diffuse air-water interface is added to the system results in the energy remaining constant because the generation of surface waves prevents the establishment of a net pressure increase across the domain. The difference in the perturbation energy in the Boussinesq and non-Boussinesq simulations is accounted for by the surface waves.

Energetics of internal solitary waves in a background sheared current

Carter, G. S., Gregg, M. C., and Lien, R.-C.: Internal waves, solitary-like waves, and mixing on the Monterey Bay shelf, Cont. Shelf Res., 25, 1499–1520, 2005.; Fabrikant, A. and Stepanyants, Y. A.: Propagation of waves in shear flows, World Scientific, 1998.; Gear, J. A. and Grimshaw, R.: A second-order theory for solitary waves in shallow fluids, Phys. Fluids, 26, 14–29, 1983.; Grimshaw, R.: Wave action and wave-mean flow interaction, with application to stratified shear flows, Annu. Rev. Fluid Mech., 16, 11–44, 1985.; Bell, J. B. and Marcus, D. J.: A second-order projection method for variable-density flows, J. Comput. Phys., 101, 334–348, 1992.; Bell, J. B., Colella, P., and Glaz, H. M.: A second order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., 85, 257–283, 1989.; Benney, D. J.: Long nonlinear waves in fluid flows, J. Math. Phys., 45, 52–63, 1966.; Bourgault, D., Blokhina, M. D., Mirshak, R., and Kelley, D. E.: Evolution of a shoaling internal solitary wavetrain, Geophys. Res. Lett., 34, L03601, doi:10.1029/2006GL028462, 2007.; Bretherton, F. P.: On the mean motion induced by internal gravity waves, J. Fluid Mech., 36, 785–803, 1969.; Bretherton, F. P. and Garrett, C. J. R.: The propagation of wave trains in moving media, Proc. R. Soc. Lon. Ser.-A, 302, 529–545, 1968.; Craik, A. D. D.: Wave interactions and fluid flows, Cambridge University Press, Cambridge, UK, 1985.; Grimshaw, R., Pelinovsky, E., and Talipova, T.: Solitary wave transformation in a medium with sign-variable quadratic nonlinear and cubic nonlinearity, Physica D, 132, 40–62, 1999.; Grimshaw, R., Pelinovsky, E., and Poloukhina, O.: Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface, Nonlin. Processes Geophys., 9, 221–235, doi:10.5194/npg-9-221-2002, 2002.; Helfrich, K. R.: Internal solitary wave breaking and run-up on a uniform slope, J. Fluid Mech., 243, 133–154, 1992.; Jeans, D. R. G. and Sherwin, T. J.: The evolution and energetics of large amplitude nonlinear internal waves on the Portuguese shelf, J. Mar. Res., 59, 327–353, 2001.; Klymak, J. M., Pinkel, R., Liu, C.-T., Liu, A. K., and David, L.: Prototypical solitons in the South China Sea, Geophys. Res. Lett., 33, L11607, doi:10.1029/2006GL025 932, 2006.; Lamb, K. G.: Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge, J. Geophys. Res., 99, 843–864, 1994.; Lamb, K. G.: Conjugate flows for a three-layer fluid, Phys. Fluids, 12, 2169–2185, 2000.; Lamb, K. G.: Shoaling solitary internal waves: on a criterion for the formation of waves with trapped cores, J. Fluid Mech., 478, 81–100, doi:10.1017/S0022112002003269, 2003.; Lamb, K. G.: Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography, Cont. Shelf Res., 27, 1208–1232, doi:10.1016/j.csr.2007.01.020, 2007.; Lamb, K. G. and Wan, B.: Conjugate flows and flat solitary waves for a continuously stratified fluid, Phys. Fluids, 10, 2061–2079, 1998.; Lamb, K. G.: On the Calculation of the Available Potential Energy of an Isolated Perturbation in a Density Stratified Fluid, J. Fluid Mech., 597, 415–427, doi:10.1017/S0022112007009743, 2008.; Lamb, K. G. and Nguyen, V. T.: Calculating Energy Flux in Internal Solitary Waves with an Application to Reflectance, J. Phys. Oceanogr., 39, 559–580, doi:10.1175/2008JPO3882.1, 2009.; Michallet, H. and Ivey, G. N.: Experiments on mixing due to internal solitary waves breaking on uniform slopes, J. Geophys. Res., 104, 13467–13477, 1999.; Moum, J. N., Klymak, J. M., Nash, J. D., Perlin, A., and Smyth, W. D.: Energy transport by non


Click To View

Additional Books

  • Conjugate Fluctuation Analysis for a Set... (by )
  • Particle Acceleration in Tangential Disc... (by )
  • Multiscaling and Joint Multiscaling Desc... (by )
  • Short-term Prediction of Rain Attenuatio... (by )
  • Lyapunov, Floquet, and Singular Vectors ... (by )
  • Improved Singular Spectrum Analysis for ... (by )
  • Surface Flow Structure of the Gulf Strea... (by )
  • Loading Rates in California Inferred fro... (by )
  • Conditional Nonlinear Optimal Perturbati... (by )
  • Projection of Compact Fractal Sets: Appl... (by )
  • Implicit Particle Filtering for Models w... (by )
  • On the Cascade Mechanism of Short Surfac... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.