Physics of Fluids
Feedback | Help | Exit
Search:
   
 
 
 
Previous Article
A Lagrangian approach to droplet condensation in atmospheric clouds
The condensation of microdroplets in model systems, reminiscent of atmospheric clouds, is investigated numerically and analytically. Droplets have been followed through a synthetic turbulent flow fiel...
Next Article
Spectral and particle dispersion properties of steady two-dimensional multiscale flows
The spectral and particle dispersion characteristics of steady multiscale laminar thin-layer flows are investigated through numerical simulations of a two-dimensional layer-averaged model. The model a...

On fully nonlinear, vertically trapped wave packets in a stratified fluid on the f-plane

Phys. Fluids 21, 106604 (2009); doi:10.1063/1.3253400

Published 29 October 2009

You are not logged in to this journal. Log in

M. Stastna, F. J. Poulin, K. L. Rowe, and C. Subich
Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
The ubiquity of solitary and solitarylike internal waves in the coastal ocean has been recognized for some time. Recent theoretical studies of a strongly nonlinear, weakly nonhydrostatic set of layer-averaged model equations have predicted that rotation, for example, on the f-plane, can lead to the decay and subsequent reemergence of internal solitary waves. We reconsider this problem using high resolution numerical simulations of the rotating stratified Euler equations. We find that in certain cases the initial disturbances indeed fission into nonlinear wave packets, with the constituent waves making up the wave packet being, in themselves, nonlinear. However, for typical coastal ocean parameters this only occurs at rotation rates higher than those on Earth on the time scales we are able to simulate. We confirm, using the Dubreil–Jacotin–Long equation, that the vertical structure of the wave-induced currents is well predicted by the fully nonlinear theory of nonrotating internal solitary waves and that weakly nonlinear Korteweg–de Vries equation-based theory fails to describe this structure accurately. Subsequently, we consider flat-crested solitary waves that allow us to fix the wave amplitude while varying the horizontal wavelength. We find that as the waves' horizontal extent nears the baroclinic Rossby radius more energy is deposited into the wave tail. However, no wave overtaking is observed, and an explanation for this fact is proposed. Finally, we discuss the effects of the horizontal component of the rotation vector and derive an exact equation for rotation modified waves near the equator. This equation demonstrates that in this situation, rotation modifies the structure of the fully nonlinear waves but does not lead to solitary wave decay. ©2009 American Institute of Physics
History: Received 19 December 2008; accepted 10 September 2009; published 29 October 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/106604/1
BUY THIS ARTICLE   (US$24)
Download PDF (1096 kB) View Cart

KEYWORDS and PACS

Keywords
PACS

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (29)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. J. R. Apel, J. R. Holbrook, A. K. Liu, and J. J. Tsai, “The Sulu Sea internal soliton experiment,” J. Phys. Oceanogr. 15, 1625 (1985).
  2. A. R. Osborne and T. L. Burch, “Internal solitons in the Andaman Sea,” Science 208, 451 (1980).
  3. J. N. Moum and W. D. Smyth, “The pressure disturbance of a nonlinear internal wave train,” J. Fluid Mech. 558, 153 (2006).
  4. J. Pedlosky, Geophysical Fluid Dynamics, 2nd ed. (Springer, New York, 1987).
  5. D. J. Benney, “Long nonlinear waves in fluid flows,” J. Math. Phys. 45, 52 (1966).
  6. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Mathematical Society Lecture Notes Vol. 149 (Cambridge University Press, Cambridge, England, 1991).
  7. C. Yih, Dynamics of Nonhomogeneous Fluids (Macmillan, New York, 1965).
  8. B. Turkington, A. Eydeland, and S. Wang, “A computational method for solitary internal waves in a continuously stratified fluid,” Stud. Appl. Math. 85, 93 (1991).
  9. K. G. Lamb and B. Wan, “Conjugate flows and flat solitary waves for a continuously stratified fluid,” Phys. Fluids 10, 2061 (1998).
  10. M. Stastna and K. G. Lamb, “Large fully nonlinear internal solitary waves: The effect of background current,” Phys. Fluids 14, 2987 (2002).
  11. M. V. Trevorrow, “Observations of internal solitary waves near the Oregon coast with an inverted echo sounder,” J. Geophys. Res. 103, 7671, doi:10.1029/98JC00101 (1998).
  12. K. G. Lamb, The 1998 WHOI/IOSA/ONR Internal Solitary Wave Workshop: Contributed Papers, edited by T. F. Duda and D. M. Farmer (Woods Hole Oceanographic Institution, Woods Hole, MA, 1999).
  13. K. G. Lamb and L. Yan, “The evolution of internal wave undular bores: Comparisons of a fully nonlinear numerical model with weakly nonlinear theory,” J. Phys. Oceanogr. 26, 2712 (1996).
  14. T. Gerkema and V. I. Shrira, “Near-inertial waves in the ocean: Beyond the `traditional approximation',” J. Fluid Mech. 529, 195 (2005).
  15. A. E. Gill, Atmosphere-Ocean Dynamics (Academic, New York, 1982).
  16. R. Grimshaw, “Evolution equations for weakly nonlinear internal waves in a rotating fluid,” Stud. Appl. Math. 73, 1 (1985).
  17. R. Grimshaw, L. Ostrovsky, V. I. Shrira, and Y. A. Stepanyants, “Long nonlinear surface and internal gravity waves in a rotating ocean,” Rev. Geophys. 19, 289 (1998).
  18. C. Katsis and T. R. Akylas, “Solitary internal waves in rotating channels: A numerical study,” Phys. Fluids 30, 297 (1987).
  19. K. R. Helfrich, “Decay and return of internal solitary waves with rotation,” Phys. Fluids 19, 026601 (2007).
  20. M. Stastna and K. Rowe, “On weakly nonlinear descriptions of nonlinear internal gravity waves in a rotating reference frame,” Atlantic Electronic Journal of Mathematics 2, 30 (2007).
  21. T. B. Benjamin, J. L. Bona, and J. J. Mahony, “Model equations for long waves in nonlinear dispersive systems,” Philos. Trans. R. Soc. London, Ser. A 272, 47 (1972).
  22. K. Helfrich and R. Grimshaw, “Nonlinear disintegration of the internal tide,” J. Phys. Oceanogr. 38, 686 (2008).
  23. P. Kundu and I. M. Cohen, Fluid Mechanics, 3rd ed. (Elsevier, New York, 2004).
  24. K. G. Lamb, “A numerical investigation of solitary internal waves with trapped cores formed via shoaling,” J. Fluid Mech. 451, 109 (2002).
  25. K. G. Lamb, “Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge,” J. Geophys. Res. 99, 843, doi:10.1029/93JC02514 (1994).
  26. J. B. Bell and D. L. Marcus, “A second-order projection method for variable-density flows,” J. Comput. Phys. 101, 334 (1992).
  27. L. G. Margolin, P. K. Smolarkiewicz, and A. A. Wyszogradzki, “Implicit turbulence modeling for high Reynolds number flows,” ASME Trans. J. Fluids Eng. 124, 862 (2002).
  28. L. G. Margolin, P. K. Smolarkiewicz, and A. A. Wyszogradzki, “Dissipation in implicit turbulence models: A computational study,” ASME Trans. J. Appl. Mech. 73, 469 (2006).
  29. R. Grimshaw and K. Helfrich, “Long time solutions of the Ostrovsky equation,” Stud. Appl. Math. 121, 71 (2008).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics