Effect of a Background Shear Current on Models for Nonlinear Long Internal Waves
Abstract
The Korteweg—de Vries equation is a standard model for the description of long nonlinear internal waves in the ocean. When the effect of weak transverse variations and the Earth's background rotation are taken into account, this is replaced by the rotation-modified Kadomtsev—Petviashvili equation. In this short note we revisit the asymptotic derivation of this equation, incorporating a background shear flow as well as the background stratification.
References
1. Grimshaw R. Internal solitary waves. Environmental Stratified Flows. Chapter 1. Ed. R. Grimshaw. Kluwer, Boston, 2001. P. 1—29.
2. Helfrich K. R., Melville W. K. Long nonlinear internal waves. Ann. Rev. Fluid Mech. 2006, 38, 395—425.
3. Grimshaw R. Evolution equations for weakly nonlinear, long internal waves in a rotating fluid. Stud. Appl. Math. 1985, 73, 1—33.
4. Kadomtsev B. B., Petviashvili V. I. On the stability of solitary waves in weakly dispersive media. Sov. Phys. Dokl. 1970, 15, 539—541.
5. Ostrovsky L. A. Nonlinear internal waves a in rotating ocean. Oceanology. 1978, 18, 119—125.
6. Grimshaw R., Helfrich K. R. The effect of rotation on internal solitary waves. IMA J. Appl. Math. 2012, 77, 326—339.
7. Grimshaw R. Models for nonlinear long internal waves in a rotating fluid. Fundam. Prikl. Gidrofiz. 2013, 6, 4—13.
8. Alias A., Grimshaw R. H. J., Khusnutdinova K. R. Coupled Ostrovsky equations for internal waves in a shear flow. Phys. Fluids. 2014, 26, 1226603.
Review
For citations:
Grimshaw R. Effect of a Background Shear Current on Models for Nonlinear Long Internal Waves. Fundamental and Applied Hydrophysics. 2015;8(3):20-23. (In Russ.)
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