NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-3-110-1996 A centre manifold approach to solitary waves in a sheared, stably stratified fluid layer Zimmerman W. B. 1 Velarde M. G. 2 Department of Chemical Engineering, UMIST, Sackville Street, PO Box 88, Manchester M60 1QD, England Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, No. 1, Madrid 28040 Spain 30 06 1996 3 2 110 114 Copyright: © 1996 W. B. Zimmerman 1996 This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Generic License. To view a copy of this licence, visit https://creativecommons.org/licenses/by-nc-sa/2.5/ This article is available from https://npg.copernicus.org/articles/3/110/1996/npg-3-110-1996.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/3/110/1996/npg-3-110-1996.pdf

The centre manifold approach is used to derive an approximate equation for nonlinear waves propagating in a sheared, stably stratified fluid layer. The evolution equation matches limiting forms derived by other methods, including the inviscid, long wave approximation leading to the Korteweg- deVries equation. The model given here allows large modulations of the height of the waveguide. This permits the crude modelling of shear layer instabilities at the upper material surface of the waveguide which excite solitary internal waves in the waveguide. An energy argument is used to support the existence of these waves.