Articles | Volume 20, issue 2
Nonlin. Processes Geophys., 20, 213–219, 2013
https://doi.org/10.5194/npg-20-213-2013

Special issue: Nonlinear dynamics of the coastal zone

Nonlin. Processes Geophys., 20, 213–219, 2013
https://doi.org/10.5194/npg-20-213-2013

Research article 14 Mar 2013

Research article | 14 Mar 2013

Derivation of Boussinesq's shoaling law using a coupled BBM system

H. Kalisch and A. Senthilkumar H. Kalisch and A. Senthilkumar
  • Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway

Abstract. This paper is focused on finding rules for waveheight change in a solitary wave as it runs up a slowly increasing bottom. A coupled BBM system is used to describe the solitary waves. Expressions for energy density and energy flux associated with the BBM system are derived, and the principle of energy conservation is used to develop an equation relating the waveheight and undisturbed depth to the initial undisturbed depth and the incident waveheight. In the limit of zero waveheight, Boussinesq's shoaling law is recovered.