Derivation of Boussinesq's shoaling law using a coupled BBM system Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway
14 Mar 2013
Received: 30 November 2012 – Revised: 17 February 2013 – Accepted: 20 February 2013 – Published: 14 March 2013Abstract. 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.
Citation: Kalisch, H. and Senthilkumar, A.: Derivation of Boussinesq's shoaling law using a coupled BBM system, Nonlin. Processes Geophys., 20, 213-219, doi:10.5194/npg-20-213-2013, 2013.