Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway
Received: 30 Nov 2012 – Revised: 17 Feb 2013 – Accepted: 20 Feb 2013 – Published: 14 Mar 2013
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.
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.