Boussinesq-type equations with improved nonlinear performance

In this paper, we derive and test a set of extended Boussinesq equations with improved nonlinear performance. To do this, the concept of a reference elevation is further generalised to include a time-varying component that moves with the instantaneous free surface. It is found that, when compared to Stokes-type expansions of the second harmonic and fully nonlinear potential flow computations, both theoretical and practical nonlinear performance can be considerably improved. Finally, a special case of the extended equations is found to have properties which are invariant with respect to the still water datum. © 2001 Elsevier Science B.V. All rights reserved.