Kadomtsev–Petviashvili type equation for entire range of relative water depths

ABSTRACT

A Kadomtsev–Petviashvili type equation valid for the entire range of relative water depths; namely, shallow, intermediate, and deep, is derived. The new equation is capable of simulating the shallow water cnoidal waves and the deep water second-order Stokes waves equally well besides accounting for wave shoaling due to varying water depths. Linear shoaling properties of the equation for unidirectional sinusoidal waves are in complete agreement with the energy flux concept. A finite-difference scheme is adopted for numerical solution of the equation to demonstrate its performance against test cases and its wide range of possible applications.

KEYWORDS:

• Kadomtsev–Petviashvili type equation
• cnoidal waves and Stokes waves
• arbitrary relative depths
• varying bathymetry

Disclosure statement

No potential conflict of interest was reported by the author.