Trapped waves generated by an accelerated moving disturbance for the Whitham equation

Abstract

In this work, we study numerically the generation of trapped waves excited by the passage of an accelerated moving disturbance along the free surface using the forced Whitham equation as a model. We show that in certain regimes trapped waves are spontaneously generated from rest and find that its time of escape increases with the amplitude of the disturbance in a band. Besides, when solitary waves are taken as initial data, we observe that when the moving disturbance changes its direction, the amplitude of this wave decays oscillating with time until it eventually escapes out. On the other hand when the moving disturbance maintains its direction the amplitude of the trapped wave increases until it escapes out and travels as a solitary wave.

Keywords

• Whitham equation
• Trapped waves
• Solitary waves