Constant vorticity equatorial flows beneath surface solitary waves with centripetal forces

Abstract

In this paper, we consider equatorial flows with Coriolis and centripetal forces, with constant vorticity beneath a two-dimensional solitary wave and above a flat bed in the $f$-plane approximation equations. We prove that the flow must be steady, two-dimensional, decayed and the vorticity may have only one nonzero component, which points in the horizontal direction orthogonal to the direction of wave propagation. Moreover, based on the vorticity equation and analytical techniques, we prove that the free surface of the flow exhibiting constant horizontal vorticity can only be two-dimensional.

Keywords:

• Constant vorticity
• equatorial flows
• f-plane approximation
• solitary waves
• centripetal forces

2010 Mathematics Subject Classifications:

• Primary: 35Q31
• 35J60
• 76B15

Disclosure statement

No potential conflict of interest was reported by the author(s).