On periodic water waves with Coriolis effects and isobaric streamlines

TL;DR

This paper proves that certain equatorial deep water waves with constant pressure along streamlines are of Gerstner type and shows that only laminar solutions exist over flat beds under these conditions.

Contribution

It establishes the specific form of solutions for geophysical deep water waves with Coriolis effects and constant pressure along streamlines, extending understanding of wave structures.

Findings

Solutions with no stagnation points are Gerstner-type waves.

Over flat beds, only laminar flow solutions meet the criteria.

Pressure remains constant along streamlines in these solutions.

Abstract

In this paper we prove that solutions of the f-plane approximation for equatorial geophysical deep water waves, which have the property that the pressure is constant along the streamlines and do not possess stagnation points,are Gerstner-type waves. Furthermore, for waves traveling over a flat bed, we prove that there are only laminar flow solutions with these properties.