Pressure beneath a periodic travelling water-wave in constant-vorticity flow over a flat bed

TL;DR

This paper analyzes how constant vorticity in water flow affects the distribution of hydrodynamic and dynamic pressures beneath a periodic wave train, revealing significant alterations in pressure extrema locations compared to irrotational flows.

Contribution

It provides a linear theory analysis of pressure behavior in flows with constant vorticity, highlighting the impact of vorticity on pressure extrema locations in water waves.

Findings

Vorticity can shift the location of pressure extrema from wave crests and troughs.

Vorticity does not change the increase of hydrodynamic pressure with depth.

Dynamic pressure extrema may occur along the bed or critical level depending on vorticity.

Abstract

We investigate within the framework of linear theory the behaviour of the total (hydrodynamic) pressure and of the dynamic pressure in a regular wave train which propagates at the surface of water with a flat bed in a flow with constant vorticity. We show that nonzero vorticity, the hallmark of a non-uniform underlying current, may strongly alter the behaviour with respect to the case of irrotational flows, for which the maximum and minimum of the dynamic pressure always occur at the wave crest and at the wave trough, respectively (the extrema of the dynamic pressure may occur along the flat bed or along the critical level, depending on the vorticity strength). While vorticity does not modify the increase of the hydrodynamic pressure with depth, it can significantly alter the location of the extrema of the hydrodynamic pressure at a fixed depth level.