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Pressure beneath a periodic travelling water wave in constant-vorticity flow over a flat bed
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DOI：10.1017/jfm.2026.11773.png)
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Abstract
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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 non-zero 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.
Keywords:
surface gravity waves
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