Free surface water-waves generated by instability of an exponential shear flow

2023/05/19 by Abid, Malek, Kharif, Christian
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.2305.11983

Abstract

The stability of an exponential current in water to infinitesimal perturbations in the presence of gravity and capillarity is investigated. Some new results on the generation of gravity-capillary waves are presented which supplement the previous works of Morland, Saffman & Yuen (1991) and Young & Wolfe (2014), namely in finite depth. To consider perturbations of much larger scales, a specific attention is paid to the stability of the exponential current only in the presence of gravity.

Related

• Existence of capillary-gravity waves that are perturbations of Crapper's waves
• Smooth stationary water waves with exponentially localized vorticity
• Time-dependent nonlinear gravity-capillary surface waves with viscous dissipation and wind forcing
• Unstable surface waves in running water
• Nonlinear viscous gravity-capillary surface waves at arbitrary wavelengths