Capillary-Gravity Waves on Depth-Dependent Currents: Consequences for the Wave Resistance

TL;DR

This paper develops a theoretical framework to analyze how depth-dependent currents influence capillary-gravity wave resistance at the water-air interface, with implications for understanding wave-current interactions.

Contribution

It derives a general expression for wave resistance in the presence of depth-dependent currents under linear wave theory, focusing on inviscid fluids.

Findings

Wave resistance depends on the current profile and wave parameters.

Linear current approximation is valid for certain wind-generated currents.

Theoretical insights into wave-current interaction mechanisms.

Abstract

We study theoretically the capillary-gravity waves created at the water-air interface by a small two-dimensional perturbation when a depth-dependent current is initially present in the fluid. Assuming linear wave theory, we derive a general expression of the wave resistance experienced by the perturbation as a function of the current profile in the case of an inviscid fluid. We then analyze and discuss in details the behavior of the wave resistance in the particular case of a linear current, a valid approximation for some wind generated currents.