Self-consistent theory of capillary-wave generation by small moving objects

TL;DR

This paper develops a theoretical framework to understand how small objects moving at the water-air interface generate capillary waves, revealing that flow regularization leads to a continuous wave drag transition near critical velocities.

Contribution

The study introduces a refined linear response theory that accounts for flow regularization, resolving the singular behavior predicted by simpler models and aligning with experimental observations.

Findings

Flow regularization ensures continuous wave drag behavior.

Linear response theory can predict smooth wave emission transition.

The model aligns with experimental data on wave generation.

Abstract

We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity $c_\text{min} = 23 {\rm cm/s}$. At higher velocities the emission of capillary-gravity waves creates an additional drag force. The behavior of this force near the critical velocity is still poorly understood. A linear response theory where the object is replaced by an effective pressure source predicts a singular behavior for the wave drag. However, experimental data tends to indicate a more continuous transition. In this article, we show that a proper treatment of the flow equations around the obstacle can regularize wave emission, even in the linear wave approximation, thereby ensuring a continuous behavior of the drag force.