Wake angle for surface gravity waves on a finite depth fluid

TL;DR

This paper investigates how the apparent wake angle behind a disturbance in a finite-depth fluid varies with the Froude number, revealing differences from classical wedge angles especially in shallow water regimes.

Contribution

It provides new insights into the relationship between apparent wake angles and Froude number in finite-depth water, highlighting differences from classical theories.

Findings

Apparent wake angle depends smoothly on Froude number in moderately deep water.

In shallow water, apparent and wedge angles tend to align, resulting in large wake angles.

The study reveals distinct behaviors of wake angles across different depth regimes.

Abstract

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.