Ship wakes: Kelvin or Mach angle?

TL;DR

This paper reveals that ship wake angles decrease with increasing speed following a Mach-like regime, challenging the classical Kelvin prediction of a constant wake angle, supported by analysis and numerical simulations.

Contribution

It introduces a model explaining the transition from Kelvin to Mach regimes in ship wakes based on finite disturbance size and Froude number analysis.

Findings

Wake angles decrease as U^{-1} at high velocities.

Transition between Kelvin and Mach regimes occurs at Froude number ~0.5.

Numerical simulations confirm the proposed model.

Abstract

From the analysis of a set of airborne images of ship wakes, we show that the wake angles decrease as $U^{-1}$ at large velocities, in a way similar to the Mach cone for supersonic airplanes. This previously unnoticed Mach-like regime is in contradiction with the celebrated Kelvin prediction of a constant angle of $19.47\degree$ independent of the ship's speed. We propose here a model, confirmed by numerical simulations, in which the finite size of the disturbance explains this transition between the Kelvin and Mach regimes at a Froude number $Fr = U/\sqrt{gL} \simeq 0.5$, where $L$ is the hull ship length.