What is the apparent angle of a Kelvin ship wave pattern?

TL;DR

This paper investigates how the apparent wake angle of ship waves varies with speed and nonlinearity, revealing regimes where the angle is less than, equal to, or greater than Kelvin's classical 19.47 degrees, with implications for real-world ship wakes.

Contribution

It introduces a detailed analysis of apparent wake angles in linear and nonlinear flows, showing nonlinearity can increase the wake angle beyond Kelvin's limit and identifying different flow regimes based on Froude number.

Findings

Apparent wake angle decreases with ship speed in linear models.

Nonlinearity can increase the apparent wake angle beyond Kelvin's classical value.

Different flow regimes are identified based on Froude number and wave peak locations.

Abstract

While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47 degrees, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.