Excitation of ship waves by a submerged object: new solution to the classical problem

TL;DR

This paper introduces a novel method for solving ship wave problems caused by submerged objects, providing new analytical solutions and asymptotic expressions for different Froude number regimes.

Contribution

The authors develop a new approach to solve classical ship wave problems, deriving exact and asymptotic solutions for a submerged ball moving at constant speed or oscillating.

Findings

Derived exact solutions involving one-dimensional integrals

Obtained asymptotic expressions for small and large Froude numbers

Described surface wave patterns including Bernoulli hump and Kelvin wedge

Abstract

We have proposed a new method for solving the problem of ship waves excited on the surface of a non-viscous liquid by a submerged object that moves at a variable speed. As a first application of this method, we have obtained a new solution to the classic problem of ship waves generated by a submerged ball that moves rectilinearly with constant velocity parallel to the equilibrium surface of the liquid. For this example, we have derived asymptotic expressions describing the vertical displacement of the liquid surface in the limit of small and large values of the Froude number. The exact solution is presented in the form of two terms, each of which is reduced to one-dimensional integrals. One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As a second example, we considered vertical oscillation of the submerged ball. In this case, the solution leads to the calculation of one-dimensional integral and describes surface waves propagating from the epicenter above the ball.