Modeling short sea wave energy distributions in the far wakes of ships

Abstract

A mathematical model based on the spectral energy balance equation for suppression of shortwave energy in centerline ship wakes is developed. At distances behind a ship of more than a few ship lengths, the dominant influences on short wave energy are the growing effects of wind and nonlinear energy transfer from longer waves, and the attenuating effects of turbulence and viscous attenuation which can be greatly enhanced by surface film distributions which are modified by passage of the ship. These influences are modeled as “source terms” in the energy balance equation. The model is exercised using turbulence data from scale model experiments and surface film distributions measured in an actual ship wake. Agreement between the resulting distribution of Bragg‐scattering wave energy and radar image intensity in the far wake is excellent. The influences of variations in the source term model parameters are explored numerically.