Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon

TL;DR

This paper develops and analyzes nonlinear asymptotic models for internal wave generation by moving ships in stratified fluids, providing insights into the dead-water phenomenon and its impact on ship drag.

Contribution

It introduces rigorously justified asymptotic models for internal waves in stratified fluids and analyzes their behavior to explain the dead-water effect.

Findings

Models accurately predict internal wave patterns.

Dead-water effect significantly increases drag under certain conditions.

Theoretical and numerical results align with observed phenomena.

Abstract

This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a disturbance moving at constant speed on top of two layers of fluids of different densities. Starting from the full Euler equations, we present several nonlinear asymptotic models, in the long wave regime. These models are rigorously justified by consistency or convergence results. A careful theoretical and numerical analysis is then provided, in order to predict the behavior of the flow and in which situations the dead-water effect appears.