On the Determination of Density Profiles in Stratified Seas from Kinematical Patterns of Ship-Induced Internal Waves

Abstract

The aim of this paper is to propose a method for determining the dispersion relation of a highly stratified medium from measured geometrical patterns of ship-generated internal waves. This is a first step towards devising a practical method for calculating the density distribution of a stratified fluid from the detectable free-surface kinematic signature of the induced internal wake, by using some optical or remote sensing means. We assume that the body which causes the wake moves with a constant velocity along a circular trajectory. By applying the constant-phase method, we derive an explicit solution for the wake crest lines. Then, for an infinitely large ship's turning radius (straight course), a closed-form expression for the dispersion relation versus wake geometry is obtained. A similar approximate form is also obtained for a circular course. Some numerical simulations are presented, and the applicability of the proposed method is demonstrated for several realistic thermocline distributions, measured in lakes and seas.