Ocean current prediction in towed cable hydrodynamics under dynamic steering

Abstract

This article considers the problem of reconstructing the velocities of ocean currents impinging on a towed streamer cable sparsely equipped with steering elements (SE). The study is based on a two-dimensional model describing the quasi-steady motion of the towed cable in the presence of hydrodynamic drag and steering forces that depend nonlinearly on the angle of attack. To derive the proposed methodology we first outline the hydrodynamic equations used in solving the forward problem by which the cable's velocity, curvature and tension are obtained in the knowledge of the towing vessel's motion, the ocean current velocities and the drag coefficient characteristics of the SE. In sequence, we formulate the inverse problem of inferring the ocean velocities using a finite set of noise-infused positioning and tension measurements showing that this is nonlinear and ill-posed. To solve the inverse problem we adopt Newton's scheme for nonlinear convex problems in conjunction with generalized Tikhonov regularization. The problem under consideration bares significant differences from the linear non-steered formulation addressed in (N. Polydorides, E. Storteig and W. Lionheart, 2007, Forward and inverse problems in towed cable hydrodynamics, Ocean Engineering 35 (2008)), due to the nonlinearity in the forward method as well as the discontinuities observed in the forward measurements due to the steering forces. A series of numerical simulation studies is subsequently presented in order to demonstrate the practical performance of the proposed technique in reconstructing the ocean currents velocity profile and angle of attack.