Submerged marine towed instrument array: A theoretical investigation using Lagrange mechanics

Abstract

Towed instrument arrays (TIA) measure physical data in the ocean surface boundary layer (OSBL). The TIA consists of probes mounted on a cable and towed behind a vessel. The comparably low interpolation errors of the two-dimensional results vastly enrich research on ocean energy dissipation. Here, we develop a new theoretical framework considering the mounted probes and their effects on the dynamics of the TIA in analogy to multiple pendulums on a moving suspension point. The dynamics are induced by external velocity-dependent drag- and coordinate-dependent depressor forces. We show that our method of including nonlinear drag forces is consistent and that our discrete approach is capable of computing continuous solutions in the limit . Hence, the proposed method unifies earlier approaches and is tested against several analytical and known numerical solutions. The phase space for the case is similar to that of a damped harmonic oscillator. A typical timescale estimates the equilibrium state of the dynamical system. We provide evidence of our method by comparing the results with real measurement data. Based on the theoretical investigations, test cases, and the comparison with real data, our method is a powerful tool, suitable for campaign planning, instrument design, and post-processing purposes.