Pitchfork bifurcations and dive plane reversal of submarines at low speeds

Abstract

The ability of a submarine to maintain ordered depth, especially during periscope depth operations at low speeds, is vital for the vessel to perform its mission and avoid detection. Modern submarines exhibit an inherent phenomenon that produces an undesirable ship response at low speeds, commonly referred to as dive plane reversal. The physical parameters that govern this occurrence are related in this thesis to the problem of multiple steady state solutions in the vertical plane. Generic solution branching, in the form of pitchfork bifurcations, can occur when the nominal level flight path loses its stability. A systematic study reveals the existence of a critical Froude number, based on the vessel's speed and metacentric height, where this branching occurs. Bifurcation theory techniques and numerical computations are utilized to classify the effect that geometric parameters, trim and ballast conditions, and hydrodynamic properties have on the existence of these multiple solutions