Analytical Expressions for Stability and Bifurcations of Turret Mooring Systems

Abstract

The eight necessary and sufficient conditions for stability of turret mooring systems (TMS) are derived analytically. Analytical expressions for TMS bifurcation boundaries where static and dynamic loss of stability occur are also derived. These analytical expressions provide physics-based means to evaluate the stability properties of TMS, find elementary singularities, and describe the morphogeneses occurring as a parameter (or design variable) or group of parameters are varied. They eliminate the need to compute numerically the TMS eigenvalues. Analytical results are verified by comparison to numerical results generated by direct computation of eigenvalues and their bifurcations. Catastrophe sets (design charts) are constructed in the two-dimensional parametric design space to show the dependence of design variables on the stability of the system. The TMS mathematical model consists of the nonlinear horizontal plane—surge, sway and yaw—fifth-order, large drift, low speed maneuvering equations. Mooring lines are modeled quasistatically by catenaries. External excitation consists of time independent current, steady wind, and second-order mean drift forces.