Insights into the dynamics of cumulative broaching in regular stern-quartering waves

The paper discusses the dynamic instability that is known as cumulative broaching. This is a mechanism of yaw instability of ships in following/quartering seas where a significant deviation from the intended course occurs without observing any precedent surf-riding phenomenon. It is believed that cumulative broaching can occur irrespectively of a vessel's size and for speeds that are not particularly close to the celerity of the encountered wave. Earlier research, based on the linear horizontal-plane ship motion theory, has established that cumulative broaching is triggered by parametric yaw instability. For predicting the inception of parametric yaw, a simple analytical criterion was proposed, and steps were taken towards its validation. In the present study, a nonlinear ship maneuvering model is employed to investigate the dynamics of cumulative broaching, with focus on understanding how the build-up of parametric yaw can lead to the dynamic jump phenomenon associated with broaching. Then, the effect of different environmental or ship parameters towards avoiding such behavior could be assessed. The main investigative tool is a numerical continuation algorithm, effectively combined with the nonlinear surge–sway–yaw ship motions model for regular stern quartering waves. • The nonlinear dynamics of cumulative broaching in regular seas are presented. • A nonlinear surge-sway-yaw mathematical model is employed. • A continuation method is combined with the mathematical model. • A period-doubling and a fold are the key phenomena of cumulative broaching. • Stability diagrams concerning cumulative broaching are presented.