Nonlinear motions and dynamic intermittency of planing hulls in random wave fields: A structure-function approach

This paper introduces the concept of dynamic intermittency into engineering-based naval architectural analysis of wave-induced motion of high-speed marine vehicles. The intermittency of wave-induced motions is used to quantify the influence of nonlinearity on deviations in the dynamic response statistics caused by the random wave field from Gaussian behaviour. Planing hulls, known for their highly nonlinear motion and broad application in coastal operations, are selected as the test case. It is hypothesised that their dynamic responses may exhibit dynamic intermittency. To test this, a high-order structure-function is introduced to quantify intermittency numerically. Three distinct planing hulls are simulated in unidirectional random wave fields, and both heave and pitch intermittency are observed. It is demonstrated that resolving timescales shorter than 10 % of the encounter period permits capturing the non-Gaussian behavior of the heave and pitch responses. The intermittency results show that intermittency in heave motion increases with vessel speed and wave steepness. This observed trend is attributed to the greater level of nonlinearity of body hydrodynamics, which becomes more pronounced as these parameters change. Pitch intermittency is also observed and is found to increase with both speed and wave steepness, although it is observed to be less significant than heave intermittency. A comparison of heave and pitch intermittency across different hull forms reveals that a planing surface with a lower deadrise angle exhibits greater intermittency in both heave and pitch responses. The observations presented in this paper demonstrate the importance of considering intermittency when analysing the dynamic responses of high-speed marine vehicles. Hence, it can be concluded that dynamic intermittency has potential applications in the design of safer vessels and ride control systems, and may also contribute to ensuring structural integrity.