A theoretical framework for robust implementation of in situ measurements of ocean currents and waves in dynamics of mooring systems

Abstract

We develop an approximated method to solve analytically the equations of motion that describe mooring line dynamics in a one-dimensional model. For the first time, we derive integral closed-form expressions to compute dynamic properties of mooring lines subject to ocean currents and waves of arbitrary time and spatial dependence, in terms of modified Bessel functions. This is done by decomposing the mooring line in three regions where different approximations and mathematical techniques of solution are carried out. Our analytical results provide a robust framework to simulate and analyze extreme realistic oceanic events when data from in situ ocean observation systems are available, regardless of the resolution or coarseness of subsurface measurements and even for long acquisition times. In order to prove the advantages of this approach, we have processed data from two stations in the National Data Buoy Center of the National Oceanic and Atmospheric Administration. From simulations with ocean currents data, we have gained insights into the coupling of the spatial modulation of ocean currents with the characteristic wavelengths of elastic lines. From simulations with ocean waves data, we have defined a scheme to analyze wave data and identify the contribution of each subset of frequency peaks to the net fluctuation of mooring line tension. This could be useful for classification of irregular waves based on their impact on mooring line tension. The development of better tools that integrate theoretical and experimental findings is necessary for the assessment of marine structures under the environmental conditions associated with climate change.