Equilibrium configurations of line arrays with respect to the deviatoric mean drift forces

Abstract

Monochromatic waves incident on an array of structures give rise to nonlinear, time-constant mean drift forces (MDFs). These forces depend on the array's spatial configuration; their magnitude and the direction is, in general, different for every structure in the array. If the spatial configuration of an array is not fixed, as is the case in arrays of individually anchor-moored structures, the time-constant differences in MDF on individual bodies can lead to a change in spatial configuration, which could, in turn, significantly affect both the first-order, time-harmonic response of the array, as well as the downwave component of the MDF. Here, we explore the dependency of these deviatoric forces on array configurations and on the frequency of the incident monochromatic waves. We consider configurations of line arrays (consisting of 2–5 vertical circular cylinders) that are described by 1 or 2 parameters, and we focus on the along-array component of deviatoric forces. Using multiple scattering computational simulations, we identify the array configurations in which the deviatoric drift forces are zero, and we discuss the stability of these equilibrium configurations with respect to class-preserving configuration perturbations. Both stable and unstable equilibria exist, but the relative number of unstable equilibria grows as the number of degrees of freedom of the configuration perturbations increases. Interestingly, the stable configurations experience a generally lower downwave mean drift force on the entire array than the unstable ones. Overall, the variations in the deviatoric and the downwave MDFs between equilibria are significant (on the order of the isolated body MDF).