Chapter 11 - Phase-Averaging Wave Propagation Array Models

Abstract

Models of wave energy converter (WEC) arrays that use phase-averaged wave propagation models, also called spectral wave models, rely on the conservation of action (energy) density, which propagated across a grid of points. The action density is defined as the spectral energy density divided by the wave frequency and is used (rather than the energy density) because this is conserved in the presence of marine currents; however, they are equivalent in still water. In a spectral wave model the action (energy) density is propagated using linear wave theory, with energy added and removed through source terms. In a standard spectral wave model these source terms include wave breaking, white-capping, bottom friction, wind growth, triad, and quadruplet wave–wave interactions; WECs or wave farms can be added as additional source terms. The WECs or wave farms can be represented using either a supragrid or subgrid model. In a supragrid model the WEC or wave farm is represented as a boundary that spans one or more grid points, with the wave action redistributed based on the characteristics defined by the supragrid model, which is normally defined with reflection, absorption, and transmission coefficients. In a subgrid model each WEC is defined by a single grid point, with the wave action redistributed based on transmission, absorption, and diffraction/radiation coefficients (which may be defined using Kochin functions). Although a phase-averaged wave propagation model can be used to model the interactions between WECs in an array, or to determine the distal effects of a wave farm, a separate model is required to define the characteristics of the supragrid or subgrid model. Thus, these models are best described as hybrid models. Although WEC arrays have been modelled in phase-averaged wave propagation models, there further development is required; in particular, there has been very little validation of these models, which is an area where further work is required.