A New Parametric Definition of Wave Energy

Abstract

The global kinetic energy of regular waves is usually characterized through wave parameters,namely height and wave length, without reference to its vertical distribution. A newmethodology to evaluate the vertical energy distribution from the velocity components wasdeveloped (Taveira Pinto and Silva, 2006). The squared velocity components functions foreach depth level may be theoretically calculated or determined from long enoughmeasurements time series. The average of those functions at one specific depth level over thelength of interest gives the mean horizontal and vertical specific kinetic energy at that level. Inthis paper, this new methodology to evaluate the vertical energy distribution from the velocitycomponents is applied to irregular wave fields, to which the traditional method in theevaluation of the energy per unit area or wave length is not applicable. The theoreticalgeneralization is based on Fourier series expansion of the surface elevation which is extendedto the velocity potential, as predicted by their relation, given by the small-amplitude wavetheory. From the velocity potential the generalized velocity components at each depth levelmay also be calculated. Numerically simulated specific kinetic energy profiles using theFourier approximation and corresponding values calculated from measured velocitycomponents for irregular wave fields are presented.