Envelope, Phase, and Narrow‐Band Models of Sea Waves

Two alternate sets of definitions for the wave envelope and phase which follow from the Rice‐Dugundji and Crandall‐Mark representation of random wave forms are compared. Theoretical constraints implied by these representations, criteria regarding the selection of certain characteristic frequencies, and whether such representations permit generalization to nonlinear models of sea waves are examined in some detail. In particular, the possibility of extending the Rice‐Dungundji representation to nonlinear waves is explored in terms of a simple conceptual model, which can be used to predict some specific effects of nonlinearities on the wave envelope and phase. The theoretical forms of spectra associated with the Rice‐Dugundji envelope and with its various powers are considered in a separate paper.