A note on the imaginary part of bispectra

Abstract

Asymmetric wave forms caused by non-linear secondary forced waves are suggested to have a close relationship with the imaginary part of bispectra; waves tilted forward are likely to be associated with negative imaginary parts. As waves of asymmetric forms due to non-linearity are found in various fields of physics, the present interpretation of the imaginary part of bispectra has a wide range of possible applications. By way of example two theoretical models of complex bispectra are proposed for gravity waves in deep water; temporal anisotropy is explicitly introduced by (a) Rayleigh drag and (b) Miles' mechanism. In either case the ratio of the imaginary to real parts is shown to be of the order of the decay or growth rate normalized by the characteristic frequency.