Rotary Cross-Bispectra and Energy Transfer Functions Between Non-Gaussian Vector Processes I. Development and Example

Abstract

Bispectrum and cross-bispectrum analyses of the rotary components of stationary random vector processes are more easily interpreted than similar analyses of their scalar components, and have the advantage that the bispectral estimates are invariant to coordinate rotation. Application to some wind-ocean current data shows these to be non-Gaussian and subject to significant nonlinear coupling over a wide range of interacting triplets of rotary components. A set of complex-valued energy transfer functions are developed by which the magnitudes of the linear and quadratic interactions may be compared.