  Several methods have been proposed to characterize the complex interactions
in turbulent wakes, especially for flows with strong cyclic dynamics. This
paper introduces the concept of Fourier-Averaged Navier-Stokes (FANS) equations
as a framework to obtain direct insights into the dynamics of complex coherent
wake interactions. The method simplifies the interpretations of flow physics by
identifying terms contributing to momentum transport at different timescales.
The method also allows for direct interpretation of non-linear interactions of
the terms in the Navier-Stokes equations. By analysing well-known cases, the
characteristics of FANS are evaluated. Particularly, we focus on physical
interpretation of the terms as they relate to the interactions between modes at
different timescales. Through comparison with established physics and other
methods, FANS is shown to provide insight into the transfer of momentum between
modes by extracting information about the contributing pressure, convective,
and diffusive forces. FANS provides a simply calculated and easily interpreted
set of equations to analyse flow physics by leveraging momentum conservation
principles and Fourier analysis. The method is applicable to flows with complex
cyclic waveforms, including broadband spectral energy distributions.
