Fourier Transforms when used in the fluid turbulence theory and analysis can be thought of as a decomposition of the flow into eddies of a spectrum of sizes. He

Fourier Transforms when used in the fluid turbulence theory and analysis can be thought of as a decomposition of the flow into eddies of a spectrum of sizes. Here the Fourier variable is length not time and the wavelength of a Fourier component defines the size of and eddy in the decomposition, the amplitude of the Fourier component defines the amount of kinetic energy in an eddy and the cutoff wavelength of the eddy decomposition is related to the viscosity of the flow. The problem to be solved by Fluid Turbulence Theory is to understand the transfer of energy over time between the eddies representing the flow field as defined by the Fourier representation of the Navier-Stokes Equation. Your are correct to note that the interpretation of a Fourier series has a great variance and can become quite abstract.