A Transformation relating temporal and spatial spectra of turbulent kinetic energy

Book excerpt: A transformation is developed, based upon the scale dependence of turbulent diffusion, that relates temporal and spatial spectra of turbulent kinetic energy. The basic idea is that an eddy diffusivity is appropriate when scales of the flow smaller than a length e and a time tare unresolved. An expression similar to Heisenberg's for eddy diffusivity is used to obtain the connection between e and t necessary to transform temporal spectra into spatial spectra. This transformation reveals a close connection between Webster's Site D spectrum of turbulent kinetic energy in the ocean and Okubo's diagrams of oceanic mixing. Furthermore, all spectra obtained from dimensional arguments satisfy this transformation.