Fft-length

The lowest wavenumber that one wishes to resolve in a spectrum is determined by the length of the segments of data that are processed by a fast Fourier transform. The lowest wavenumber resolved by a spectrum is the inverse of the length of the fft-segments. This choice is influenced by the (so far mostly unknown) rate of dissipation, statistical reliability, and the length of the vehicle that carries the shear-probe. Very low [math]\displaystyle{ \varepsilon }[/math] values ([math]\displaystyle{ \sim 10^{-10} }[/math] W/kg) require spectra down to 0.5 to 1 cpm. Moderate rates ([math]\displaystyle{ 10^{-8} }[/math] to [math]\displaystyle{ 10^{-7} }[/math] W/kg) require resolutions of [math]\displaystyle{ \sim }[/math]1 cpm, while higher rates require [math]\displaystyle{ \sim }[/math]2 cpm.

A fairly common processing technique is to window each fft segment with a cosine bell and to overlap the segments by 50%. The degrees of freedom (dof) produced by this method is 1.9 times the number of fft segments used to estimate the spectrum. The statistical reliability of a spectrum increases with the number of dof. Thus, the ratio of dissipation length to fft length is also driven by the statistical reliability to one wishes to achieve. As a general rule this ratio should never be less than 2, and a ratio of 5 or larger is highly desirable. Finally, the length of the vehicle that carries the shear probe also sets a lower limit to the wavenumber of shear that can be resolved. The fft-length should never exceed the length of the profiler, unless the profiler is a rigidly fixed platform that is not swayed by the eddies in the flow.

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