Estimation of wavenumber and frequency spectra using fixed probe pairs

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Abstract
We introduce the concept of the local wavenumber and frequency spectral density, which can be estimated using spatially fixed, point data sources (’’fixed probe pairs’’), and discuss the relationship of this spectral density to the conventional wavenumber and frequency spectral density and the cross‐power spectral density. The local wavenumber and frequency spectral density is shown to be equivalent to the conventional wavenumber and frequency spectral density when the fluctuation is stationary and homogeneous and consists of a superposition of wave packets; such a fluctuation is the basic model used in many turbulence theories. A digital method for estimating the local wavenumber spectrum is described and applied to the study of drift‐wave turbulence in an rf‐excited discharge. The statistical dispersion relation and wavenumber spectral width, computed from the local wavenumber and frequency spectrum of the drift‐wave turbulence, are compared with the conventional spectral moments computed using the correlation method of Iwama and Tsukishima; good agreement is found over a wide range of frequency. A frequency‐integrated wavenumber spectrum is computed; both frequency and wavenumber spectral indices are found independently. The local wavenumber and frequency spectrum is a completely new approach to the use of fixed‐probe data, and we believe it can greatly extend the quantity of information available from fixed probes, which are the principle tools in many, if not most, fluctuation experiments.