QUASI-WAVELET MODEL OF VON KÁRMÁN SPECTRUM OF TURBULENT VELOCITY FLUCTUATIONS

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Abstract

The von Kármán spectra of turbulent temperature and velocity fluctuations have been widely used in the literature on turbulence and electromagnetic, seismic, and acoustic wave propagation in random media. In this paper we provide a phenomenological motivation for the von Kármán velocity spectrum in terms of the quasi-wavelet model of turbulence developed recently. In this model, turbulence is represented as a superposition of self-similar localized eddies of many different scales. We find a functional form for these eddies that yields the von Kármán velocity spectrum exactly. We also show that other eddy functions produce velocity spectra that have the same general form as the von Kármán spectrum, and we consider possible quasi-wavelet representations of the ‘Kansas’ spectrum and the ‘−1’ spectrum. We also present a systematic determination, based on turbulence similarity theories, of the parameters of the von Kármán spectra of temperature and velocity fluctuations in an unstable atmospheric boundary layer.

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