Quasi-wavelet model of von Kármán spectrum of turbulent velocity fluctuations

The von Karman spectra of turbulent temperature andvelocity fluctuations have been widely used in the literature on turbulenceand electromagnetic, seismic, and acoustic wave propagation in random media.In this paper we provide a phenomenological motivation for the vonKarman velocity spectrum in terms of the quasi-wavelet model ofturbulence developed recently. In this model, turbulence is represented as asuperposition of self-similar localized eddies of many different scales. Wefind a functional form for these eddies that yields the von Karman velocity spectrum exactly. We also show that other eddy functions producevelocity spectra that have the same general form as the von Karman spectrum, and we consider possible quasi-wavelet representations of the`Kansas' spectrum and the `-1' spectrum. We also present asystematic determination, based on turbulence similarity theories, of theparameters of the von Karman spectra of temperature and velocityfluctuations in an unstable atmospheric boundary layer.