Fine-structure of energy spectra of velocity fluctuations in the transition region of a two-dimensional wake

Abstract

Measurements of the fine-structure of the energy spectrum of the velocity fluctuations were made in the transition region of a two-dimensional wake. Line and continuous spectra were determined separately with a high-selectivity band-pass filter. The transition was initiated by an external sinusoidal sound. The sound-induced periodic fluctuation and the natural random fluctuation in the wake were added and a system of line and continuous spectra was formed. Higher harmonics of the periodic component were produced by the nonlinear interaction. As a result of the interaction between discrete and continuous components, a continuous spectrum was generated at low wavenumbers. A simple model for the interaction is proposed. The evolution of the spectrum is explained by three fundamental rules concerning the nonlinear interaction between spectral components: (i) the growth of a spectral component is suppressed by the presence of another strong component, (ii) mutual interaction is more effective when the amplitudes of interacting components are closer, and (iii) a stronger interaction takes place between components of closer wavenumbers. The randomization of the regular fluctuation is properly expressed as the growth of the ‘randomness factor’, the ratio of the energy of the random components to the total fluctuation energy.