Space-time energy spectra for turbulence shear flows

A space-time (frequency-wavenumber) energy spectrum describes the energy distribution of velocity fluctuations over a broad range of spatial and temporal length scales. It not only characterizes dynamic coupling between spatial and temporal scales in turbulent flows but also plays a key role in turbulence-generated noise. In this lecture, our recent work is introduced on space-time energy spectra and its application to turbulence-generated noise. The Taylor, Kraichnan-Tennekes, and elliptic approximation (EA) models are re-examined in terms of the picture of turbulent passage, which is proposed by Taylor's frozen-flow hypothesis and the Kraichnan-Tennekes random sweeping hypothesis; The composite resolvent operators are developed for space-time energy spectra; the large-eddy simulation for frequency spectra is used to study the noise radiated by turbulent flows around an axisymmetric body of revolution.