Space-time energy spectra in turbulent shear flows

This article presents a review and perspectives on the models for space-time energy spectra in turbulent shear flows. 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 stochastic dynamic models for reproduction of space-time energy spectra, such as dynamic autoregression model, are discussed; and the statistical models for reconstruction of space-time energy spectra from incomplete data sets in experimental measurements are revisited. We present three distinct approaches of successive approximation for developing the models of space-time energy spectra and use the conditional moments of energy distribution to characterize space-time energy spectra, such as propagation velocities and spectral bandwidths