Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Anisotropy is induced by body forces and/or mean large-scale gradients in turbulent flows. For flows without energy production, the dynamics of second-order velocity or second-order vorticity statistics are essentially governed by triple correlations, which are at the origin of the anisotropy that penetrates towards the inertial range, deeply altering the cascade and the eventual dissipation process, with a series of consequences on the evolution of homogeneous turbulence statistics: in the case of rotating turbulence, the anisotropic spectral transfer slaves the multiscale anisotropic energy distribution; nonlinear dynamics are responsible for the linear growth in terms of Ωt of axial integral length-scales; third-order structure functions, derived from velocity triple correlations, exhibit a significant departure from the 4/5 Kolmogorov law. We describe all these implications in detail, starting from the dynamical equations of velocity statistics in Fourier space, which yield third-order correlations at...