The energy cascade in near-field non-homogeneous non-isotropic turbulence

Abstract

We perform particle image velocimetry (PIV) measurements of various terms of the non-homogeneous Kármán–Howarth–Monin equation in the most inhomogeneous and anisotropic region of grid-generated turbulence, the production region which lies between the grid and the peak of turbulence intensity. We use a well-documented fractal grid which is known to magnify the streamwise extent of the production region and abate its turbulence activity. On the centreline around the centre of that region the two-point advection and transport terms are dominant and the production is significant too. It is therefore impossible to apply usual Kolmogorov arguments based on the Kármán–Howarth–Monin equation and resulting dimensional considerations to deduce interscale flux and spectral properties. The interscale energy transfers at this location turn out to be highly anisotropic and consist of a combined forward and inverse cascade in different directions which, when averaged over directions, gives an interscale energy flux that is negative (hence forward cascade on average) and not too far from linear in $r$, the modulus of the separation vector $\boldsymbol{r}$ between two points. The energy spectrum of the streamwise fluctuating component exhibits a well-defined $-5/3$ power law over one decade, even though the streamwise direction is at a small angle to the inverse cascading direction.