  For a Z-pinch geometry, we report on the nonlinear redistribution of free
energy across scales perpendicular to the magnetic guide field, for a turbulent
plasma described in the framework of gyrokinetics. The analysis is performed
using a local flux-surface approximation, in a regime dominated by
electrostatic fluctuations driven by the entropy mode, with both ion and
electron species being treated kinetically. To explore the anisotropic nature
of the free energy redistribution caused by the emergence of zonal flows, we
use a polar coordinate representation for the field-perpendicular directions
and define an angular density for the scale flux. Positive values for the
classically defined (angle integrated) scale flux, which denote a direct energy
cascade, are shown to be also composed of negative angular sections, a fact
that impacts our understanding of the backscatter of energy and the way in
which it enters the modeling of sub-grid scales for turbulence. A definition
for the flux of free energy across each perpendicular direction is introduced
as well, which shows that the redistribution of energy in the presence of zonal
flows is highly anisotropic.
