  We derive a reduced model for the electrostatic turbulence in a Tokamak edge,
when dealing with a resistive plasma and neglecting the spatial gradient of the
background density which triggers the linear drift wave response. The obtained
dynamics, de facto equivalent to a Hasegawa-Wakatani model, is characterized by
a constitutive relation between the electric potential Laplacian and the
density, which allows to deal with a single 3D equation governing the electric
potential fluctuations. We study the evolution of the model, by separating the
$n=0$ ($n$ indicating toroidal-like number) mode from all the other ones. Then,
we linearize the dynamics of the $n\neq 0$ modes around the steady 2D spectrum,
which describes the spectral features of the electrostatic 2D turbulence. We
theoretically and numerically demonstrate the existence of decaying branch of
the 3D turbulence, having such a 2D steady spectrum as a natural attractor.
This result suggests that the basic constituent of the self-sustained
non-linear drift response in the plasma edge has to be individualized in the
non-linear 2D electrostatic turbulence.
