  Advective nature of the electrostatic turbulent flux of plasma energy is
studied numerically in a nearly adiabatic state. Such a state is represented by
the Hasegawa-Mima equation that is driven by a noise that may model the
destabilization due to the phase mismatch of the plasma density and the
electric potential. The noise is assumed to be Gaussian and not to be invariant
under reflection along a direction $\hat s$. It is found that the flux density
induced by such noise is anisotropic: While it is random along $\hat s$, it is
not along the perpendicular direction ${\hat s}_\perp$ and the flux is not
diffusive. The renormalized response may be approximated as advective with the
velocity being proportional to $(k\rho_s)^2$ in the Fourier space $\vec k$.
