  The behaviour of turbulent flows within the single-layer quasi-geostrophic
(Charney--Hasegawa--Mima) model is shown to be strongly dependent on the Rossby
deformation wavenumber $\lambda$ (or free-surface elasticity). Herein, we
derive a bound on the inverse energy transfer, specifically on the growth rate
$\d\ell/\dt$ of the characteristic length scale $\ell$ representing the energy
centroid. It is found that $\d\ell/\dt\le2\norm q_\infty/(\ell_s\lambda^2)$,
where $\norm q_\infty$ is the supremum of the potential vorticity and $\ell_s$
represents the potential enstrophy centroid of the reservoir, both invariant.
This result implies that in the potential energy dominated regime
($\ell\ge\ell_s\gg\lambda^{-1}$), the inverse energy transfer is strongly
impeded, in the sense that under the usual time scale no significant transfer
of energy to larger scales occurs. The physical implication is that the
elasticity of the free surface impedes turbulent energy transfer in wavenumber
space, effectively rendering large-scale vortices long-lived and inactive.
Results from numerical simulations of forced-dissipative turbulence confirm
this prediction.
