  Experiments and numerical simulations reveal that in the forward cascade
regime, the energy spectrum of two-dimensional turbulence with Ekman friction
deviates from Kraichnan's prediction of $k^{-3}$ power spectrum. In this letter
we explain this observation using an analytic model based on variable enstrophy
flux arising due to Ekman friction. We derive an expression for the enstrophy
flux which exhibits a logarithmic dependence in the inertial range for the
Ekman-friction dominated flows. The energy spectrum obtained using this
enstrophy flux shows a power law scaling for large Reynolds number and small
Ekman friction, but has an exponential behaviour for large Ekman friction and
relatively small Reynolds number.
