  In this paper we investigate the properties of rapidly rotating decaying
turbulence using numerical simulations and phenomenological modelling. We find
that as the turbulent flow evolves in time, the Rossby number decreases to
$\sim 10^{-3}$, and the flow becomes quasi-two-dimensional with strong coherent
columnar structures arising due to the inverse cascade of energy. We establish
that a major fraction of energy is confined in Fourier modes $(\pm1,0,0)$ and
$(0,\pm1,0)$ that correspond to the largest columnar structure in the flow. For
wavenumbers ($k$) greater than the enstrophy dissipation wavenumber ($k_d$),
our phenomenological arguments and numerical study show that the enstrophy flux
and spectrum of a horizontal cross-section perpendicular to the axis of
rotation are given by $\epsilon_\omega\exp(-C(k/k_d)^2)$ and
$C\epsilon_\omega^{2/3}k^{-1}\exp(-C(k/k_d)^2)$ respectively; for this 2D flow,
$\epsilon_\omega$ is the enstrophy dissipation rate, and $C$ is a constant.
Using these results, we propose a new form for the energy spectrum of rapidly
rotating decaying turbulence:
$E(k)=C\epsilon_\omega^{2/3}k^{-3}\exp(-C(k/k_d)^2)$. This model of the energy
spectrum is based on wavenumber-dependent enstrophy flux, and it deviates
significantly from power law energy spectrum reported earlier.
