  Decaying three-dimensional (3D) turbulence is studied via direct numerical
simulations (DNS) for an isotropic non-rotating flow and for rotating flows
with and without helicity. We analyze the cases of moderate Rossby number and
large Reynolds number focusing on the behavior of the energy spectrum at large
scales and studying its effect on the time evolution of the energy and integral
scales for $E(k) \sim k^4$ initial conditions. In the non-rotating case we
observe the classical energy decay rate $t^{-10/7}$ and a growth of the
integral length proportional to $t^{2/7}$ in agreement with the prediction
obtained assuming conservation of the Loitsyanski integral. In the presence of
rotation we observe a decoupling in the decay of the modes perpendicular to the
rotation axis from the remaining 3D modes. These slow modes show a behavior
similar to that found in two-dimensional (2D) turbulence whereas the 3D modes
decay as in the isotropic case. We phenomenologically explain the decay
considering integral conserved quantities that depend on the large scale
anisotropic spectrum. The decoupling of modes is also observed for a flow with
a net amount of helicity. In this case, the 3D modes decay as an isotropic
fluid with a constant, constrained integral length, and the 2D modes decay as a
constrained rotating fluid with maximum helicity.
