  Pulsar glitches offer an insight into the dynamics of superfluids in the high
density interior of a neutron star. To model these phenomena, however, one
needs to have an understanding of the dynamics of a turbulent array of
superfluid vortices moving through a pinning lattice. In this paper we develop
a theoretical approach to describe vortex mediated mutual friction in a pinned,
turbulent and rotating superfluid. Our model is then applied to the study of
the post glitch rotational evolution in the Vela pulsar and in PSR J0537-6910.
We show that in both cases a turbulent model fits the evolution of the spin
frequency derivative better than a laminar one. We also predict that the second
derivative of the frequency after a glitch should be correlated with the
waiting time since the previous glitch, which we find to be consistent with
observational data for these pulsars. The main conclusion of this paper is that
in the post-glitch rotational evolution of these two pulsars we are most likely
observing the response to the glitch of a pinned turbulent region of the star
(possibly the crust) and not the laminar response of a regular straight vortex
array.
