  The degree of turbulent pressure support by residual gas motions in galaxy
clusters is not well known. Mass modelling of combined X-ray and Sunyaev
Zel'dovich observations provides an estimate of turbulent pressure support in
the outer regions of several galaxy clusters. Here, we test two different
filtering techniques to disentangle bulk from turbulent motions in
non-radiative high-resolution cosmological simulations of galaxy clusters using
the cosmological hydro code ENZO. We find that the radial behavior of the ratio
of non-thermal pressure to total gas pressure as a function of cluster-centric
distance can be described by a simple polynomial function. The typical
non-thermal pressure support in the centre of clusters is $\sim$5%, increasing
to $\sim$15% in the outskirts, in line with the pressure excess found in recent
X-ray observations. While the complex dynamics of the ICM makes it impossible
to reconstruct a simple correlation between turbulent motions and hydrostatic
bias, we find that a relation between them can be established using the median
properties of a sample of objects. Moreover, we estimate the contribution of
radial accelerations to the non-thermal pressure support and conclude that it
decreases moving outwards from 40% (in the core) to 15% (in the cluster's
outskirts). Adding this contribution to one provided by turbulence, we show
that it might account for the entire observed hydrostatic bias in the innermost
regions of the clusters, and for less than 80% of it at $r > 0.8 r_{200, m}$.
