  In this paper, we undertake a study to determine what insight can be reliably
gleaned from the comparison of the X-ray and the weak lensing mass maps of
galaxy clusters. We do this by investigating the 2D substructure within three
high-resolution cosmological simulations of galaxy clusters. Our main results
focus on non-radiative gas dynamics, but we also consider the effects of
radiative cooling at high redshift. For our analysis, we use a novel approach,
based on unsharp-masking, to identify substructures in 2D surface mass density
and X-ray surface brightness maps. At full resolution (~ 15 h^-1 kpc), this
technique is capable of identifying almost all self-bound dark matter subhaloes
with M>10^12 h^-1 M_sun. We also report a correlation between the mass of a
subhalo and the area of its corresponding 2D detection; such a correlation,
once calibrated, could provide a useful estimator for substructure mass.
Comparing our 2D mass and X-ray substructures, we find a surprising number of
cases where the matching fails: around one third of galaxy-sized substructures
have no X-ray counterpart. Some interesting cases are also found at larger
masses, in particular the cores of merging clusters where the situation can be
complex. Finally, we degrade our mass maps to what is currently achievable with
weak-lensing observations (~100 h^-1 kpc at z=0.2). While the completeness mass
limit increases by around an order of magnitude, a mass-area correlation
remains. Our paper clearly demonstrates that the next generation of lensing
surveys should start to reveal a wealth of information on cluster substructure.
(Abridged)

Cosmology and Nongalactic Astrophysics