  The interaction of a shock with a cloud has been extensively studied in the
literature, where the effects of magnetic fields, radiative cooling and thermal
conduction have been considered. However, the formation of fully developed
turbulence has often been prevented by the artificial viscosity inherent in
hydrodynamical simulations, and a uniform post-shock flow has been assumed in
all previous single-cloud studies. In reality, the flow behind the shock is
also likely to be turbulent, with non-uniform density, pressure and velocity
structure created as the shock sweeps over inhomogenities upstream of the
cloud. To address these twin issues we use a sub-grid compressible k-epsilon
turbulence model to estimate the properties of the turbulence generated in
shock-cloud interactions and the resulting increase in the transport
coefficients that the turbulence brings. A detailed comparison with the output
from an inviscid hydrodynamical code puts these new results into context.
  We find that cloud destruction in inviscid and k-epsilon models occurs at
roughly the same speed when the post-shock flow is smooth and when the density
contrast between the cloud and inter-cloud medium is less than 100. However,
there are increasing and significant differences as this contrast increases.
Clouds subjected to strong ``buffeting'' by a highly turbulent post-shock
environment are destroyed significantly quicker. Additional calculations with
an inviscid code where the post-shock flow is given random, grid-scale, motions
confirms the more rapid destruction of the cloud.
  Our results clearly show that turbulence plays an important role in
shock-cloud interactions, and that environmental turbulence adds a new
dimension to the parameter space which has hitherto been studied (abridged).
