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).
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