Gravitational collapse in an expanding background and the role of substructure – I. Planar collapse

We study the interplay of clumping at small scales with the collapse and relaxation of perturbations at much larger scales. We present results of our analysis when the large-scale perturbation is modelled as a plane wave. We find that in the absence of substructure, collapse leads to formation of a pancake with multistream regions. Dynamical relaxation of the plane wave is faster in the presence of substructure. Scattering of substructures and the resulting enhancement of transverse motions of haloes in the multistream region lead to a thinner pancake. In turn, collapse of the plane wave leads to formation of more massive collapsed haloes as compared to the collapse of substructure in the absence of the plane wave. The formation of more massive haloes happens without any increase in the total mass in collapsed haloes. A comparison with the Burgers equation approach in the absence of any substructure suggests that the preferred value of effective viscosity depends primarily on the number of streams in a region.