SKEWNESS OF THE LARGE-SCALE VELOCITY DIVERGENCE FROM NON-GAUSSIAN INITIAL CONDITIONS

We compute the skewness t(3) and the corresponding hierarchical amplit ude T-3 of the divergence of the velocity field for arbitrary non-Gaus sian initial conditions. We find that T-3 qualitatively resembles the corresponding hierarchical amplitude for the density field, S-3, in th at it contains a term proportional to the initial skewness, which deca ys inversely as the linear growth factor, plus a constant term which d iffers from the corresponding Gaussian term by a complex function of t he initial three- and four-point functions. We extend the results for S-3 and T-3 with non-Gaussian initial conditions to evolved fields smo othed with a spherical top-hat window function. We show that certain l inear combinations, namely S-3 + 1/2T(3), S-3 + T-3 and s(3) + t(3), l ead to expressions which are much simpler, for non-Gaussian initial co nditions, than S-3 and T-3 (or s(3) and t(3)) considered separately.