Skewness of the large-scale velocity divergence from non-Gaussian initial conditions

We compute the skewness t3 and the corresponding hierarchical amplitude T3 of the divergence of the velocity field for arbitrary non-Gaussian initial conditions. We find that T3 qualitatively resembles the corresponding hierarchical amplitude for the density field, S3, in that it contains a term proportional to the initial skewness, which decays inversely as the linear growth factor, plus a constant term which differs from the corresponding Gaussian term by a complex function of the initial three- and four-point functions. We extend the results for S3 and T3 with non-Gaussian initial conditions to evolved fields smoothed with a spherical top-hat window function. We show that certain linear combinations, namely S3 + 1/2T3, S3 + T3and s3 +t3, lead to expressions which are much simpler, for non-Gaussian initial conditions, than S3 and T3 (or s3 and t3) considered separately.