Numerical Analyses of Weakly Nonlinear Velocity-Density Coupling

We study evolution of various statistical quantities of smoothed cosmic density and velocity fields using N-body simulations. The parameter C ≡ 〈V 2δ〉 /(〈V 2〉 〈δ2〉) characterizes nonlinear coupling of these two fields and determines behavior of bulk velocity dispersion as a function of local density contrast. It is found that this parameter depends strongly on the smoothing scale even in quasi-linear regimes where the skewness parameter S3 ≡ 〈 δ3 〉 / 〈 δ2 〉2 is nearly constant and close to the predicted value by the second-order perturbation theory. We also analyze weakly nonlinear effects caused by an adaptive smoothing known as the gather approach.