  We present a simple physically motivated picture for the mildly non-linear
regime of structure formation, which captures the effects of the bulk flows. We
apply this picture to develop a method to significantly reduce the sample
variance in cosmological N-body simulations at the scales relevant to the
Baryon Acoustic Oscillations (BAO). The results presented in this paper will
allow for a speed-up of an order of magnitude (or more) in the scanning of the
cosmological parameter space using N-body simulations for studies which require
a good handle of the mildly non-linear regime, such as those targeting the BAO.
Using this physical picture we develop a simple formula, which allows for the
rapid calculation of the mildly non-linear matter power spectrum to percent
level accuracy, and for robust estimation of the BAO scale.
