TRANSFER OF POWER IN NONLINEAR GRAVITATIONAL CLUSTERING

We investigate the transfer of power between different scales and the coupling of modes during the non-linear evolution of gravitational clu stering in an expanding universe. We start with a power spectrum of de nsity fluctuations that is exponentially damped outside a narrow range of scales, and use numerical simulations to study the evolution of th is power spectrum. Non-linear effects generate power at other scales, with most power flowing from larger to smaller scales. The 'cascade' o f power leads to equipartition of energy at smaller scales, implying a power spectrum with index n approximate to -1. We find that such a sp ectrum is produced in the range 1 < delta < 200 for density contrast d elta. This result continues to hold even when small-scale power is add ed to the initial power spectrum. Semi-analytic models for gravitation al clustering suggest a tendency for the effective index to move towar ds a critical index n(c) approximate to -1 in this range. For n < n(c) , power in this range grows faster than linear rate, while if n > n(c) , it grows at a slower rate - thereby changing the index closer to n(c ). At scales larger than the narrow range of scales with initial power , a k(4) tail is produced. We demonstrate that non-linear small scales do not affect the growth of perturbations at larger scales.