The stable clustering hypothesis is a key analytical anchor on the nonlinear dynamics of gravitational clustering in cosmology .
It states that on sufficiently small scales the mean pair velocity approaches zero , or equivalently , that the mean number of neighbours of a particle remains constant in time at a given physical separation .
N-body simulations have only recently achieved sufficient resolution to probe the regime of correlation function amplitudes \xi \sim 100 - 10 ^ { 4 } in which stable clustering might be valid .
In this paper we use N-body simulations of scale free spectra P ( k ) \propto k ^ { n } with -2 \leq n \leq 0 and of the CDM spectrum to apply two tests for stable clustering : the time evolution and shape of \xi ( x,t ) , and the mean pair velocity on small scales .
We solve the pair conservation equation to measure the mean pair velocity , as it provides a more accurate estimate from the simulation data .
For all spectra the results are consistent with the stable clustering predictions on the smallest scales probed , x < 0.07 x _ { nl } ( t ) , where x _ { nl } ( t ) is the correlation length .
The measured stable clustering regime corresponds to a typical range of 200 \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } \xi \lower 2.15 pt \hbox { $ % \buildrel < \over { \sim } $ } 2000 , though spectra with more small scale power ( n \simeq 0 ) approach the stable clustering asymptote at larger values of \xi .

We test the amplitude of \xi predicted by the analytical model of Sheth & Jain ( 1996 ) , and find agreement to within 20 \% in the stable clustering regime for nearly all spectra .
For the CDM spectrum the nonlinear \xi is accurately approximated by this model with n \simeq - 2 on physical scales \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 100 - 300 h ^ { -1 } { kpc } for \sigma _ { 8 } = 0.5 - 1 , and on smaller scales at earlier times .
The growth of \xi for CDM-like models is discussed in the context of a power law parameterization often used to describe galaxy clustering at high redshifts .
The growth parameter \epsilon is computed as a function of time and length scale , and found to be larger than 1 in the moderately nonlinear regime – thus the growth of \xi is much faster on scales of interest than is commonly assumed .