In a serie of three papers, the dynamical interplay between environments and dark matter haloes is investigated, while focussing on the dynamical flows through their virial sphere. Our method relies on both cosmological simulations, to constrain the environments, and an extension to the classical matrix method to derive the response of the halo (see Pichon & Aubert (2006), paper I). The current paper focuses on the statistical characterisation of the environments surrounding haloes, using a set of large scale simulations. Our description relies on a `fluid halocentric representation where the interactions between the halo and its environment are investigated in terms of a time dependent external tidal field and a source term characterizing the infall. The method is applied to 15000 haloes, with masses between 5 x 10^12 Ms and 10^14 Ms evolving between z = 1 and z = 0. The net accretion at the virial radius is found to decrease with time, resulting from both an absolute decrease of infall and from a growing contribution of outflows. Infall is found to be mainly radial and occurring at velocities ~ 0.75 V200. Outflows are also detected through the virial sphere and occur at lower velocities ~ 0.6 V200 on more circular orbits. The external tidal field is found to be strongly quadrupolar and mostly stationnary, possibly reflecting the distribution of matter in the halos near environment. The coherence time of the small scale fluctuations of the potential hints a possible anisotropic distribution of accreted satellites. The flux density of mass on the virial sphere appears to be more clustered than the potential while the shape of its angular power spectrum seems stationnary.
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