  Comparisons are presented between a hybrid Vlasov-Maxwell (HVM) simulation of
turbulence in a collisionless plasma and fluid reductions. These include
Hall-magnetohydrodynamics (HMHD) and Landau fluid (LF) or FLR-Landau fluid
(FLR-LF) models that retain pressure anisotropy and low-frequency kinetic
effects such as Landau damping and, for the last model, finite Larmor radius
(FLR) corrections. The problem is considered in two space dimensions, when
initial conditions involve moderate-amplitude perturbations of a homogeneous
equilibrium plasma subject to an out-of-plane magnetic field. LF turns out to
provide an accurate description of the velocity field up to the ion Larmor
radius scale, and even to smaller scales for the magnetic field.
Compressibility nevertheless appears significantly larger at the sub-ion scales
in the fluid models than in the HVM simulation. High frequency kinetic effects,
such as cyclotron resonances, not retained by fluid descriptions, could be at
the origin of this discrepancy. A significant temperature anisotropy is
generated, with a bias towards the perpendicular component, the more intense
fluctuations being rather spread out and located in a broad vicinity of current
sheets. Non-gyrotropic pressure tensor components are measured and their
fluctuations are shown to reach a significant fraction of the total pressure
fluctuation, with intense regions closely correlated with current sheets.
