  Bow shock pulsar wind nebulae (BSPWNe) are know to show a large variety of
shapes and morphologies, both when comparing different objects, and for the
same object in different energy bands. It is unclear if such a variety is
related to differences in the pulsar wind properties, or to differences in the
conditions of the ambient medium. We present here a set of full
three-dimensional, relativistic and magneto-hydrodynamic simulations of BSPWNe,
with the intention of determining how differences in the injection conditions
by the pulsar wind reflect in the nebular dynamics. To achieve a good coverage
of the available parameter space we have run several simulations varying those
parameters that are most representative of the wind properties: the latitudinal
anisotropy of the wind energy flux with respect to the pulsar spin axis, the
level of magnetization, the inclination of the pulsar spin axis with respect to
the pulsar direction of motion. We have followed the dynamics in these systems,
not just in the very head, but also in the tail, trying to assess if and how
the system retains memory of the injection at large distances from the pulsar
itself. In this paper we focus our attention on the characterization of the
fluid structure and magnetic field properties. We have tried to evaluate the
level of turbulence in the tail, and its relation to injection, the survival of
current sheets, and the degree of mixing between the shocked ambient medium and
the relativistic pulsar wind material.
