  We analyze a long-lived hyper-massive neutron star merger remnant
(post-merger lifetime $>250$ ms) that has been obtained via large eddy
simulations with a gradient subgrid-scale model. We find a clear helicoidal
magnetic field structure that is governed by the toroidal component of the
magnetic field. Although no jet emerges during the simulation time, we observe
at late times a significant increase of the poloidal component of the magnetic
field at all scales. We also compare with the results of several binary neutron
star simulations with moderate resolution of $120$~m, that are evolved up to
$50$~ms after the merger, which differ in terms of the initial topology and
strength of the magnetic field. We find that the best choice is an isotropic
small-scale magnetic field distribution that mimics the turbulent state that
generically develops during the merger. This initial configuration reaches a
closer agreement with our high-resolution simulation results than the purely
dipolar large-scale fields that are commonly employed in these type of
simulations. This provides a recipe to perform such simulations avoiding the
computationally expensive grids required to faithfully capture the
amplification of the magnetic field by Kelvin-Helmholtz instabilities.
