  We investigate the influence of background shear flow on linear resistive
tearing instabilities with Joule heating for two compressible plasma slab
configurations: a Harris current sheet and a force-free, shearing magnetic
field that varies its direction periodically throughout the slab, possibly
resulting in multiple magnetic nullplanes. To do so, we exploit the latest
version of the open-source, magnetohydrodynamic spectroscopy tool Legolas.
Shear flow is shown to dramatically alter tearing behaviour in the presence of
multiple magnetic nullplanes, where the modes become propagating due to the
flow. Finally, the tearing growth rate is studied as a function of resistivity,
showing where it deviates from analytic scaling laws, as well as the Alfv\'en
speed, the plasma-beta, and the velocity parameters, revealing surprising
nuance in whether the velocity acts stabilising or destabilising. We show how
both slab setups can produce growth rate regimes which deviate from analytic
scaling laws, such that systematic numerical spectroscopic studies are truly
necessary, for a complete understanding of linear tearing behaviour in flowing
plasmas.
