  We investigate the vorticity-preserving properties of the compressible,
second-order residual-based scheme, "RBV2". The scheme has been extensively
tested on hydrodynamical problems, and has been shown to exhibit remarkably
accurate results on the propagation of inviscid compressible vortices,
airfoil-vortex interactions on a curvilinear mesh, vortex mergers in an
astrophysical accretion disk, and the establishment of a two-dimensional
inverse cascade in high-resolution turbulent simulations. Here, we demonstrate
that RBV2 sustains the analytic solution for a one-dimensional shear flow. We
assess the fidelity by which the algorithm maintains a skewed shear flow, and
present convergence tests to quantify the magnitude of the expected numerical
dispersion. We propose an adjustment to the dissipation in the algorithm that
retains the vorticity-preserving qualities, and accurately incorporates
external body forces, and demonstrate that it indefinitely maintains a
steady-state hydrostatic equilibrium between a generic acceleration and a
density gradient. We present a novel numerical assessment of vorticity
preservation for discrete-wavenumber vortical modes up to the Nyquist
wavenumber. We apply this assessment to RBV2 in order to quantify the extent to
which the scheme preserves vorticity for the full Euler equations. We find that
RBV2 perfectly preserves vorticity for modes with symmetric wavenumbers, i.e.,
$k_x=k_y$, and that the error increases with asymmetry. We simulate the
dynamical interaction of vortices in a protoplanetary disk to demonstrate the
utility of the updated scheme for rendering astrophysical flows replete with
vortices and turbulence. We conclude that RBV2 is a competitive treatment for
evolving vorticity-dominated astrophysical flows with minimal dissipation.

Fluid Dynamics;Earth and Planetary Astrophysics;High Energy Astrophysical Phenomena;Computational Physics