  We propose a WENO finite difference scheme to approximate anelastic flows,
and scalars advected by them, on staggered grids. In contrast to existing WENO
schemes on staggered grids, the proposed scheme is designed to be arbitrarily
high-order accurate as it judiciously combines ENO interpolations of velocities
with WENO reconstructions of spatial derivatives. A set of numerical
experiments are presented to demonstrate the increase in accuracy and
robustness with the proposed scheme, when compared to existing WENO schemes and
state-of-the-art central finite difference schemes.
