  We study the propagation and dissipation of magnetohydrodynamic waves in a
set of numerical models that each include a solar--like stratified atmosphere
and a magnetic field with a null point. All simulations have the same magnetic
field configuration but different transition region heights. Compressive wave
packets introduced in the photospheric portion of the simulations refract
towards the null and collapse it into a current sheet, which then undergoes
reconnection. The collapsed null forms a current sheet due to a strong magnetic
pressure gradient caused by the inability of magnetic perturbations to cross
the null. Although the null current sheet undergoes multiple reconnection
episodes due to repeated reflections off the lower boundary, we find no
evidence of oscillatory reconnection arising from the dynamics of the null
itself. Wave mode conversion around the null generates a series of slow mode
shocks localized near each separatrix. The shock strength is asymmetric across
each separatrix, and subsequent shock damping therefore creates a tangential
discontinuity across each separatrix, with long--lived current densities. A
parameter study of the injected wave energy to reach the null confirms our
previous WKB estimates. Finally, using current estimates of the photospheric
acoustic power, we estimate that the shock and Ohmic heating we describe may
account for $\approx1-10\%$ of the radiative losses from coronal bright points
with similar topologies, and are similarly insufficient to account for losses
from larger structures such as ephemeral regions. At the same time, the
dynamics are comparable to proposed mechanisms for generating type--II
spicules.

Solar and Stellar Astrophysics;Computational Physics;Fluid Dynamics;Plasma Physics