  In rapidly rotating bose systems we show that there is a region of anomalous
hydrodynamics whilst the system is still condensed, which coincides with the
mean field quantum Hall regime. An immediate consequence is the absence of a
normal fluid in any conventional sense. However, even the superfluid
hydrodynamics is not described by conventional Bernoulli and continuity
equations. We show there are kinematic constraints which connect spatial
variations of density and phase, that the positions of vortices are not the
simplest description of the dynamics of such a fluid (despite their utility in
describing the instantaneous state of the condensate) and that the most compact
description allows solution of some illuminating examples of motion. We
demonstrate, inter alia, a very simple relation between vortices and surface
waves. We show the surface waves can form a "normal fluid" which absorbs energy
and angular momentum from vortex motion in the trap. The time scale of this
process is sensitive to the initial configuration of the vortices, which can
lead to long-lived vortex patches - perhaps related to those observed at JILA.
