  In this work the issue of whether key energetic properties (nonlinear,
exponential-type dissipation in the abscence of forcing and long-term stability
under conditions of time dependent loading) are automatically inherited by
deforming reference descriptions is resolved. These properties are intrinsic to
real flows and the conventional Navier-Stokes equations. A completely general
reference description of an incompressible, Newtonian fluid, which reconciles
the differences between opposing schools of thought in the literature is
derived for the purposes of this investigation.
  The work subsequently focusses on establishing a class of time
discretisations which inherit these self-same energetic properties,
irrespective of the time increment employed. The findings of this analysis have
profound consequences for the use of certain classes of finite difference
schemes in the context of deforming references. It is significant that many
algorithms presently in use do not automatically inherit the fundamental
qualitative features of the dynamics. An `updated' approach as a means of
avoiding ever burgeoning deformation gradients and a still further simplified
implementation are further topics explored.
