  This paper is the second part of a two-fold study of mixing, i.e. the
formation of layers and upwelling of buoyancy, in axially stratified
Taylor--Couette flow, with fixed outer cylinder. In a first paper, we showed
that the dynamics of the flow was dominated by coherent structures made of a
superposition of nonlinear waves. (Mixed)-ribbons and (mixed)-cross-spirals are
generated by interactions between a pair of linearly unstable helical modes of
opposite `handedness', and appear to be responsible for the formation of
well-mixed layers and sharp density interfaces. In this paper, we show that
these structures are also fully accountable for the upwards buoyancy flux in
the simulations. The mechanism by which this occurs is a positive coupling
between the density and vertical velocity components of the most energetic
waves. This coupling is primarily caused by diffusion of density at low Schmidt
number Sc, but can also be a nonlinear effect at larger Sc. Turbulence was
found to contribute negatively to the buoyancy flux at Sc=1,10,16, which lead
to the conclusion that mass upwelling is a consequence of chaotic advection,
even at large Reynolds number. Artificially isolating the coherent structure
therefore leads to excellent estimates of the flux Richardson numbers Ri_f from
the DNS. We also used the theoretical framework of Winters et al. (1995) to
analyse the energetics of mixing in an open control volume, shedding light on
the influence of end effects in the potential energy budget. The potential
connection with the buoyancy flux measurements made in the recent experiment of
Oglethorpe et al. (2013) is also discussed.
