  We review our version of the classical field approximation to the dynamics of
a finite temperature Bose gas. In the case of a periodic box potential, we
investigate the role of the high momentum cut-off, essential in the method. In
particular, we show that the cut-off going to infinity limit decribes the
particle number going to infinity with the scattering length going to zero. In
this weak interaction limit, the relative population of the condensate tends to
unity. We also show that the cross-over energy, at which the probability
distribution of the condensate occupation changes its character, grows with a
growing scattering length. In the more physical case of the condensate in the
harmonic trap we investigate the dissipative dynamics of a vortex. We compare
the decay time and the velocities of the vortex with the available analytic
estimates.
