  We present a phenomenological study of the phase dynamics of the
one-dimensional stochastically forced Burgers equation, and of the same
equation under a Fourier mode reduction on a fractal set. We study the
connection between coherent structures in real space and the evolution of
triads in Fourier space. Concerning the one-dimensional case, we find that
triad phases show alignments and synchronisations that favour energy fluxes
towards small scales --a direct cascade. In addition, strongly dissipative
real-space structures are associated with entangled correlations amongst the
phase precession frequencies and the amplitude evolution of Fourier triads. As
a result, triad precession frequencies show a non-Gaussian distribution with
multiple peaks and fat tails, and there is a significant correlation between
triad precession frequencies and amplitude growth. Links with dynamical systems
approach are briefly discussed, such as the role of unstable critical points in
state space. On the other hand, by reducing the fractal dimension $D$ of the
underlying Fourier set, we observe: i) a tendency toward a more Gaussian
statistics, ii) a loss of alignment of triad phases leading to a depletion of
the energy flux, and iii) the simultaneous reduction of the correlation between
the growth of Fourier mode amplitudes and the precession frequencies of triad
phases.
