  The evolution of non-hydrodynamic slow processes near the QCD critical point
is explored with the novel Hydro+ framework, which extends the conventional
hydrodynamic description by coupling it to additional explicitly evolving slow
modes describing long wavelength fluctuations. Their slow relaxation is
controlled by critical behavior of the correlation length and is independent
from gradients of matter density and pressure that control the evolution of the
hydrodynamic quantities. In this exploratory study we follow the evolution of
the slow modes on top of a simplified QCD matter background, allowing us to
clearly distinguish, and study both separately and in combination, the main
effects controlling the dynamics of critical slow modes. In particular, we show
how the evolution of the slow modes depend on their wave number, the expansion
of and advection by the fluid background, and the behavior of the correlation
length. Non-equilibrium contributions from the slow modes to bulk matter
properties that affect the bulk dynamics (entropy, pressure, temperature and
chemical potential) are discussed and found to be small.
