  $Context$: Vela X-1 is the prototype of the classical sgHMXB systems. Recent
continuous and long monitoring campaigns revealed a large hard X-rays
variability amplitude with strong flares and off-states. This activity has been
interpreted invoking clumpy stellar winds and/or magnetic gating mechanisms.
  $Aims$: We are probing if the observed behaviour could be explained by
unstable hydrodynamic flows close to the neutron star rather than the more
exotic phenomena.
  $Methods$: We have used the hydrodynamic code VH-1 to simulate the flow of
the stellar wind with high temporal resolution and to compare the predicted
accretion rate with the observed light-curves.
  $Results$: The simulation results are similar to the observed variability.
Off-states are predicted with a duration of 5 to 120 minutes corresponding to
transient low density bubbles forming around the neutron star. Oscillations of
the accretion rate with a typical period of $\sim$ 6800 sec are generated in
our simulations and observed. They correspond to the complex motion of a bow
shock, moving either towards or away from the neutron star. Flares are also
produced by the simulations up to a level of $10^{37}$ erg/s.
  $Conclusions$: We have qualitatively reproduced the hard X-ray variations
observed in Vela X-1 with hydrodynamic instabilities predicted by a simple
model. More sophisticated phenomena, such as clumpy winds or the magnetic
gating mechanism, are not excluded but not required to explain the basic
phenomenology.
