  We present a stochastic turbulence generator based on a vorticity formulation
where the generated turbulent field implicitly fulfills the kinematic
constraints of an incompressible flow. The generator allows direct access to
the turbulent velocity and vorticity field. Enforcing additional constraints
such as a divergence-free vorticity field and a specified differentiability of
the flow field can also implemented directly within this formulation. The
resulting turbulent field contain improved kinematic properties and may be
imported into numerical simulations without an excessive loss of energy.
