  Recent high resolution AIA/SDO images show evidence of the development of the
Kelvin-Helmholtz instability, as coronal mass ejections (CMEs) expand in the
ambient corona. A large-scale magnetic field mostly tangential to the interface
is inferred, both on the CME and on the background sides. However, the magnetic
field component along the shear flow is not strong enough to quench the
instability. There is also observational evidence that the ambient corona is in
a turbulent regime, and therefore the criteria for the development of the
instability are a-priori expected to differ from the laminar case. To study the
evolution of the Kelvin-Helmholtz instability with a turbulent background, we
perform three-dimensional simulations of the incompressible magnetohydrodynamic
equations. The instability is driven by a velocity profile tangential to the
CME-corona interface, which we simulate through a hyperbolic tangent profile.
The turbulent background is generated by the application of a stationary
stirring force. We compute the instability growth-rate for different values of
the turbulence intensity, and find that the role of turbulence is to attenuate
the growth. The fact that the Kelvin-Helmholtz instability is observed, sets an
upper limit to the correlation length of the coronal background turbulence.
