Numerical study of the effective viscosity and pressure in perturbed turbulent flows

We present a numerical investigation of the linear response of a turbulent flow to a perturbation at large scale. In the incompressible case, we show that part of the small scale action corresponds to the standard turbulent viscosity, but that there are also other terms which are important for the system dynamics and which do not reduce to a simple turbulent viscous effect. In the compressible case, we show that the small scales of the turbulent flow create a turbulent pressure force which resists compression. An adiabatic index is estimated for this pressure and is found to decrease with time scale, from a strongly adiabatic behavior down to a subisothermal behavior.