Simulation of induction at low magnetic Prandtl number

We consider the induction of magnetic field in flows of electrically conducting fluid at low magnetic Prandtl number and large kinetic Reynolds number. Using the separation between the magnetic and kinetic diffusive lengthscales, we propose a new numerical approach. The coupled magnetic and fluid equations are solved using a mixed scheme, where the magnetic field fluctuations are fully resolved and the velocity fluctuations at small scale are modelled using a Large Eddy Simulation (LES) scheme. We study the response of a forced Taylor-Green flow to an externally applied field: tology of the mean induction and time fluctuations at fixed locations. The results are in remarkable agreement with existing experimental data; a global $1/f$ behavior at long times is also evidenced.