Taming turbulence via spectral and real space nudging

The technique of spectral nudging is commonly used to incorporate empirical data into a simulation in order to control its evolution and reproduce a given dynamical benchmark. We show how to do this in fully developed three dimensional turbulence. We give physical arguments for the choice of optimal parameters, based on the Reynolds number and on the amount of control provided by the nudging. We show how the algorithm can be used to extract unknown information from the data. Furthermore, we extend the technique to real space nudging, where the penalty is now performed in volumes in configuration space.