Reduced Basis modelling of turbulence with well-developed inertial range

In this work, we introduce a Reduced Basis model for turbulence at statistical equilibrium. This is based upon an a-posteriori error estimation procedure that measures the distance from a trial solution to the K41 theory energy spectrum. We apply this general idea to build a Reduced Basis Smagorinsky turbulence model through a Greedy Algorithm. We derive some error estimates that make apparent the role of the energy spectrum in the ROM approximation. We carry on some tests for some academic unsteady 2D flows at large Reynolds number, that present well developed inertial spectrum. The methods presents a high efficiency, as the error achieved with the reduced method is 3 to 4 times the ones achieved if the exact error is used in the Greedy Algorithm.