Degrees of freedom and the dynamics of fully developed turbulence

While the degrees of freedom needed to represent the dynamics of high Reynolds number turbulence are extremely large, we show using well-resolved direct numerical simulations that one can capture essential physics with only a fraction of modes obeying the Navier-Stokes equations; the other modes can be modeled with very simple dynamics. This result suggests that the attractor for the dynamics of fully developed turbulence is robust to modeling errors and the strongly nonlinear dynamics may reside on fewer degrees of freedom than traditionally thought. The proposed approach is validated in terms of dissipation rate, skewness of velocity gradients, the energy and transfer spectrum, and structure functions. The mixed-dynamics model explored here, which may open different venues for turbulence modeling, may also be applicable to a broader set of physical phenomena governed by nonlinear complex dynamics with a wide range of scales.