Chaos viscosity and turbulent viscosity

Chaos or turbulence induces a viscosity by the contraction of motion. The driven damped pendulum which shows chaos is rewritten in the form that has viscosity derived from the nonlinear term. It is shown that the fluctuation–dissipation theory holds between the dissipation and the random force derived from the nonlinear term. Then we see that the power spectrum which takes account of the chaos viscosity has smaller low-frequency power and larger high-frequency power compared to the original power spectrum. Further the turbulence viscosity is calculated for Kuramoto–Sivashinsky equation.