Determining dynamic content of turbulent flow LES using the Lyapunov exponent

Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) have been em- ployed for computing turbulent flows . While DNS resolves all turbulent scales involved in the dynamics with no physical modeling, LES represents the energy contained in the large scales, and effects of the smaller scales are taken into account either explicitly through a subgrid scale model or implicitly through the numerical dissipation of the nu- merical method. Besides numerical algorithms, two factors determine the quality of LES: the physical model or dissipation of the subgrid scales (SGS), which are filtered out in the governing equations, and the filter width, which describes the numerical resolution of the resolved scales