The explicit mapping method is used to analyze the nonlinear dynamical behavior for cascade in isotropic turbulence. This deductive scale analysis is shown to provide the first visual evidence of the celebrated Richardson-Kolmogorv cascade, and reveals in particular its multiscale character based on the statistical solutions of Navier-Stokes equations. The results also indicate that the energy cascading process has remarkable similarities with the deterministic construction rules of the logistic map. Cascade of period-doubling bifurcations have been seen in this isotropic turbulent system that exhibit chaotic behavior. The "cascade" appears as an infinite sequence of period-doubling bifurcations.
Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter.Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and the second-order structure function),we have studied the relative scaling using the ESS method.It is found that the relative EES scaling exponent Sis greater than the real or theoretical inertial range scaling exponentξ,which is attributed to an evident bump in the ESS range.
Shuxiao Wan,and Zheng Ran~(a) Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China
