Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

The longitudinal structure function (LSF) and the transverse structure function (TSF) in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations

Pattern Selection and Low-Dimensional Chaos in Systems of Coupled Nonlinear Oscillators

The longtime behavior of a number of one- and two-dimensional driven, dissipative, dispersive, many-degree-of-freedom systems is studied. It is shown numerically that the attractors are characterized by strong mode-locking into a small number of (nonlinear) modes. On the basis of the observed profiles, estimates of chaotic attractor dimensions, and projections into nonlinear mode bases, it is argued that the same few modes may (in these extended systems) give a unified picture of spatial pattern selection, low-dimensional chaos, and coexisting coherence and chaos. Analytic approaches to this class of problem are summarized