Local dimensionality and inverse persistence analysis of atmospheric turbulence in the stable boundary layer.

The dynamics across different scales in the stable atmospheric boundary layer has been investigated by means of two metrics, based on instantaneous fractal dimensions and grounded in dynamical systems theory. The wind velocity fluctuations obtained from data collected during the Cooperative Atmosphere-Surface Exchange Study-1999 experiment were analyzed to provide a local (in terms of scales) and an instantaneous (in terms of time) description of the fractal properties and predictability of the system. By analyzing the phase-space projections of the continuous turbulent, intermittent, and radiative regimes, a progressive transformation, characterized by the emergence of multiple low-dimensional clusters embedded in a high-dimensional shell and a two-lobe mirror symmetrical structure of the inverse persistence, have been found. The phase space becomes increasingly complex and anisotropic as the turbulent fluctuations become uncorrelated. The phase space is characterized by a three-dimensional structure for the continuous turbulent samples in a range of scales compatible with the inertial subrange, where the phase-space-filling turbulent fluctuations dominate the dynamics, and is low dimensional in the other regimes. Moreover, lower-dimensional structures present a stronger persistence than the higher-dimensional structures. Eventually, all samples recover a three-dimensional structure and higher persistence level at large scales, far from the inertial subrange. The two metrics obtained in the analysis can be considered as proxies for the decorrelation time and the local anisotropy in the turbulent flow.

Transition to turbulence in a five-mode Galerkin truncation of two-dimensional magnetohydrodynamics.

The chaotic dynamics of a low-order Galerkin truncation of the two-dimensional magnetohydrodynamic system, which reproduces the dynamics of fluctuations described by nearly incompressible magnetohydrodynamic in the plane perpendicular to a background magnetic field, is investigated by increasing the external forcing terms. Although this is the case closest to two-dimensional hydrodynamics, which shares some aspects with the classical Feigenbaum scenario of transition to chaos, the presence of magnetic fluctuations yields a very complex interesting route to chaos, characterized by the splitting into multiharmonic structures of the field amplitudes, and a mixing of phase-locking and free phase precession acting intermittently. When the background magnetic field lies in the plane, the system supports the presence of Alfvén waves thus lowering the nonlinear interactions. Interestingly enough, the dynamics critically depends on the angle between the direction of the magnetic field and the reference system of the wave vectors. Above a certain critical angle, independently from the external forcing, a breakdown of the phase locking appears, accompanied with a suppression of the chaotic dynamics, replaced by a simple periodic motion.