Noise-sustained structure,intermittency, and the Ginzburg-Landau equation

The time-dependent generalized Ginzburg-Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in thestationary frame of reference and with anonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested.     

On the localness of the spectral energy transfer in turbulence

By utilizing available experimental data for net energy transfer spectra for homogeneous turbulence, contributions P(, ) to the energy transfer at a wavenumber from various other wavenumbers are calculated. This is done by fitting a truncated power-exponential series in and to the experimental data for the net energy transfer T(), and using known properties of P(, ). Although the contributions P(, ) obtained by using this procedure are not unique, the results obtained by using various assumptions do not differ significantly. It seems clear from the results that for a region where the energy entering a wavenumber band dominates that leaving, much of the energy entering the band comes from wavenumbers which are about an order of magnitude smaller. That is, the energy transfer is rather nonlocal. This result is not significantly dependent on Reynolds number (for turbulence Reynolds numbers based on microscale from 3 to 800). For lower wavenumbers, where more energy leaves than enters a wavenumber band, the energy transfer into the band is more local, but much of the energy then leaves at distant wavenumbers.     

One-dimensional strings, random fluctuations, and complex chaotic structures

The effect of random fluctuations on the set of equations resulting from coupling 200 points with one-dimensional maps is studied. This dynamical system exhibits a spatial exponential growth in fluctuations, resulting in a complex chaotic structure. The system suggests a closer look at stability in complex systems.     

Weak locally homogeneous turbulence in idealized flow through a cone

Résumé On analyse la turbulence d'un écoulement idéalisé à travers un cône, au moyen des équations de corrélation généralisées à deux points, basées sur les équations de Navier-Stokes et de continuité. La viscosité et les effets de déformation moyenne sont retenus dans l'analyse, mais on suppose que la turbulence est assez faible pour qu'on puisse négliger, dans les équations, les termes de corrélation triples par rapport aux autres termes. On calcule les composantes des variations de vitesse de tourbillon et de formation de tourbillon, ainsi que les spectres de ces grandeurs. On considère également, dans l'équation du spectre, un terme de transport d'énergie de déformation moyenne qui transfère des composantes d'énergie entre les caractèristiques d'onde. On utilise l'analogie du transfert énergétique de chaleur pour relier les résultats obtenus au transfert de chaleur entre le fluide et la paroi du cône.     

Growth due to buoyancy of weak homogeneous turbulence with shear

Résumé Une analyse est faite dans le but de déterminer la façon dont l'énergie change après un laps de temps dans une turbulence faible et homogène soumise à la flottabilité et au cisaillement. Bien que la turbulence dépérisse en fin de compte en l'absence de flottabilité, on remarque que la présence de flottabilité empêche ce dépérissement et fait que l'énergie turbulente augmente sans limite à mesure de l'augmentation de temps.