Turbulence cascade and dynamical exchange between spatial scales

Abstract

The information exchange dynamics between different spatial scales of a turbulent field is experimentally investigated, with particular reference to the energy cascade process. This is done by use of the collective light scattering (CLS) diagnostic, a new optical setting tuned for the observation of atomic number density fluctuations at macroscopic scales. A two-channel scattering device is described that provides simultaneously the fluctuations at two different spatial scales. The turbulent system is an axisymmetric air jet. With this system, time correlations between signal amplitudes for two different scales show a characteristic time width. This time does not depend on the observed scales: it is close to the turbulence production time. Nevertheless, signal amplitude autocorrelation shows a shorter characteristic time. The autocorrelation time scaling law behaves almost like the eddy turnover time from Kolmogorov theory.

Scaling laws of density fluctuations in tokamak plasmas

“…This exponent is generally used for a practical transport coefficient estimate from the fluctuation level. For comparison, in 3D fluid turbulence, light scattering has also permitted to measure the k-spectrum [66] indicating a very good agreement between the measured spectral index of −3.6, and that expected from the Kolmogorov law…”

Dynamics of density fluctuations in a turbulent flow

“…In Ref. [4], two of us have demonstrated experimentally that the long auto-correlation times are related to crosscorrelations between two different spatial scales, and that this crosscorrelation time is independent of the particular choice of vectors k. This is consistent to interpreting long correlation time events as vortex since the latter are multi-scale objects. Clusters in a time series of our single-k measurement can then be seen as the density fluctuation traces of vortex dynamics.…”

“…The light source is a visible laser (λ = 514 nm). Very similar experiments are described in [4,5], where it can also be found the details of the CLS principle.…”

“…5 a piece of time series of the numerical integration of Eqs. (4) and (3) with D = 0.5 × 10 −3 . It can be observed segments of rather periodic oscillations and segments with more irregular behavior.…”

A diffusion equation to describe scale–and time–dependent dimensions of turbulent interfaces

“…They measured, for different thresholds, a mean fractal dimension as a function of time. Concerning interaction between spatial scales, let us quote the experimental work of Honoré & Grésillon (2000), who, by using a new diagnostic technique (collective light scattering), have been able to investigate the information exchange dynamics between different spatial scales of a turbulent field.…”