Nicolas Rimbert

Crossover between Rayleigh-Taylor instability and turbulent cascading atomization mechanism in the bag-breakup regime.

The question of whether liquid atomization depends on instability dynamics (through refinements of Rayleigh-Plateau, Rayleigh-Taylor, or Kelvin-Helmholtz mechanisms) or on turbulent cascades, as suggested by Richardson and Kolmogorov, is still open. In this paper, experimental results reveal that both mechanisms are needed to explain the probability density functions (PDFs) of the droplets in a spray obtained from an industrial fan spray nozzle. Instability of Rayleigh-Taylor type controls the size of the largest droplets while the smallest droplets follow a PDF given by a turbulent cascading mechanism characterized by a log-Lévy stable law that has a stability parameter equal to 1.70. This value is very close to the inverse value of the Flory exponent and can be related to a recent model developed by N. Rimbert for intermittency modeling stemming from self-avoiding random vortex stretching.

Simple model for turbulence intermittencies based on self-avoiding random vortex stretching

Whether statistics of intermittencies (between small and large eddies) in homogeneous and isotropic turbulence should be described by a logarithmic-Poisson, a logarithmic-stable probability density function, or other is still debated nowadays. In this paper, a bridge between polymer physics, self-avoiding walk, and random vortex stretching is established which may help to obtain new insights on this topic. A very simple relationship between the stability index of the Lévy stable law and Florys exponent stemming from statistics of linear polymer growth is established. Moreover, the scaling of turbulence intermittencies with Reynolds number is also explained and the overall picture is given of smallest vortex tubes of Kolmogorov length width (i.e., the smallest dissipative eddies) bent by bigger vortices of Taylor length scale (i.e., the mean dissipative eddies), themselves stretched by the bigger eddies in a continuous cascade. This results in both a simple and sound model with no fitting parameters required.

Dependence of Levy Statistics With Reynolds Number Application to turbulence intermittency and spray modeling

In this poster, we show that Kidas log-stable law for the intermittency of turbulence can be extended over a wide Range of Taylor scale Reynolds number Re »elds a simple relation between the scale parameter of the law and Re » log-normal laws were firstly introduced by Kolmogorov for the size of particles under pulverization, log-stable laws are applied to the experimental drop size p.d.f in an annular gas-liquid flow. Though the fitting is quite good there does not seem to be any clear relationship between the parameters of the law and the external parameters of the experiment. This may be related to a breaking of the homogeneity hypothesis.

Extension of the Kida law in turbulence

Abstract We extend the validity range of Kidas log-stable law of stability index α =1.65 and intermittency parameter μ =0.2 to a new range of Reynolds number. This law describes intermittencies in fully developed turbulent flows or more precisely the p.d.f. of turbulence dissipation. Former measurements of the hyper-flatness factors of order 4, 5, 6 of turbulent velocity increments, coming from both experimental works and numerical simulations are used. We show that the power-law variation of these hyper-flatness factors with Taylor scale based Reynolds numbers Re λ can be fitted, for Re λ ranging from 35 to 750, by a log-stable law of stability index α =1.65 and intermittency parameter μ =0.21. To cite this article: N. Rimbert, O. Sero-Guillaume, C. R. Mecanique 331 (2003).