Turbulent intermittency plays a fundamental role in fields ranging from combustion physics and chemical engineering to meteorology. There is a rather general agreement that multifractals are being very successful at quantifying this intermittency. However, we argue that cascade processes are the appropriate and necessary physical models to achieve dynamical modeling of turbulent intermittency. We first review some recent developments and point out new directions which overcome either completely or partially the limitations of current cascade models which are static, discrete in scale, acausal, purely phenomenological and lacking in universal features. We review the debate about universality classes for multifractal processes. Using both turbulent velocity and temperature data, we show that the latter are very well fitted by the (strong) universality, and that the recent (weak, log-Poisson) alternative is untenable for both strong and weak events. Using a continuous, space-time anisotropic framework, we then show how to produce a causal stochastic model of intermittent fields and use it to study the predictability of these fields. Finally, by returning to the origins of the turbulent "shell models" and restoring a large number of degrees of freedom (the Scaling Gyroscope Cascade, SGC models) we partially close the gap between the cascades and the dynamical Navier–Stokes equations. Furthermore, we point out that beyond a close agreement between universal parameters of the different modeling approaches and the empirical estimates in turbulence, there is a rather common structure involving both a "renormalized viscosity" and a "renormalized forcing". We conclude that this gives credence to the possibility of deriving analytical/renormalized models of intermittency built on this structure.

International audienceWe empirically investigate the scaling behaviour of the horizontal wind along the vertical direction using 287 radiosonde soundings with a resolution of 50 m. We compare the results obtained with those of the horizontal temporal behaviour in the framework of Generalized Scaling Invariance and the unified Scaling model of atmospheric dynamics. We find the scaling to be very well respected over the range 50 m - 13 km (nearly the entire troposphere) and we estimate the universal multifractal indices which characterize the statistics in the vertical. By comparing our result with those obtained in the horizontal we show that the degree of stratification is different for mean and extreme structures. Finally, we theoretically discuss the necessary improvements to the Unified Multifractal model needed to account for them

Abstract. In this paper we test the Unified Mulifractal model of atmospheric dynamics in the tropics. In the first part, we empirically investigate the scaling behaviour along the horizontal, in the second part along the vertical. Here we concentrate on the presentation of basic multifractal notions and techniques and on how they give rise to self-organized critical structures. Indeed, we point out a rather simple and clear characterisation of these structures which may help to clarify both the nature of the oft-cited coherent structures and the generation of cyclones. Using 30 aircraft series of horizontal wind and temperature, we find rather remarkable constancy of the three universal multifractal indices H, C1 and α as well as the value of critical exponents qD, γD associated with multifractal phase transitions and self-organized critical structures. This constancy extends not only from wind tunnel and mid-latitude to the tropics, but also to multifractals generated by Navier-Stokes like equations.

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