MULTIFRACTAL CASCADE DYNAMICS AND TURBULENT INTERMITTENCY

Turbulent intermittency plays a fundamental role in fields ranging fro m combustion physics and chemical engineering to meteorology. There is a rather general agreement that multifractals are being very successf ul at quantifying this intermittency. However, we argue that cascade p rocesses are the appropriate and necessary physical models to achieve dynamical modeling of turbulent intermittency. We first review some re cent developments and point out new directions which overcome either c ompletely or partially the limitations of current cascade models which are static, discrete in scale, acausal, purely phenomenological and l acking 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) alterna tive is untenable for both strong and weak events. Using a continuous, space-time anisotropic framework, we then show how to produce a causa l stochastic model of intermittent fields and use it to study the pred ictability of these fields. Finally, by returning to the origins of th e turbulent ''shell models'' and restoring a large number of degrees o f freedom (the Scaling Gyrascope Cascade, SGC models) we partially clo se the gap between the cascades and the dynamical Navier-Stokes equati ons. Furthermore, we point out that beyond a close agreement between u niversal parameters of the different modeling approaches and the empir ical estimates in turbulence, there is a rather common structure invol ving both a ''renormalized viscosity'' and a ''renormalized forcing''. We conclude that this gives credence to the possibility of deriving a nalytical/renormalized models of intermittency built on this structure .