Turbulent intermittency in environmental fluid mechanics and its modeling

Many geophysical fields or processes display large fluctuations on a wide range of scales. This is particularly true of environmental turbulence, characterized by huge Reynolds numbers, and high level intermittency. A stochastic approach has been used for some time to model such turbulent intermittency with cascade models from large to small scales. Such cascades are now known to correspond to multifractal fields, whose statistics are characterized by scaling moment functions and probability distributions. We show an example of application using atmospheric velocity and temperature data and present their main multifractal scaling properties. We then describe a stochastic process able to reproduce such multiple-scale properties. This provides first steps in the development of a fully stochastic and intermittent modelling of turbulence. This approach ma be opposed to classical deterministic modelling (such as k-epsilon models and their variants) for which we show that the basic hypothesis of separation of scales is not justified. This shows that such models do not rest on solid grounds and should be abandoned, especially in environmental fluid mechanics where Reynolds numbers (and hence involved range of scales) are huge.