The random- model (Benzi et al., 1984) can be derived by invoking that the space-filling factor for the fragments at a given scale in the energy cascade is given by a random variable . The probability of occurrence of a given is assumed to be a bimodal distribution where the eddies fragmentation process generates either space-filling eddies with probability or planar sheets with probability (for conservation ). It can be found that
The -model (Meneveau, 1991; Carbone, 1993) consists in an eddies fragmentation process described by a two-scale Cantor set with equal partition intervals. An eddy at the scale , with an energy derived from the transfer rate , breaks down into two eddies at the scale , with energies and . The parameter is not defined by the model, but is fixed from the experimental data. The model gives
In the model by She and Leveque (see, e.g., She and Leveque, 1994; Politano and Pouquet, 1998) one assumes an infinite hierarchy for the moments of the energy transfer rates, leading to , and a divergent scaling law for the infinite-order moment , which describes the most singular structures within the flow. The model readset al. (1996b) models are able to capture intermittency of fluctuations in the solar wind. The agreement between the curves and normalized scaling exponents is excellent, and this means that we realistically cannot discriminate between the models we reported above.
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