We review the most important theoretical and numerical results obtained in the realm of shell models for the energy-turbulent cascade. We mainly focus here on those results that had or will have some impact on the fluid-dynamics community. In particular, we address the problem of small-scale intermittency by discussing energy–helicity interactions, energy-dissipation multifractality, and universality of intermittency, i.e., independence of anomalous scaling exponents from large-scale forcing and boundary conditions. A multifractal-based description of multiscale and multitime correlation functions in turbulence is also presented. Finally, we also briefly review the analytical difficulties, and hopes, of calculating anomalous exponents.


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  • Article Type: Review Article
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