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Shell models of energy cascade in turbulence. (English) Zbl 1041.76037
Lumley, John L. (ed.) et al., Annual review of fluid mechanics. Vol. 35. Palo Alto, CA: Annual Reviews (ISBN 0-8243-0735-6/hbk). Annu. Rev. Fluid Mech. 35, 441-468 (2003).
Summary: 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 of 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.
For the entire collection see [Zbl 1005.00021].

MSC:
76F02 Fundamentals of turbulence
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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