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Bottleneck phenomenon in developed turbulence. (English) Zbl 0865.76030
For an energy cascade in incompressible fluid, the dimensional analysis gives the energy spectrum in the form $$E(k)=\varepsilon^{2/3}k^{-5/3}f(k/k_p)$$, where $$\varepsilon$$ is the energy dissipation rate, $$k_p$$ is the cutoff wave number proportional to the dissipation wave number $$k_d=\varepsilon^{1/4}\nu^{-3/4}$$, $$\nu$$ is the viscosity of the fluid, and $$f(k/k_p)$$ is a function which is to be determined experimentally or theoretically. Many authors assumed that the function $$f$$ decreases monotonically with $$k$$. The author shows in the paper that this is not the reality. In particular, this fact is obvious in the bottleneck phenomenon in acoustic turbulence described by the author et al. in a paper quoted in the bibliography. Finally, different examples of both wave turbulence and vortex turbulence in incompressible fluid are considered.

##### MSC:
 76F99 Turbulence
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##### References:
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