Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 50, Issue 3, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1751-8121/50/3/035501
Keywords
Leith model; stationary Kolmogorov spectrum; large time behavior; self-similar solution; reflection wave
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Funding
- Grant EPRC (Engineering and Physics Research Council, UK) Fluctuation-driven phenomena and large deviations
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The last stage of evolution toward the stationary Kolmogorov spectrum of hydrodynamic turbulence is studied using the Leith model [1]. This evolution is shown to manifest itself as a reflection wave in the wavenumber space propagating from the largest toward the smallest wavenumbers, and is described by a self-similar solution of a new (third) kind. This stage follows the previously studied stage of an initial explosive propagation of the spectral front from the smallest to the largest wavenumbers reaching arbitrarily large wavenumbers in a finite time, and which was described by a self-similar solution of the second kind [2-4]. Nonstationary solutions corresponding to 'warm cascades' characterised by a thermalised spectrum at large wavenumbers are also obtained.
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