Kolmogorov's dissipation number and determining wavenumber for dyadic models

Mimi Dai; Margaret Hoeller; Qirui Peng; Xiangxiong Zhang

doi:10.1088/1361-6544/ad1af0

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arXiv · 2108.12913

Kolmogorov's dissipation number and determining wavenumber for dyadic models

Mimi Dai·Margaret Hoeller·Qirui Peng·Xiangxiong Zhang

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Abstract

We study some dyadic models for incompressible magnetohydrodynamics and Navier-Stokes equation. The existence of fixed point and stability of the fixed point are established. The scaling law of Kolmogorov's dissipation wavenumber arises from heuristic analysis. In addition, a time-dependent determining wavenumber is shown to exist; moreover, the time average of the determining wavenumber is proved to be bounded above by Kolmogorov's dissipation wavenumber. Additionally, based on the knowledge of the fixed point and stability of the fixed point, numerical simulations are performed to illustrate the energy spectrum in the inertial range below Kolmogorov's dissipation wavenumber.

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Mimi Dai, Margaret Hoeller, Qirui Peng, Xiangxiong Zhang. 2021-08-29. Kolmogorov's dissipation number and determining wavenumber for dyadic models. https://doi.org/10.1088/1361-6544/ad1af0

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