Kolmogorov's dissipation number and determining wavenumber for dyadic models
Fluid Dynamics
2024-05-21 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2108.12913,
title = {Kolmogorov's dissipation number and determining wavenumber for dyadic models},
author = {Mimi Dai and Margaret Hoeller and Qirui Peng and Xiangxiong Zhang},
journal= {arXiv preprint arXiv:2108.12913},
year = {2024}
}