论 R.I. Nigmatulin 的静力近似与 L.F. Richardson 方程
大气与海洋物理
2020-09-03 v4 流体动力学
物理学史与哲学
摘要
‘当惯性力远小于重力时大气的水动力学与热力学方程’(2018)一文中给出的定理是错误的,因为当垂直加速度趋于零时,Navier-Stokes 方程组的解并不收敛于静力近似方程组的解。其主要后果是该文给出的尺度不适用于静力近似的应用。正确的渐近应由传统的静力参数 H/L 给出,其中 H 和 L 分别为运动的垂直与水平尺度。此外,对静力近似下 L.F. Richardson 垂直速度方程所作的尺度分析也是不正确的。
引用
@article{arxiv.2001.08637,
title = {On hydrostatic approximation by R.I. Nigmatulin and L.F. Richardson's equation},
author = {I. N. Sibgatullin},
journal= {arXiv preprint arXiv:2001.08637},
year = {2020}
}
备注
Comments on the paper by R.I.Nigmatulin: The equations of hydro- and thermodynamics of the atmosphere with low inertia forces compared with gravity, published in Journal of Applied Mathematics and Mechanics, 82, 472-484, 2018. link.springer.com/article/10.1134/S0015462818040201, (also in Russian dx.doi.org/10.31857/S003282350000205-5). Submitted to the same journal