追踪对数网格上流体的复杂奇点

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-09-16 DOI:10.1088/1361-6544/ad7661

Quentin Pikeroen, Amaury Barral, Guillaume Costa, Ciro Campolina, Alexei Mailybaev and Berengere Dubrulle

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引用次数: 0

摘要

1981 年，Frisch 和 Morf（1981 年 Phys.由于在高雷诺数条件下模拟欧拉方程或纳维-斯托克斯方程所涉及的计算负担，这一猜想目前的进展受到阻碍。我们以对数晶格上的流体动力学为案例研究了这一猜想，与普通流体模拟相比，对数晶格上的计算负担是对数。我们分析了不同间距晶格的一维和三维模型中潜在复奇点的特性。我们使用奇点条带法跟踪主要的复奇点，从而获得有关接近实轴的新标度以及正耗散、超耗散和超耗散的影响。

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Tracking complex singularities of fluids on log-lattices

In 1981, Frisch and Morf (1981 Phys. Rev. A 23 2673–705) postulated the existence of complex singularities in solutions of Navier–Stokes equations. Present progress on this conjecture is hindered by the computational burden involved in simulations of the Euler equations or the Navier–Stokes equations at high Reynolds numbers. We investigate this conjecture in the case of fluid dynamics on log-lattices, where the computational burden is logarithmic concerning ordinary fluid simulations. We analyze properties of potential complex singularities in both 1D and 3D models for lattices of different spacings. Dominant complex singularities are tracked using the singularity strip method to obtain new scalings regarding the approach to the real axis and the influence of normal, hypo and hyper dissipation.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.