A survey on a class of exact solutions of the Navier-Stokes equations and a model for turbulence
type: Item
instance of: scholarly article
title: A survey on a class of exact solutions of the Navier-Stokes equations and a model for turbulence
zbMATH Open document ID: 1070.76012
author: Koji Ohkitani
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2005-07-01T00:00:00Z
review text: Summary: We review some classes of exact solutions of Navier-Stokes equations for time-independent external straining flows, centering around the celebrated Burgers vortex. The objectives are to clarify the relationship between them, and to examine them as models of turbulence. Particularly, we study the Lundgren spiral model for turbulence in the presence of azimuthal vorticity (that is, with axial velocity). The implication on linear stability of Burgers vortex is briefly discussed.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76F02
Mathematics Subject Classification ID: 76D17
zbMATH DE Number: 2185482
zbMATH Keywords: Burgers vortex
zbMATH Keywords: Lundgren spiral model
zbMATH Keywords: linear stability
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145475447
OpenAlex ID: W2088919086
cites work: Q5749023
cites work: Exact solutions of the Navier-Stokes equations via Leray's scheme
cites work: Q5838342
cites work: On velocity structure functions and the spherical vortex model for isotropic turbulence
cites work: Vortex models of isotropic turbulence
cites work: On the fine-scale structure of turbulence
cites work: Q5621212
cites work: Strained spiral vortex model for turbulent fine structure
cites work: Q4326348
cites work: A small-scale turbulence model
cites work: On the Lundgren–Townsend model of turbulent fine scales
cites work: On the spectrum of a stretched spiral vortex
cites work: Axial motion and scalar transport in stretched spiral vortices
cites work: On the viscous core of a line vortex. I, II
cites work: Vorticity and the mathematical theory of incompressible fluid flow
cites work: The interaction of a diffusing line vortex and an aligned shear flow
cites work: The spiral wind-up of vorticity in an inviscid planar vortex
cites work: On the loss of smoothness of the solutions of the Euler equations and the inherent instability of flows of an ideal fluid
cites work: Distortion and evolution of a localized vortex in an irrotational flow
cites work: Nonlinear wind-up in a strained planar vortex
DOI: 10.2977/PRIMS/1145475447
description: scientific article; zbMATH DE number 2185482