Vortices and invariant surfaces generated by symmetries for the 3D Navier–Stokes equations

V. Grassi, R.A. Leo, G. Soliani and P. Tempesta

Physica A: Statistical Mechanics and its Applications, 2000, vol. 286, issue 1, 79-108

Abstract: We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier–Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of vortices and throws light on the alignment mechanism between the vorticity ω and the vortex stretching vector Sω, where S is the strain matrix. The symmetry algebra associated with the Navier–Stokes equations turns out to be infinite-dimensional. New vortical structures, generalizing in some cases well-known configurations such as, for example, the Burgers and Lundgren solutions, are obtained and discussed in relation to the value of the dynamic angle φ=arctan|ω→∧Sω→|/ω→·Sω→. A systematic treatment of the boundary conditions invariant under the symmetry group of the equations under study is also performed, and the corresponding invariant surfaces are recognized.

Keywords: Lie groups; Fluid dynamics (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437100002235
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:286:y:2000:i:1:p:79-108

DOI: 10.1016/S0378-4371(00)00223-5

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().