Scalar description of three-dimensional vortex flows of incompressible fluid

Stepanyants, Yu. A. ORCID: https://orcid.org/0000-0003-4546-0310 and Yakubovich, Evsey (2011) Scalar description of three-dimensional vortex flows of incompressible fluid. Doklady Physics, 56 (2). pp. 130-133. ISSN 1028-3358


Abstract

An essential progress in the investigation of flows of incompressible fluid may be achieved with the help of stream-function. Flow description by means of one scalar stream-function is much simpler than the description based on the three-dimensional vector field. Many interesting and physically important problems were solved by this way. However, the traditional usage of a stream-function is restricted by the assumption of certain symmetry of the flow: the method is applicable only to two-component flows, i.e. when the corresponding velocity field is effectively two-dimensional, e.g., plane flow. This restriction essentially limits the range of applicability of such approach.
In this paper we propose another approach, also based on the introduction of only one scalar function. However, we show that with this scalar function a wide class of non-stationary three-dimensional flows can be described. This class of flows includes both potential and vortex flows. In the latter case, the corresponding vorticity field may be two-component, in general. Characteristic features of such flows are described in details. Particular examples of flows are presented in the explicit form.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to published evrsion due to publisher copyright policy. The Journal 'Doklady Physics' is English translation of the Russian journal 'Doklady Akademii Nauk'.
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited: 30 Aug 2011 06:56
Last Modified: 15 Feb 2021 23:33
Uncontrolled Keywords: vortex flow; incompressible fluid; Bernoulli's integral
Fields of Research (2008): 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
01 Mathematical Sciences > 0105 Mathematical Physics > 010501 Algebraic Structures in Mathematical Physics
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Fields of Research (2020): 40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401207 Fundamental and theoretical fluid dynamics
49 MATHEMATICAL SCIENCES > 4902 Mathematical physics > 490201 Algebraic structures in mathematical physics
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: https://doi.org/10.1134/S1028335811020169
URI: http://eprints.usq.edu.au/id/eprint/18589

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