The Bernoulli integral for a certain class of non-stationary viscous vortical flows of incompressible fluid

Stepanyants, Y. A. and Yakubovich, E. I. (2015) The Bernoulli integral for a certain class of non-stationary viscous vortical flows of incompressible fluid. Studies in Applied Mathematics, 135 (3). pp. 295-309. ISSN 0022-2526


It has been shown in our previous paper that there is a wide class of 3D motions of incompressible viscous fluid which can be described by one scalar function dabbed the quasi-potential. This class of fluid flows is characterized by three-component velocity field having two-component vorticity field; both these fields can depend of all three spatial variables and time, in general. Governing equations for the quasi-potential have been derived and simple illustrative example of 3D flow has been presented. Here, we derive the Bernoulli integral for that class of flows and compare it against the known Bernoulli integrals for the potential flows or 2D stationary vortical flows of inviscid fluid. We show that the Bernoulli integral for this class of fluid motion possesses unusual features: it is valid for the vortical nonstationary motions of a viscous incompressible fluid. We present a new very nontrivial analytical example of 3D flow with two-component vorticity which hardly can be obtained by any of known methods. In the last section, we suggest a generalization of the developed concept which allows one to describe a certain class of 3D flows with the 3D vorticity.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Files associated with this item cannot be displayed due to copyright restrictions.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 25 May 2016 04:53
Last Modified: 23 Jun 2016 05:30
Uncontrolled Keywords: Bernoulli integral; viscous flow; incompressible fluid
Fields of Research : 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective: 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: 10.1111/sapm.12087

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