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Functional and generalized separable solutions to unsteady Navier-Stokes equations

Polyanin, Andrei D. and Zhurov, Alexei 2016. Functional and generalized separable solutions to unsteady Navier-Stokes equations. International Journal of Non-Linear Mechanics 79 , pp. 88-98. 10.1016/j.ijnonlinmec.2015.10.015

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Abstract

The paper studies unsteady Navier–Stokes equations with two space variables. It shows that the non-linear fourth-order equation for the stream function with three independent variables admits functional separable solutions described by a system of three partial differential equations with two independent variables. The system is found to have a number of exact solutions, which generate new classes of exact solutions to the Navier–Stokes equations. All these solutions involve two or more arbitrary functions of a single argument as well as a few free parameters. Many of the solutions are expressed in terms of elementary functions, provided that the arbitrary functions are also elementary; such solutions, having relatively simple form and presenting significant arbitrariness, can be especially useful for solving certain model problems and testing numerical and approximate analytical hydrodynamic methods. The paper uses the obtained results to describe some model unsteady flows of viscous incompressible fluids, including flows through a strip with permeable walls, flows through a strip with extrusion at the boundaries, flows onto a shrinking plane, and others. Some blow-up modes, which correspond to singular solutions, are discussed.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Dentistry
Medicine
Uncontrolled Keywords: Unsteady Navier–Stokes equations; Exact solutions; Generalized and functional separable solutions; Solutions in elementary functions; Blow-up.
Publisher: Elsevier
ISSN: 0020-7462
Date of Acceptance: 31 October 2015
Last Modified: 11 Oct 2019 14:25
URI: http://orca.cf.ac.uk/id/eprint/103142

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