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Plane shearing waves of arbitrary form: Exact solutions of the Navier-Stokes equations
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Max Planck Institute for Solar System Research, Germany.
Number of Authors: 2
2017 (English)In: The European Physical Journal Plus, ISSN 2190-5444, E-ISSN 2190-5444, Vol. 132, no 9, 403Article in journal (Refereed) Published
Abstract [en]

We present exact solutions of the incompressible Navier-Stokes equations in a background linear shear flow. The method of construction is based on Kelvin's investigations into linearized disturbances in an unbounded Couette flow. We obtain explicit formulae for all three components of a Kelvin mode in terms of elementary functions. We then prove that Kelvin modes with parallel (though time-dependent) wave vectors can be superposed to construct the most general plane transverse shearing wave. An explicit solution is given, with any specified initial orientation, profile and polarization structure, with either unbounded or shear-periodic boundary conditions.

Place, publisher, year, edition, pages
2017. Vol. 132, no 9, 403
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-148882DOI: 10.1140/epjp/i2017-11659-5ISI: 000412066800001OAI: oai:DiVA.org:su-148882DiVA: diva2:1159047
Available from: 2017-11-21 Created: 2017-11-21 Last updated: 2017-11-29Bibliographically approved

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Singh, Nishant K.
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