Plane shearing waves of arbitrary form: Exact solutions of the Navier-Stokes equations

Plane shearing waves of arbitrary form : Exact solutions of the Navier-Stokes equations

Singh, Nishant K. (author): KTH,Stockholms universitet,Nordiska institutet för teoretisk fysik (Nordita),Max Planck Institute for Solar System Research, Germany,Nordic Institute for Theoretical Physics NORDITA

Sridhar, S. (author)

(creator_code:org_t)

2017-09-28
2017
English.
In: The European Physical Journal Plus. - : Springer Science and Business Media LLC. - 2190-5444. ; 132:9

Related links:: https://doi.org/10.1...; show more...; https://link.springe...; https://urn.kb.se/re...; https://doi.org/10.1...; https://urn.kb.se/re...; show less...

Abstract Subject headings

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.

About the subject

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