Plane shearing waves of arbitrary form: exact solutions of the NavierStokes equations
Abstract
We present exact solutions of the incompressible NavierStokes 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 timedependent) 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 shearperiodic boundary conditions.
 Publication:

arXiv eprints
 Pub Date:
 January 2011
 arXiv:
 arXiv:1101.5507
 Bibcode:
 2011arXiv1101.5507S
 Keywords:

 Astrophysics  Astrophysics of Galaxies;
 Physics  Fluid Dynamics
 EPrint:
 6 pages, 2 figures