Shearing waves of arbitrary planform: exact solutions of the Navier-Stokes equations

Details Shearing waves of arbitrary planform: exact solutions of the Navier-Stokes equations Shearing waves of arbitrary planform: exact solutions of the Navier-Stokes equations

2011-01-28

arxiv.org/abs/1101.5507v1

Astronomy and Astrophysics

Astrophysics

Galaxy Astrophysics

8 pages, 1 figure

Scientific paper

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) wavevectors 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.

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