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

  title={Plane shearing waves of arbitrary form: Exact solutions of the Navier-Stokes equations},
  author={Nishant Kumar Singh and S. Sridhar Nordita and Kth - Royal Institute of Technology and Stockholm University and Sweden. and Max Planck Institute for Solar System Research and Gottingen and H Germany and Raman Research Institute and Bangalore and India.},
  journal={European Physical Journal Plus},
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… 
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Associate DIETRICH BELITZ, University of Oregon Editors: Condensed Matter Physics (Theoretical) J. IGNACIO CIRAC, Max-Planck-Institut für Quantenoptik Quantum Information RAYMOND E. GOLDSTEIN,