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

@article{Singh2017PlaneSW,
  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},
  year={2017},
  volume={132},
  pages={403}
}
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… 
Mean field dynamo action in shear flows. I: fixed kinetic helicity
We study mean field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and non-zero correlation time (τ). We use plane shearing waves in

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