# 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…

## One Citation

Mean field dynamo action in shear flows. I: fixed kinetic helicity

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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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