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Boundary-Layer Meteorology

, Volume 118, Issue 1, pp 69–82 | Cite as

On a Non-local Parameterisation for Shear Turbulence and the Uniqueness of its Solutions

  • Benoit Cushman-Roisin
  • Alastair D. Jenkins
Article

Abstract

A non-local parameterisation of shear turbulence is proposed, which includes a dimensionless multiplicative constant as the sole tunable parameter. Analytical and numerical solutions in the case of plane Couette flow exhibit sheared velocity profiles with logarithmic behaviour near the boundaries, and the classical logarithmic flow profile is reproduced for a semi-infinite domain. We also prove that the families of analytical solutions obtained are locally unique: if the velocity is a strictly-increasing function of the distance from the boundary, a small perturbation of the velocity profile must be of the same functional form as the basic flow.

Keywords

Logarithmic boundary layer Non-local turbulence closure Turbulent Couette flow Transilient turbulence Uniqueness of solution. 

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References

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Thayer School of Engineering, Dartmouth CollegeHanoverU.S.A
  2. 2.Bjerknes Centre for Climate Research, Geophysical InstituteBergenNorway

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