On a Non-local Parameterisation for Shear Turbulence and the Uniqueness of its Solutions
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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.
KeywordsLogarithmic boundary layer Non-local turbulence closure Turbulent Couette flow Transilient turbulence Uniqueness of solution.
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- Berkowicz, R., Prahm, L.P. 1980‘On the Spectral Turbulent Diffusivity Theory for Homogeneous Turbulence’J. Fluid Mech.100433448Google Scholar
- Hinze, J.O. 1975TurbulenceMcGraw-HillNew York790Google Scholar
- Nakayama, A. and Bandou, M.: 1995, ‘Incorporation of Nonlocal Effects in Two-Equation Models’, in Proc. Int. Symp. Math. Modelling of Turbulent Flows, Tokyo, pp. 25–30.Google Scholar
- Nakayama, A., Nguyen, H. D., and Daif, M. B.: 1988, ‘Nonlocal Diffusion Model in Turbulent Boundary Layer’, in Proc. Third. Int. Symp. Refined Flow Modelling and Turbulence Measurements, International Association Hydraulic Research, pp. 305–312.Google Scholar
- Perry, A.E., Chong, M.S. 1982‘On the Mechanism of Wall Turbulence’J. Fluid Mech.119173217Google Scholar
- Robertson, J.M., Johnson, H.F. 1970‘Turbulence Structure in Plane Couette Flow’Proc. ASCE, J. Engng. Mech.9611711182Google Scholar
- Stull, R.B. 1984‘Transilient Turbulence Theory Part I: The Concept of Eddy-Mixing across Finite Distances’J. Atmos. Sci.4133513367Google Scholar