Boundary-Layer Meteorology

, Volume 42, Issue 4, pp 337–369 | Cite as

Models of eddy viscosity for numerical simulation of horizontally inhomogeneous, neutral surface-layer flow

  • Martin Claussen
Article
Revised:

Abstract

Modification of a turbulent flow due to a change from a smooth to a rough surface has been studied by means of a stream function-vorticity model. Results of four models of eddy viscosity (or turbulent exchange coefficient) Kmhave been compared. The models are: (1) Km = l2S, where l is the mixing length and S is the deformation of mean flow; (2) Km ∼ E/S, which is based on the assumption that turbulent momentum flux is proportional to turbulent kinetic energy E; (3) Km ∼ lE1/2, the so called Prandtl-Kolmogoroff approach; and (4) Km ∼ E2/ɛ, the E — ɛ closure, where ɛ is the dissipation of turbulent kinetic energy.

It is found that net-production, i.e., the difference of production and dissipation of turbulent kinetic energy counteracts the influence of mean shear on turbulent shear stress and diminishes turbulent shear stress. The reduction of mixing-length, being predicted by Model 4 only, adds to this attenuation. As a consequence, in Models 2 and 4, loss of horizontal mean momentum is concentrated close to the ground, which results in an inflexion point in the logarithmic, vertical profile of horizontal mean velocity. By contrast, in Models 1 and 3, modification of turbulent shear stress reaches larger heights causing deeper internal boundary layers. Concerning the existence of an inflexion point in U(lnz), the depth of the internal boundary layer for mean velocity, and the modification of bottom shear stress, Model 4 comes closest to experimental data.

A remarkable difference of Models 1, 2, 3 and Model 4 is that only Model 4 predicts a very slow relaxation of eddy viscosity which can be attributed to the reduction of mixing-length.

Keywords

Shear Stress Turbulent Kinetic Energy Inflexion Point Vertical Profile Remarkable Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© D. Reidel Publishing Company 1988

Authors and Affiliations

  • Martin Claussen
    • 1
  1. 1.Forschungszentrum GeesthachtGeesthachtF.R.G.

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