Models of eddy viscosity for numerical simulation of horizontally inhomogeneous,neutral surface-layer flow |
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| Authors: | Martin Claussen |
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| Institution: | (1) Forschungszentrum Geesthacht, Postfach 1160, D-2054 Geesthacht, F.R.G. |
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| 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) K
mhave been compared. The models are: (1) K
m = l2S, where l is the mixing length and S is the deformation of mean flow; (2) K
m  E/S, which is based on the assumption that turbulent momentum flux is proportional to turbulent kinetic energy E; (3) K
m lE1/2, the so called Prandtl-Kolmogoroff approach; and (4) K
m E2/ , the E — closure, where 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. |
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