MODELS OF EDDY VISCOSITY FOR NUMERICAL SIMULATION OF HORIZONTALLY INHOMOGENEOUS, NEUTRAL SURFACE-LAYER FLOW MARTIN CLAUSSEN Forschungszentrum Geesthacht. Postfach 1160, D-2054 Geesthacht, F.R. G. (Received in final form 31 July, 1987) 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,,, have been compared. The models are: (1) K, = 1’S, where I is the mixing length and S is the deformation of mean flow; (2) K, u E/S, which is based on the assumption that turbulent momentum flux is proportional to turbulent kinetic energy E; (3) K, N lE’12, the so called Prandtl-Kolmogoroff approach; and (4) Km N E*/e, 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. 1. Introduction Modification of a neutrally stratified, turbulent flow due to a changein surfaceroughness has been studied for almost thirty years. A variety of turbulent closures has been proposed for investigation of horizontally inhomogeneous flow. Early models were analytically solvable integral models based on von K&rmti’s integral theorem, for instance (Elliott, 1958). Peterson (1969) and Taylor (1970) were the first to set up numerical models using different assumptions concerning eddy viscosity coefficients. Taylor (1970) has followed the mixing-length theory, which had been widely used in the study of horizontally homogeneous flow. (A steady-state, horizontally-homogeneous flow will be called equilibrium flow in the following.) The mixing-length theory states that turbulent shear stress z is a function of a mixing-length IO= KZ (IC is the von K&rmBn’s constant and z the height above ground) and the mean shear S: z = 12S2 0 . (1) Peterson (1969) has suggested that turbulent shear stress should be proportional to turbulent kinetic energy: Boundary-Layer Meteorology 42 (1988) 337-369. 0 1988 by D. Reidel Publishing Company.