On the non-uniqueness of solutions in the modelling of steady wind flows

The two-dimensional, steady, turbulent Navier-Stokes Equations are explored for the case of a logarithmic profile. A general, analytical solution technique is presented, using potential functions; it contains two arbitrary functions. Example solutions are derived with the symbolic manipulator Maple; they show various shear stress profiles derived from a single form for the velocity profile. These stress variations occur within an 'equilibrium profile' and are affected by boundary conditions and upstream effects. Shear stress and dynamic roughness values derived from velocity profiles should be used with caution.