Experimental behaviour of the free surface in a uniform laminar stream

It has been experimentally shown that in a uniform laminar free surface flow, the boundary conditions at the free surface cannot be represented by a simple non-shear condition. This statement is in particular supported by some experiments performed by the author on a high viscosity oil flow in a rectangular pipe. A surface shear viscosity may be introduced in order to characterize the behavior of the free surface (Boussinesq). The velocity profile was measured along the axis of symmetry of the cross section. The results were in agreement with those of some numerical computations based on the above model. Similar agreement was not achieved on comparing the experimental and theoretical values obtained for the shape factor, a global parameter depending on the shape of the cross section. Such a disagreement cannot be due to experimental error and suggests that the above model is inadequate.