Measurements of the mean velocity profiles of a free turbulent mercury jet in the presence of an axial magnetic field, with Reynolds numbers between 1 × 103and 6 × 103are reported. The Hartmann number, based on nozzle conditions, varied from zero to 40. It is found that the eddy viscosity divided by the square root of the kinematic momentum has a sharp maxima as a function of (Reynolds number)−1. A simple model which is consistent with the data is developed. The model suggests that, (1) the jet, although self similar, has a rate of energy dissipation which depends on phenomena occurring at the nozzle. (2) the maxima in eddy viscosity are caused by the excitation of a helical instability near the nozzle.