The steady flow in and near a turbulent boundary layer on a sloping boundary is considered, for a nonrotating stratified fluid. It is shown that the effect of nonuniform stratification in the interior (i.e., away from the turbulent layer) is to induce a convergent--divergent flow in the boundary layer which results in an inflow or outflow to the intetior. This inflow-outflow acts in a divergent-convergent manner on the interior isopycnals. Use of a filling-box argument for the slow time variation of the interior then produces an approximate expression for an effective interior vertical diffusivity. The parameter dependence of this diffusivity is very strong; however, with realistic geophysical values (subject to the omission of rotation), e.g., a mixed layer depth of 50 m, Munk's canonical value of 10-4 m2 s-1 can easily be achieved. This work thus supports the view that boundary mixing is likely to be an important process in setting the vertical density profile in the ocean. ¿ American Geophysical Union 1991