On turbulent entrainment at a stable density interface

Turbulent entrainment at the density interface of a stable two-layer stratified fluid is studied in the laboratory, a constant surface stress being applied at the free surface. Conservation of mass requires that the overall Richardson number Ri = Dg δρ/ρ u * 2 is constant in each experiment, where D is the depth of the mixed layer, g δρ/ρ the buoyancy difference and u * the friction velocity. If the entrainment rate E = u e / u * is a function only of Ri , it is therefore constant in each experiment and can be measured with a greater accuracy than has previously been attained. The functional dependence of u e / u * on Ri is established over the range 30 < Ri < 1000; it is found not to follow any simple power law. The entrainment rates are considerably higher than those measured by Kato & Phillips (1969), for which the fluid below the mixed layer was linearly stratified. Such a condition allows internal gravity waves to be radiated downwards and the reduction in entrainment rate is consistent with that found by Linden (1975).