Dependence of mixed-layer entrainment on shear stress and velocity jump

From rotating-screen annulus experiments the entrainment rate, w e , normalized by the friction velocity, u * , has been found to be a function of both the overall Richardson number, R T , and the inverse Froude number, R v . The R T −½ dependence deduced by Price (1979) and Thompson (1979) satisfactorily explains the present data if multiplied by an approximate R v −1·4 dependence. The measurements indicate that R v is a variable that is influenced by side-wall friction, time after onset of the surface stress, or other factors. The greater w e / u * values of experiments of the type of Kantha, Phillips & Azad (1977) over that of the Kato & Phillips (1969) experiment can be explained by somewhat greater R v values in the latter case. A close connection is now apparent between entrainment experiments in two-layer systems designed to have only one velocity scale (the interfacial velocity jump, Δ v ), and the rotating-screen annulus experiments having two velocity scales ( u * and Δ v ). The former also have (at least) two velocity scales, the second one being associated with the presence of turbulence throughout one or both of the fluid layers. The turbulent layer is found to be quite well mixed in density only if w e / u * does not exceed about 0·03, or w e /|Δ v | does not exceed about 0·003. The present data suggest more rapid entrainment when temperature rather than salt provides the density jump, as first noted by Turner (1968) in oscillating grid experiments. If this is a Peclet-number effect, the trend did not continue for still greater P e values, the data for kaolin (clay) being very compatible with that for salt.