Internal mixing in stratified fluids

Using experimental measurements, estimates are made of the efficiency of conversion of kinetic energy into potential energy through vertical mixing in a continuously stratified fluid. In the experiments kinetic energy was supplied continuously at a rate of ε to a fundamental internal wave mode in a rectangularly bounded and initially linear stable stratification. Mixing resulted from the instability of this wave and its consequent ‘breaking’. Potential energy was gained by the system at rate $\dot{p}$ through the gradual weakening of the stratification. The instability is predictable using wave-interaction theory, affording a means of estimating the amount of kinetic energy lost (at rate ε_V) to laminar viscosity without first cascading to the fine scales characteristic of turbulent mixing. With account taken of this viscous loss the mixing efficiency $\dot{p}/\epsilon_{\rm M}$, based upon the residual kinetic energy input ε_M (= ε − ε_V) was found to be approximately constant, and not significantly correlated with the rate at which energy was supplied, nor with the estimated instantaneous minimum gradient Richardson number. The average value for eight separate experimental runs using two different experimental configurations was 0·26 with a sample standard deviation of 0·06. Measured density profiles also afforded an estimate of the effective vertical diffusivity κ _d of density as a result of mixing. Vertically averaged values of the product of κ _d and the squared local static buoyancy frequency N, $\overline{\kappa_{\rm d}N^2}$, were found to have an average for seven runs of 0·24ε _M , with a standard deviation for the coefficient of 0·1, and no significant correlation with energy supply rate. These results, the first of their kind to correct for incidental losses, substantiate the values previously assumed in estimates of dissipation and vertical diffusion in the ocean and the atmosphere, and validate the assumption of similarity between buoyancy and mass transfer on which they are based. The efficiency value also agrees with the kinematic prediction for localized homogenization in small discrete volumes made in the companion paper (McEwan 1983). On the basis of that work it is inferred from the present results that the mixing efficiency is only weakly dependent upon Prandtl number provided that this is of order unity or greater.