Measurements of diapycnal diffusivities in stratified fluids

Linearly stratified salt solutions of different Prandtl number were subjected to turbulent stirring by a horizontally oscillating vertical grid in a closed laboratory system. The experimental set-up allowed the independent direct measurement of a root mean square turbulent lengthscale L-t, turbulent diffusivity for mass K-rho, rate of dissipation of turbulent kinetic energy epsilon, buoyancy frequency N and viscosity nu, as time and volume averaged quantities. The behaviour of both L-t and K-rho, was characterized over a wide range of the turbulence intensity measure, epsilon/nuN(2), and two regimes were identified. In the more energetic of these regimes (Regime E, where 300 < epsilon /vN(2) < 10(5)) was found to be a function of nu, kappa and N, whilst K-rho was a function of v, kappa and (epsilon/nuN(2))(1/3). From these expressions for L-t and K-rho a scaling relation for the root mean square turbulent velocity scale U-t was derived, and this relationship showed good agreement with direct measurements from other data sets. In the weaker turbulence regime (Regime W, where 10 < epsilon/nuN(2) < 300) K-rho was a function of nu, kappa and epsilon/nuN(2). For 10 < epsilon/nuN(2) < 1000, our directly measured diffusivities, K-rho are approximately a factor of 2 different to the diffusivity predicted by the model of Osborn (1980). For epsilon/nuN(2) > 1000, our measured diffusivities diverge from the model prediction. For example, at epsilon/nuN(2) there is at least an order of magnitude difference between the measured and predicted diffusivities.