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 ρ , rate of dissipation of turbulent kinetic energy ε, buoyancy frequency N and viscosity v , as time and volume averaged quantities. The behaviour of both L t and K ρ was characterized over a wide range of the turbulence intensity measure, ε/ vN 2 , and two regimes were identified. In the more energetic of these regimes (Regime E, where 300 < ε/ vN 2 < 10 5 ), L t was found to be a function of v , κ and N , whilst K ρ was a function of v , κ and (ε/ vN 2 ) 1/3 . From these expressions for L t and K ρ , 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 < ε/ vN 2 < 300) K ρ was a function of v , κ and ε/ vN 2 . For 10 < ε/ vN 2 < 1000, our directly measured diffusivities, K ρ , are approximately a factor of 2 different to the diffusivity predicted by the model of Osborn (1980). For ε/ vN 2 > 1000, our measured diffusivities diverge from the model prediction. For example, at ε/ vN 2 ≈ 10 4 there is at least an order of magnitude difference between the measured and predicted diffusivities.