Advanced Ocean Modelling: Using Open-Source Software

3.10 Mechanical Turbulence 49Fig. 3.23 Mixing of a two-layer stratified fluid with flow shear. Adapted from Cushman-Roisin (1994)be performed to raise heavier fluid parcels and to lower lighter fluid parcels againstthe reduced-gravity force. Hence, density stratification generally operates to lowerturbulence levels.Let us consider a simplified system pictured in Fig. 3.23. Initially, there aretwo superimposed layers of different densities in a stable stratification (lighterwater on top of heavier water). Each layer is in motion at a certain uniformspeed, but there is a strong velocity shear across the density interface. With equallayer thicknesses, energy conservation suggests that complete mixing occurs for(Cushman-Roisin, 1994):(ρ 2 − ρ 1 ) gHρ o (U 2 − U 1 ) 2 < 1where ρ o ≈ ρ 1 ≈ ρ 2 is a mean density, using the Boussinesq approximation.Localised mixing in vicinity of the density interface, however, is possible, if thewavelength of a perturbation λ is such that (Kundu, 1990):π (ρ 2 − ρ 1 ) gρ o (U 2 − U 1 ) 2 λ