Goldilocks mixing in oceanic shear-induced turbulent overturns

We present a new, simple and physically motivated parameterization, based on the ratio of Thorpe Ozmidov scales, for irreversible turbulent flux coefficient $\varGamma _{\mathcal {M}}= {\mathcal {M}}/\epsilon$ , i.e. rate ${\mathcal {M}}$ at which background potential energy increases in stratified flow due to macroscopic motions dissipation kinetic $\epsilon$ . Our parameterization covers all three key phases (crucially, time) shear-induced turbulence life cycle: initial, ‘hot’ growing phase, intermediate energetically forced phase final ‘cold’ fossilization decaying phase. Covering allows us highlight importance one, we refer as ‘Goldilocks’ its apparently optimal (and so neither too hot nor cold, but just right) balance, transfer from shear mixing is most efficient. The value close 1/3 during this demonstrate appears be related an adjustment towards critical or marginal Richardson number sustained ${\sim }0.2\text {--}0.25$ Importantly, although buoyancy effects are still significant leading order dynamics balance ensures that (density) scalar nevertheless effectively ‘locked’ momentum. supporting evidence our through comparison with six oceanographic datasets span various generation regimes wide range geographical location depth. Using these observations, significance parameterizing inherently variable capturing associated rare energetic, yet fundamentally shear-driven not strongly stratified) overturns make disproportionate contribution total mixing. also representation young patches connecting small scale physics larger applications such ocean circulation tracer budgets. Shear-induced therefore central world's oceans, even seafloor, it critically important appreciate inherent time dependence evolution events: history matters