Quantifying Diapycnal Mixing in an Energetic Ocean

Turbulent diapycnal mixing controls global circulation and the distribution of tracers in the ocean. For turbulence in stratified shear flows, we introduce a new turbulent length scaleL ρdependent on χ. We show the flux Richardson number Ri f is determined by the dimensionless ratio of three length scales: the Ozmidov scale L O , the Corrsin shear scale L S , andL ρ . This new model predicts that Ri f varies from 0 to 0.5, which we test primarily against energetic field observations collected in 100 m of water on the Australian North West Shelf (NWS), in addition to laboratory observations. The field observations consisted of turbulence microstructure vertical profiles taken near moored temperature and velocity turbulence time series. Irrespective of the value of the gradient Richardson number Ri, both instruments yielded a median R i f = 0.17 , while the observed Ri f ranged from 0.01 to 0.50, in agreement with the predicted range of Ri f . Using a Prandtl mixing length model, we show that diapycnal mixingK ρcan be predicted fromL ρand the background vertical shear S. Using field and laboratory observations, we show thatL ρ = 0.3 L Ewhere L E is the Ellison length scale. The diapycnal diffusivity can thus be calculated fromK ρ = 0.09 L E S 2 . This prediction agrees very well with the diapycnal mixing estimates obtained from our moored turbulence instruments for observed diffusivities as large as10 − 1m 2 s −1 . Moorings with relatively low sampling rates can thus provide long time series estimates of diapycnal mixing rates, significantly increasing the number of diapycnal mixing estimates in the ocean.