Parameterization of mixing in stratified open channel flow

The dynamics and parameterization of mixing in temporally evolving turbulent open-channel flow is investigated through direct numerical simulations as the flow transitions from an initially neutral state to stable stratification. We observe three distinctly different mixing regimes separated by transitional values of turbulent Froude number Fr: a weakly stratified regime for Fr > 1; an intermediate regime for 0.3 < Fr < 1; and a saturated regime for Fr < 0.3. The mixing coefficient Gamma =B/epsilon(K), (where B is the buoyancy flux and epsilon(K) is the dissipation rate of kinetic energy), is well predicted by the parameterization schemes of Maffioli et al. (J. Fluid Mech., vol. 794, 2016) and Garanaik & Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323-333) across all three regimes through instantaneous measurements of Fr and the ratio L-E/L-O, where L-E and L-O are the Ellison and Ozmidov length scales, respectively. The flux Richardson number R-f = B/(B + epsilon(K)) shows linear dependence on the gradient Richardson number Ri(g) up to a transitional value of Ri(g) = 0.25, past which it saturates again to a constant value independent of Fr or Ri(g). By examining the flow as a balance of inertial, shear and buoyancy forces, we derive physically based scaling relationships to demonstrate that Ri(g) similar to Fr-2 and Ri(g) similar to Fr-1 in the weakly and moderately stratified regimes and that Ri(g) becomes independent of Fr in the saturated regime. Our results suggest that the L-E/L-O similar to Fr-1 scaling of Garanaik & Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323-333) in the intermediate regime manifests due to the influence of mean shear. The differences in the relationships between Fr and L-E/L-O for non-sheared flows within this regime are discussed.

Automated summary

This study investigates the dynamics and parameterization of mixing in temporally evolving turbulent open-channel flow through direct numerical simulations. Three different mixing regimes are observed and the relationship between the mixing coefficient, flux Richardson number, and the gradient Richardson number is analyzed. Scaling relationships between Ri(g) and Fr are derived, and differences in the scaling of L-E/L-O with Fr-1 in the intermediate regime are discussed.