Mixing in forced stratified turbulence and its dependence on large-scale forcing

• Published in: Journal of fluid mechanics Vol. 898
• Main Authors: Howland, Christopher J., Taylor, John R., Caulfield, C. P.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.09.2020
• Subjects: Buoyancy; Buoyancy flux; Computational fluid dynamics; Computer simulation; Density; Dimensional analysis; Eddy kinetic energy; Efficiency; Energy; Energy budget; Energy dissipation; Energy exchange; Flow velocity; Fluid mechanics; Froude number; Gravitational waves; Gravity; Gravity waves; Internal waves; JFM Papers; Kinematics; Numerical analysis; Potential energy; Quasi-steady states; Reynolds number; Simulation; Stratification; Studies; Turbulence; Variance analysis; stratified turbulence; stratified flows; turbulent mixing
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2020.383

We study direct numerical simulations of turbulence arising from the interaction of an initial background shear, a linear background stratification and an external body force. In each simulation the turbulence produced is spatially intermittent, with dissipation rates varying over orders of magnitude in the vertical. We focus analysis on the statistically quasi-steady states achieved by applying large-scale body forcing to the domain, and compare flows forced by internal gravity waves with those forced by vertically uniform vortical modes. By considering the turbulent energy budgets for each simulation, we find that the injection of potential energy from the wave forcing permits a reversal in the sign of the mean buoyancy flux. This change in the sign of the buoyancy flux is associated with large, convective density overturnings, which in turn lead to more efficient mixing in the wave-forced simulations. The inhomogeneous dissipation in each simulation allows us to investigate localised correlations between the kinetic and potential energy dissipation rates. These correlations lead us to the conclusion that an appropriate definition of an instantaneous mixing efficiency, $\unicode[STIX]{x1D702}(t):=\unicode[STIX]{x1D712}/(\unicode[STIX]{x1D712}+\unicode[STIX]{x1D700})$ (where $\unicode[STIX]{x1D700}$ and $\unicode[STIX]{x1D712}$ are the volume-averaged turbulent viscous dissipation rate and fluctuation density variance destruction rate respectively) in the wave-forced cases is independent of an appropriately defined local turbulent Froude number, consistent with scalings proposed for low Froude number stratified turbulence.