Lagrangian Estimates of Diapycnal Mixing in a Simulated K–H Instability

Abstract

The Lagrangian properties of a high-resolution, three-dimensional, direct numerical simulation of Kelvin? Helmholtz (K?H) instability are examined with the goal of assessing the ability of Lagrangian measurements to determine rates and properties of ocean mixing events. The size and rotation rates of the two-dimensional K?H vortices are easily determined even by individual trajectories. Changes in density along individual trajectories unambiguously show diapycnal mixing. These changes are highly structured during the early phases of the instability but become more random once the flow becomes turbulent. Only 36 particles were tracked, which is not enough to usefully estimate volume-averaged fluxes from the average rates of temperature change. Similarly, time-and volume-averaged vertical advective flux can be estimated to only 20% accuracy. Despite the relatively low Reynolds number of the flow, R? ≈ 100, the dissipation rates of energy ε and density variance ? are correlated with the spectral levels of transverse velocity and density in an inertial subrange, as expected for high-Reynolds-number turbulence. The Kolmogorov constants are consistent with previous studies. This suggests that these inertial dissipation methods are the most promising techniques for making useful measurements of diapycnal mixing rates from practical Lagrangian floats because they converge rapidly and have a clear theoretical basis.