Efficiency of shear-driven mixing forced by internal waves

The dependence of mixing efficiency on time-varying forcing is studied by direct numerical simulation (DNS) of Kelvin-Helmholtz (KH) instability. Timedependent forcing fields are designed to mimic a breaking internal wave by solving the equations of motion in a tilted coordinate frame and allowing the tilt angle to vary in time. Mixing efficiency Γc is defined as the ratio of potential energy gain to dissipation, both averaged over one wave cycle and examined via parameters representing forcing waves; minimum Richardson number Rimin and normalized frequency of the forcing ω/N . The effect of Reynolds number Re0 and the initial random disturbance amplitude b are also examined. In our experiments, Γc varies between 0.21 and 0.36 and is controlled by the timing of two events; the emergence of KH billows and arrival of the deceleration of the mean shear by the wave forcing. Γc is higher than canonical value of 0.2 when the deceleration phase of the wave suppresses less efficient turbulence after breakdown of KH billows. However, when Rimin and ω/N are small, KH billows start to develop before Rimin is achieved. Therefore, the forcing accelerates mean shear and thereby sustains turbulence after breakdown of KH billows. The canonical value is then reproduced in the DNS. Although larger values of Re0 and b intensify the development of KH billows and modify Γc, this effect is less significant when forcing fields act to sustain turbulence. The time averaged Thorpe scale and Ozmidov scale are also used to see how mixing is modified by forcing fields and compared with past microstructure measurements. We find that DNS also corresponds to past observations if the forcing accelerates mean shear to sustain turbulence.