- The dependence of mixing efficiency on time-varying forcing is studied by direct numerical simulation
(DNS) of Kelvin–Helmholtz (KH) instability. Time-dependent forcing fields are designed to reproduce a
wavelike oscillation 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 forcing cycle and first examined via parameters characterizing waves: the minimum
Richardson number Riₘᵢₙ and the normalized frequency of the forcing ω/N. The effect of Reynolds number
Re₀ and the initial random disturbance amplitude b are also examined. In the experiments presented, Γ𝒸
varies between 0.21 and 0.36 and is controlled by the timing of two events: the emergence of KH billows and
the arrival of the deceleration of the mean shear by the wavelike forcing. Here, Γ𝒸 is higher than a canonical
value of 0.2 when the deceleration phase of the forcing suppresses the 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 the mean shear and thereby sustains turbulence after the
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. It is found that DNS also
corresponds to past observations if the forcing accelerates the mean shear to sustain turbulence.
- Inoue, Ryuichiro, William D. Smyth, 2009: Efficiency of Mixing Forced by Unsteady Shear Flow. J. Phys. Oceanogr., 39, 1150–1166.
|Funding Statement (additional comments about funding)
- This work is supported by the Office of Naval Research, the Natural Sciences and Engineering Research Council of Canada, and the National Science Foundation (Grants OCE0095640 and OCE0622922).
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