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Scaling of shear-generated turbulence: the equatorial thermocline, a case study
  • Kelvin J Richards,
  • Andrei Natarov,
  • Glenn S. Carter
Kelvin J Richards
University of Hawaii at Manoa

Corresponding Author:[email protected]

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Andrei Natarov
IPRC/SOEST, University of Hawaii at Manoa
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Glenn S. Carter
University of Hawaii at Manoa
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We formulate an expression for the turbulent kinetic energy dissipation rate, $\epsilon$, associated with shear–generated turbulence in terms of readily measured properties of the flow or easily derived quantities in models. The expression depends on the turbulent vertical length scale, $\ell_v$, the inverse time scale $N$ and the Richardson number $Ri=N^2/S^2$, where $S$ is the vertical shear, with $\ell_v$ scaled in a way consistent with theories and observations of stratified turbulence. Unlike previous studies the focus is not so much on the functional form of $Ri$, but the vertical variation of the length scale $\ell_v$. Using data from two $\sim$7 day time series in the western equatorial Pacific the scaling is compared with the observed $\epsilon$. The scaling works well with the estimated $\epsilon$ capturing the differences in amplitude and vertical distribution of the observed $\epsilon$ between the two times series. Much of those differences are attributable to changes in the vertical distribution of the length scale $\ell_v$, and in particular the associated turbulent velocity scale, $u_t$. We relate $u_t$ to a measure of the fine-scale variations in velocity, $\tilde{u}$. Our study highlights the need to consider the length scale and its estimation in environmental flows. The implications for the vertical variation of the associated turbulent diffusivity are discussed.
May 2021Published in Journal of Geophysical Research: Oceans volume 126 issue 5. 10.1029/2020JC016978