Abstract
A long-term mean turbulent mixing in the depth range of 200–1000 m produced by breaking of internal waves across the middle and low latitudes (40°S–40°N) of the Pacific between 160°W and 140°W is examined by applying fine-scale parameterization depending on strain variance to 8-year (2005–2012) Argo float data. Results show that elevated turbulent dissipation rate (ε) is related to significant topographic regions, along the equator, and on the northern side of 20°N spanning to 24°N throughout the depth range. Two patterns of latitudinal variations of ε and the corresponding diffusivity (Kρ) for different depth ranges are confirmed: One is for 200–450 m with significant larger ε and Kρ, and the maximum values are obtained between 4°N and 6°N, where eddy kinetic energy also reaches its maximum; The other is for 350–1000 m with smaller ε and Kρ, and the maximum values are obtained near the equator, and between 18°S and 12°S in the southern hemisphere, 20°N and 22°N in the northern hemisphere. Most elevated turbulent dissipation in the depth range of 350–1000 m relates to rough bottom roughness (correlation coefficient = 0.63), excluding the equatorial area. In the temporal mean field, energy flux from surface wind stress to inertial motions is not significant enough to account for the relatively intensified turbulent mixing in the upper layer.
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Acknowledgements
We would like to thank Prof. Kitade Yujiro from Tokyo University of Marine Science and Technology for his helpful advices and comments. We are also grateful to the three anonymous reviewers for their constructive comments to improve this study. Argo float data were collected and made freely available by the International Argo Program and the national programs that contribute to it (http://www.argo.ucsd.edu, http://argo.jcommops.org). The Argo Program is part of the Global Ocean Observing System. NCEP Reanalysis data were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their website at http://www.esrl.noaa.gov/psd/. This work is supported by Shanghai Pujiang Program (Grant No. 15PJ1403000) and the National Natural Science Foundation of China (Grant No. 41506219).
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Appendix
Appendix
The damped slab model (D’Asaro 1985).
Mixed layer currents are triggered by sea surface wind stress, which can be expressed as
where, u and v are zonal and meridional components of the mixed layer velocity, t is time, f is inertial frequency, H is the mixed layer depth, \(\tau_{x}\) and \(\tau_{y}\) are zonal and meridional components of wind stress, and r is an artificial damping constant that parameterizes the transfer of energy from the mixed layer to the deeper ocean. Equations (9) and (10) can be expressed as
by using complex quantities
For a steady wind, the solution of Eq. (11) is \(Z_{\text{E}} = \frac{T}{\omega H}\), which is the Ekman transport. Then, the inertial oscillations \(Z_{\text{I}} = Z - Z_{\text{E}}\) in the rest solution can be described by
in which H changes much slower than the wind stress, thus dH/dt can be ignored.
An energy equation for the inertial motions is obtained by multiplying (15) by \(Z_{I}^{*}\), the complex conjugate of \(Z_{I}\),
where \(\varPi (H)\) is the energy flux from the wind stress into inertial motions in the mixed layer. For a short time interval \(\Delta t\) from t1 to t2, in Eq. (15), ZI2 can be solved as
where \(T_{t} = \Delta T/\Delta t\). The average flux of energy transferred to the inertial motions is finally obtained by
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Cheng, L., Gao, G. Evaluation of spatial distribution of turbulent mixing in the central Pacific. J Oceanogr 74, 471–483 (2018). https://doi.org/10.1007/s10872-018-0473-1
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DOI: https://doi.org/10.1007/s10872-018-0473-1