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Mixed layer deepening due to wind-induced shear-driven turbulence and scaling of the deepening rate in the stratified ocean

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Wind-induced mixing forms the surface mixed layer (ML) above the stratified interior oceans. The ML depth (MLD), a key quantity for several upper ocean processes such as the air-sea interaction and primary production of phytoplankton biomass, is often scaled as \(U_{*}/\sqrt {Nf}\), where U is the friction velocity, N is the Brunt-Väisälä frequency, and f is the Coriolis parameter. Here, we performed large-eddy simulations (LESs) to evaluate this scaling. It was found that the ML deepens rapidly until one-half inertial period (0.5Tf) by which the MLD becomes \(1.6 - 1.7 U_{*}/\sqrt {Nf}\). Thereafter, the ML deepening slows down but never stops, and the MLD keeps increasing gradually. The MLDs at Tf, 1.5Tf, and 5Tf become greater than those at 0.5Tf by 6.2 %, 16 %, and 40 %, respectively. Therefore, time-dependent scaling of the MLD is necessary for more quantitative estimates than the classical theory. LESs performed with several U, N, and f showed that the deepening rate of the ML depends on the Rossby number and the Froude number. The present study proposes time-dependent scalings of the ML deepening rate and the MLD as a function of the Rossby number and the Froude number, which cover the classical scaling but can be extended even after 0.5Tf.

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Numerical computations were conducted using large-scale computer systems at the Cybermedia Center, Osaka University.


This work was financially supported by JSPS KAKENHI Grant Numbers JP15H05824.

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Correspondence to Yusuke Ushijima.

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Responsible Editor: Sandro Carniel

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The data used in this study are available online (

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Ushijima, Y., Yoshikawa, Y. Mixed layer deepening due to wind-induced shear-driven turbulence and scaling of the deepening rate in the stratified ocean. Ocean Dynamics 70, 505–512 (2020).

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