Front. Mar. Sci. Frontiers in Marine Science Front. Mar. Sci. 2296-7745 Frontiers Media S.A. 10.3389/fmars.2024.1408850 Marine Science Correction Corrigendum: Turbulent diapycnal fluxes as a pilot Essential Ocean Variable Le Boyer Arnaud 1 * Couto Nicole 1 * Alford Matthew H. 1 Drake Henri F. 2 Bluteau Cynthia E. 3 Hughes Kenneth G. 4 Naveira Garabato Alberto C. 5 Moulin Aurélie J. 6 Peacock Thomas 7 Fine Elizabeth C. 1 Mashayek Ali 8 Cimoli Laura 9 Meredith Michael P. 10 Melet Angelique 11 Fer Ilker 12 Dengler Marcus 13 Stevens Craig L. 14 15 1 Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA, United States 2 Department of Earth System Science, University of California, Irvine, Irvine, CA, United States 3 Institute of Ocean Sciences, Fisheries and Oceans Canada, Sidney, BC, Canada 4 College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR, United States 5 Ocean and Earth Science, University of Southampton, Southampton, United Kingdom 6 Applied Physics Laboratory, University of Washington, Seattle, WA, United States 7 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States 8 Department of Earth Sciences, University of Cambridge, Cambridge, United Kingdom 9 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom 10 British Antarctic Survey, Cambridge, United Kingdom 11 Scientific Directorate, Mercator Ocean International, Toulouse, France 12 Geophysical Institute, University of Bergen, Bergen, Norway 13 Research Division 1, Physical Oceanography, GEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany 14 National Institute of Water and Atmospheric Research, Wellington, New Zealand 15 Department of Physics, University of Auckland, Auckland, New Zealand

Edited and Reviewed by: Junhong Liang, Louisiana State University, United States

*Correspondence: Arnaud Le Boyer, aleboyer@ucsd.edu; Nicole Couto, ncouto@ucsd.edu

03 05 2024 2024 11 1408850 28 03 2024 08 04 2024 Copyright © 2024 Le Boyer, Couto, Alford, Drake, Bluteau, Hughes, Naveira Garabato, Moulin, Peacock, Fine, Mashayek, Cimoli, Meredith, Melet, Fer, Dengler and Stevens 2024 Le Boyer, Couto, Alford, Drake, Bluteau, Hughes, Naveira Garabato, Moulin, Peacock, Fine, Mashayek, Cimoli, Meredith, Melet, Fer, Dengler and Stevens

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 A Corrigendum on Turbulent diapycnal fluxes as a pilot Essential Ocean Variable by Le Boyer A, Couto N, Alford MH, Drake HF, Bluteau CE, Hughes KG, Naveira Garabato AC, Moulin AJ, Peacock T, Fine EC, Mashayek A, Cimoli L, Meredith MP, Melet A, Fer I, Dengler M and Stevens CL (2023). Front. Mar. Sci. 10:1241023. doi: 10.3389/fmars.2023.1241023 turbulent fluxes ocean turbulence turbulent diffusivity turbulent dissipation mixing efficiency dissipation rate GOOS EOV section-in-acceptance Physical Oceanography

Error in Figure/Table

In the published article, there was an error in Table 1 as published. The equations for eddy diffusion coefficients KT , KS , and Kρ in the “Mathematical Definition” column wrongly all began with Kρ . The corrected Table 1 and its caption “b is buoyancy; q is enthalpy; S is the salinity concentration; and C is an arbitrary scalar tracer concentration. u′,v′,w′ are microscale perturbations of ocean velocities. ρ is the water density. g is the gravitational constant. N is the buoyancy frequency. cp is the water thermal capacity. θ is the potential temperature. k0,kc represents the wavenumber range for spectral integration. ϕ u z   and ϕ θ z are the spectra of vertical shear and temperature gradient.” appear below.

Ocean Turbulent Mixing variable and its sub-variables.

Name Description Mathematical Definition Units
Essential Ocean Variable J b ,   J q ,   J S ,   J C Subsurface turbulent fluxes J b =   − g ρ 0 { w ′ ρ ′ } ¯ ≈ K ρ N 2 W kg-1
J q =   − ρ c p { w ′ θ ′ } ¯ ≈ ρ c p K θ d θ ¯ d z W m-2
J S =   − { w ′ S ′ } ¯ ≈ K S d S ¯ d z psu m s-1
J C =   − { w ′ C ′ } ¯ ≈ K C d C ¯ d z [C] m s-1
Sub-variables ϵ Rate of turbulent kinetic energy dissipation per unit mass ϵ = 7.5   ν ∫ k 0 k c ϕ u z 2 ( k ) d k W kg-1
χ Rate of temperature dissipation per unit mass χ = 6 κ θ ∫ k 0 k c ϕ θ z 2 ( k ) d k K2 s-1
Γ Mixing coefficient Γ = χ N 2 2 ϵ ( ∂ θ ¯ ∂ z ) 2 unitless
K T ,   K S ,   K ρ Eddy diffusion coefficient across density surfaces (of temperature, salinity, density, oxygen, nutrients, etc.) K T = χ θ / 2 θ z 2 K S = χ S / 2 S z 2 K ρ = Γ ϵ / N 2 m-2 s-1
Supporting variables d t ¯ d z ,   d S ¯ d z ,   d C ¯ d z Background vertical gradient of temperature, salinity, and tracer C K m-1, psu m-1, [C] m-1

b is buoyancy; q is enthalpy; S is the salinity concentration; and C is an arbitrary scalar tracer concentration. u′,v′,w′ are microscale perturbations of ocean velocities. ρ is the water density. g is the gravitational constant. N is the buoyancy frequency. cp is the water thermal capacity. θ is the potential temperature. k0,kc represents the wavenumber range for spectral integration. ϕ u z   and ϕ θ z are the spectra of vertical shear and temperature gradient.

The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.

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