### Abstract

Osborn's method is commonly used to obtain diffusion coefficient K from the turbulent dissipation rate e. This method is the relational expression K=Γε/N^{2}. The dissipation flux coefficient Γ is often set to a constant value of 0.2, but this study of LES revealed that γ varies greatly vertically in the bottom boundary layer because of the influence of the seabed. Consequently, the eddy diffusion coefficient is overestimated in the lower part of the bottom boundary, but it is slightly underestimated in the upper part. Therefore, Osborn's method with constant Γ cannot give the correct diffusivity. Furthermore, even if treating Γ as a function of flux Richardson number R_{f} as defined originally by Osborn, the estimation is underestimated by the advection effect because of the influence of spatial nonuniformity. Energy budget analysis revealed that this defect can be improved using the extended flux Richardson number, which can be estimated by multiplying R_{f} using a constant correction factor. Furthermore, we proposed two alternative estimation methods. For the first method, which estimates the relation between R_{f} and the gradient Richardson number R_{g}, Γ can be expressed with R_{g} instead of R_{f} with a correction factor. We can estimate the reasonable diffusivity if we have current data supplementary to obtain . For the second method, Γ can be expressed as a similarity function of the height above the bottom normalized by the Ozmidov scale. This method can provide an acceptable estimate of diffusivity without current data for several circumstances.

Original language | English |
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Pages (from-to) | 1903-1920 |

Number of pages | 18 |

Journal | Journal of Physical Oceanography |

Volume | 48 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Oceanography

### Cite this

*Journal of Physical Oceanography*,

*48*(8), 1903-1920. https://doi.org/10.1175/JPO-D-17-0165.1

**LES study of vertical eddy diffusivity estimation in bottom boundary layers.** / Wakata, Yoshinobu.

Research output: Contribution to journal › Article

*Journal of Physical Oceanography*, vol. 48, no. 8, pp. 1903-1920. https://doi.org/10.1175/JPO-D-17-0165.1

}

TY - JOUR

T1 - LES study of vertical eddy diffusivity estimation in bottom boundary layers

AU - Wakata, Yoshinobu

PY - 2018/8/1

Y1 - 2018/8/1

N2 - Osborn's method is commonly used to obtain diffusion coefficient K from the turbulent dissipation rate e. This method is the relational expression K=Γε/N2. The dissipation flux coefficient Γ is often set to a constant value of 0.2, but this study of LES revealed that γ varies greatly vertically in the bottom boundary layer because of the influence of the seabed. Consequently, the eddy diffusion coefficient is overestimated in the lower part of the bottom boundary, but it is slightly underestimated in the upper part. Therefore, Osborn's method with constant Γ cannot give the correct diffusivity. Furthermore, even if treating Γ as a function of flux Richardson number Rf as defined originally by Osborn, the estimation is underestimated by the advection effect because of the influence of spatial nonuniformity. Energy budget analysis revealed that this defect can be improved using the extended flux Richardson number, which can be estimated by multiplying Rf using a constant correction factor. Furthermore, we proposed two alternative estimation methods. For the first method, which estimates the relation between Rf and the gradient Richardson number Rg, Γ can be expressed with Rg instead of Rf with a correction factor. We can estimate the reasonable diffusivity if we have current data supplementary to obtain . For the second method, Γ can be expressed as a similarity function of the height above the bottom normalized by the Ozmidov scale. This method can provide an acceptable estimate of diffusivity without current data for several circumstances.

AB - Osborn's method is commonly used to obtain diffusion coefficient K from the turbulent dissipation rate e. This method is the relational expression K=Γε/N2. The dissipation flux coefficient Γ is often set to a constant value of 0.2, but this study of LES revealed that γ varies greatly vertically in the bottom boundary layer because of the influence of the seabed. Consequently, the eddy diffusion coefficient is overestimated in the lower part of the bottom boundary, but it is slightly underestimated in the upper part. Therefore, Osborn's method with constant Γ cannot give the correct diffusivity. Furthermore, even if treating Γ as a function of flux Richardson number Rf as defined originally by Osborn, the estimation is underestimated by the advection effect because of the influence of spatial nonuniformity. Energy budget analysis revealed that this defect can be improved using the extended flux Richardson number, which can be estimated by multiplying Rf using a constant correction factor. Furthermore, we proposed two alternative estimation methods. For the first method, which estimates the relation between Rf and the gradient Richardson number Rg, Γ can be expressed with Rg instead of Rf with a correction factor. We can estimate the reasonable diffusivity if we have current data supplementary to obtain . For the second method, Γ can be expressed as a similarity function of the height above the bottom normalized by the Ozmidov scale. This method can provide an acceptable estimate of diffusivity without current data for several circumstances.

UR - http://www.scopus.com/inward/record.url?scp=85052159351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052159351&partnerID=8YFLogxK

U2 - 10.1175/JPO-D-17-0165.1

DO - 10.1175/JPO-D-17-0165.1

M3 - Article

VL - 48

SP - 1903

EP - 1920

JO - Journal of Physical Oceanography

JF - Journal of Physical Oceanography

SN - 0022-3670

IS - 8

ER -