---
_id: '9145'
abstract:
- lang: eng
  text: "We have found a new way to express the solutions of the RSM (Reynolds Stress
    Model) equations that allows us to present the turbulent diffusivities for heat,
    salt and momentum in a way that is considerably simpler and thus easier to implement
    than in previous work. The RSM provides the dimensionless mixing efficiencies
    Γα (α stands for heat, salt and momentum). However, to compute the diffusivities,
    one needs additional information, specifically, the dissipation ε. Since a dynamic
    equation for the latter that includes the physical processes relevant to the ocean
    is still not available, one must resort to different sources of information outside
    the RSM to obtain a complete Mixing Scheme usable in OGCMs.\r\nAs for the RSM
    results, we show that the Γα’s are functions of both Ri and Rρ (Richardson number
    and density ratio representing double diffusion, DD); the Γα are different for
    heat, salt and momentum; in the case of heat, the traditional value Γh = 0.2 is
    valid only in the presence of strong shear (when DD is inoperative) while when
    shear subsides, NATRE data show that Γh can be three times as large, a result
    that we reproduce. The salt Γs is given in terms of Γh. The momentum Γm has thus
    far been guessed with different prescriptions while the RSM provides a well defined
    expression for Γm(Ri, Rρ). Having tested Γh, we then test the momentum Γm by showing
    that the turbulent Prandtl number Γm/Γh vs. Ri reproduces the available data quite
    well.\r\n\r\nAs for the dissipation ε, we use different representations, one for
    the mixed layer (ML), one for the thermocline and one for the ocean’s bottom.
    For the ML, we adopt a procedure analogous to the one successfully used in PB
    (planetary boundary layer) studies; for the thermocline, we employ an expression
    for the variable εN−2 from studies of the internal gravity waves spectra which
    includes a latitude dependence; for the ocean bottom, we adopt the enhanced bottom
    diffusivity expression used by previous authors but with a state of the art internal
    tidal energy formulation and replace the fixed Γα = 0.2 with the RSM result that
    brings into the problem the Ri, Rρ dependence of the Γα; the unresolved bottom
    drag, which has thus far been either ignored or modeled with heuristic relations,
    is modeled using a formalism we previously developed and tested in PBL studies.\r\nWe
    carried out several tests without an OGCM. Prandtl and flux Richardson numbers
    vs. Ri. The RSM model reproduces both types of data satisfactorily. DD and Mixing
    efficiency Γh(Ri, Rρ). The RSM model reproduces well the NATRE data. Bimodal ε-distribution.
    NATRE data show that ε(Ri < 1) ≈ 10ε(Ri > 1), which our model reproduces. Heat
    to salt flux ratio. In the Ri ≫ 1 regime, the RSM predictions reproduce the data
    satisfactorily. NATRE mass diffusivity. The z-profile of the mass diffusivity
    reproduces well the measurements at NATRE. The local form of the mixing scheme
    is algebraic with one cubic equation to solve."
article_processing_charge: No
article_type: original
author:
- first_name: V.M.
  full_name: Canuto, V.M.
  last_name: Canuto
- first_name: A.M.
  full_name: Howard, A.M.
  last_name: Howard
- first_name: Y.
  full_name: Cheng, Y.
  last_name: Cheng
- first_name: Caroline J
  full_name: Muller, Caroline J
  id: f978ccb0-3f7f-11eb-b193-b0e2bd13182b
  last_name: Muller
  orcid: 0000-0001-5836-5350
- first_name: A.
  full_name: Leboissetier, A.
  last_name: Leboissetier
- first_name: S.R.
  full_name: Jayne, S.R.
  last_name: Jayne
citation:
  ama: 'Canuto VM, Howard AM, Cheng Y, Muller CJ, Leboissetier A, Jayne SR. Ocean
    turbulence, III: New GISS vertical mixing scheme. <i>Ocean Modelling</i>. 2010;34(3-4):70-91.
    doi:<a href="https://doi.org/10.1016/j.ocemod.2010.04.006">10.1016/j.ocemod.2010.04.006</a>'
  apa: 'Canuto, V. M., Howard, A. M., Cheng, Y., Muller, C. J., Leboissetier, A.,
    &#38; Jayne, S. R. (2010). Ocean turbulence, III: New GISS vertical mixing scheme.
    <i>Ocean Modelling</i>. Elsevier. <a href="https://doi.org/10.1016/j.ocemod.2010.04.006">https://doi.org/10.1016/j.ocemod.2010.04.006</a>'
  chicago: 'Canuto, V.M., A.M. Howard, Y. Cheng, Caroline J Muller, A. Leboissetier,
    and S.R. Jayne. “Ocean Turbulence, III: New GISS Vertical Mixing Scheme.” <i>Ocean
    Modelling</i>. Elsevier, 2010. <a href="https://doi.org/10.1016/j.ocemod.2010.04.006">https://doi.org/10.1016/j.ocemod.2010.04.006</a>.'
  ieee: 'V. M. Canuto, A. M. Howard, Y. Cheng, C. J. Muller, A. Leboissetier, and
    S. R. Jayne, “Ocean turbulence, III: New GISS vertical mixing scheme,” <i>Ocean
    Modelling</i>, vol. 34, no. 3–4. Elsevier, pp. 70–91, 2010.'
  ista: 'Canuto VM, Howard AM, Cheng Y, Muller CJ, Leboissetier A, Jayne SR. 2010.
    Ocean turbulence, III: New GISS vertical mixing scheme. Ocean Modelling. 34(3–4),
    70–91.'
  mla: 'Canuto, V. M., et al. “Ocean Turbulence, III: New GISS Vertical Mixing Scheme.”
    <i>Ocean Modelling</i>, vol. 34, no. 3–4, Elsevier, 2010, pp. 70–91, doi:<a href="https://doi.org/10.1016/j.ocemod.2010.04.006">10.1016/j.ocemod.2010.04.006</a>.'
  short: V.M. Canuto, A.M. Howard, Y. Cheng, C.J. Muller, A. Leboissetier, S.R. Jayne,
    Ocean Modelling 34 (2010) 70–91.
date_created: 2021-02-15T14:40:19Z
date_published: 2010-05-12T00:00:00Z
date_updated: 2022-01-24T13:51:35Z
day: '12'
doi: 10.1016/j.ocemod.2010.04.006
extern: '1'
intvolume: '        34'
issue: 3-4
keyword:
- Computer Science (miscellaneous)
- Geotechnical Engineering and Engineering Geology
- Atmospheric Science
- Oceanography
language:
- iso: eng
month: '05'
oa_version: None
page: 70-91
publication: Ocean Modelling
publication_identifier:
  issn:
  - 1463-5003
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: 'Ocean turbulence, III: New GISS vertical mixing scheme'
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 34
year: '2010'
...