# Comparison of vertical and isopycnal mixing models in the deep sea based on radon 222 measurements

## Abstract

A two-dimensional model is developed for the one-dimensional depth-dependent distribution of a radioactive tracer with a bottom source (e.g., radon 222) in a weakly baroclinic fluid. The tracer transport away from the boundary is separated into components with cardinal directions along and perpendicular to isopycnal surfaces in the fluid. Contrary to the case of a strictly one-dimensional mixing model, where properties such as heat and buoyancy have the same vertical eddy diffusivity as the tracer so that their vertical fluxes are uniquely related, this model yields a relation between vertical buoyancy and heat fluxes and the tracer flux which depends on the relative magnitude of the isopycnal and cross-isopycnal diffusivities. To close the problem, we assume that the interior vertical buoyancy flux is balanced by a horizontal cross-isopycnal Ekman drift at the bottom. As an example, a bottom radon 222 profile (Geosecs station 31) is analyzed. The buoyancy flux implied by the apparent vertical radon 222 diffusivity of 46 cm/sup 2/ s/sup -1/ is 2.1 x 10/sup -6/ cm/sup 2/ s/sup -3/, requiring a bottom friction velocity (u/sub asterisk/) of 0.94 cm s/sup -1/ to balance it in a one-dimensional model. In the two-dimensional isopycnal mixing model the buoyancy fluxmore »

- Authors:

- Publication Date:

- Research Org.:
- Geophysical Fluid Dynamics Laboratory, Princeton University, Princeton, New Jersey 08540

- OSTI Identifier:
- 5431177

- Resource Type:
- Journal Article

- Journal Name:
- J. Geophys. Res.; (United States)

- Additional Journal Information:
- Journal Volume: 85:C3

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 58 GEOSCIENCES; SEAS; MIXING; BOUNDARY LAYERS; DIFFUSION; HEAT FLUX; MASS TRANSFER; OCEANOGRAPHY; RADON 222; TRACER TECHNIQUES; TWO-DIMENSIONAL CALCULATIONS; ALPHA DECAY RADIOISOTOPES; DAYS LIVING RADIOISOTOPES; EVEN-EVEN NUCLEI; HEAVY NUCLEI; ISOTOPE APPLICATIONS; ISOTOPES; LAYERS; NUCLEI; RADIOISOTOPES; RADON ISOTOPES; SURFACE WATERS; 580500* - Oceanography- (1980-1989)

### Citation Formats

```
Sarmiento, J L, and Rooth, C G.H.
```*Comparison of vertical and isopycnal mixing models in the deep sea based on radon 222 measurements*. United States: N. p., 1980.
Web. doi:10.1029/JC085iC03p01515.

```
Sarmiento, J L, & Rooth, C G.H.
```*Comparison of vertical and isopycnal mixing models in the deep sea based on radon 222 measurements*. United States. doi:10.1029/JC085iC03p01515.

```
Sarmiento, J L, and Rooth, C G.H. Thu .
"Comparison of vertical and isopycnal mixing models in the deep sea based on radon 222 measurements". United States. doi:10.1029/JC085iC03p01515.
```

```
@article{osti_5431177,
```

title = {Comparison of vertical and isopycnal mixing models in the deep sea based on radon 222 measurements},

author = {Sarmiento, J L and Rooth, C G.H.},

abstractNote = {A two-dimensional model is developed for the one-dimensional depth-dependent distribution of a radioactive tracer with a bottom source (e.g., radon 222) in a weakly baroclinic fluid. The tracer transport away from the boundary is separated into components with cardinal directions along and perpendicular to isopycnal surfaces in the fluid. Contrary to the case of a strictly one-dimensional mixing model, where properties such as heat and buoyancy have the same vertical eddy diffusivity as the tracer so that their vertical fluxes are uniquely related, this model yields a relation between vertical buoyancy and heat fluxes and the tracer flux which depends on the relative magnitude of the isopycnal and cross-isopycnal diffusivities. To close the problem, we assume that the interior vertical buoyancy flux is balanced by a horizontal cross-isopycnal Ekman drift at the bottom. As an example, a bottom radon 222 profile (Geosecs station 31) is analyzed. The buoyancy flux implied by the apparent vertical radon 222 diffusivity of 46 cm/sup 2/ s/sup -1/ is 2.1 x 10/sup -6/ cm/sup 2/ s/sup -3/, requiring a bottom friction velocity (u/sub asterisk/) of 0.94 cm s/sup -1/ to balance it in a one-dimensional model. In the two-dimensional isopycnal mixing model the buoyancy flux can take on any value between 0 and 2.1 x 10/sup -6/ cm/sup 2/ s/sup -3/ with corresponding values for u/sub asterisk/, which was not measured, of 0--0.94 cm s/sup -1/. For an assumed u/sub asterisk/ value of 0.1 cm s/sup -1/ the cross-isopycnal diffusivity is 0.5 cm/sup 2/ s/sup -1/, implying a vertical buoyancy flux of 2.3 x 10/sup -8/ cm/sup 2/ s/sup -3/, and the diffusivity parallel to the isopycnals is 3.8 x 10/sup 6/ cm/sup 2/ s/sup -1/.},

doi = {10.1029/JC085iC03p01515},

journal = {J. Geophys. Res.; (United States)},

number = ,

volume = 85:C3,

place = {United States},

year = {1980},

month = {3}

}