# How we compute N matters to estimates of mixing in stratified flows

## Abstract

We know that most commonly used models for turbulent mixing in the ocean rely on a background stratification against which turbulence must work to stir the fluid. While this background stratification is typically well defined in idealized numerical models, it is more difficult to capture in observations. Here, a potential discrepancy in ocean mixing estimates due to the chosen calculation of the background stratification is explored using direct numerical simulation data of breaking internal waves on slopes. There are two different methods for computing the buoyancy frequency$N$$, one based on a three-dimensionally sorted density field (often used in numerical models) and the other based on locally sorted vertical density profiles (often used in the field), are used to quantify the effect of$$N$$on turbulence quantities. It is shown that how$$N$$is calculated changes not only the flux Richardson number$$R_{f}$$, which is often used to parameterize turbulent mixing, but also the turbulence activity number or the Gibson number$$Gi$$, leading to potential errors in estimates of the mixing efficiency using$$Gi$-based parameterizations.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Colorado State Univ., Fort Collins, CO (United States). Dept. of Civil and Environmental Engineering; Stanford Univ., CA (United States). Bob and Normal Street Environmental Fluid Mechanics Lab., Dept. of Civil and Environmental Engineering
- Stanford Univ., CA (United States). Bob and Normal Street Environmental Fluid Mechanics Lab., Dept. of Civil and Environmental Engineering

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1414351

- Report Number(s):
- LLNL-JRNL-733364

Journal ID: ISSN 0022-1120; applab; TRN: US1800685

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 831; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 58 GEOSCIENCES; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; internal waves; stratified turbulence; turbulent mixing

### Citation Formats

```
Arthur, Robert S., Venayagamoorthy, Subhas K., Koseff, Jeffrey R., and Fringer, Oliver B. How we compute N matters to estimates of mixing in stratified flows. United States: N. p., 2017.
Web. doi:10.1017/jfm.2017.679.
```

```
Arthur, Robert S., Venayagamoorthy, Subhas K., Koseff, Jeffrey R., & Fringer, Oliver B. How we compute N matters to estimates of mixing in stratified flows. United States. doi:10.1017/jfm.2017.679.
```

```
Arthur, Robert S., Venayagamoorthy, Subhas K., Koseff, Jeffrey R., and Fringer, Oliver B. Fri .
"How we compute N matters to estimates of mixing in stratified flows". United States. doi:10.1017/jfm.2017.679. https://www.osti.gov/servlets/purl/1414351.
```

```
@article{osti_1414351,
```

title = {How we compute N matters to estimates of mixing in stratified flows},

author = {Arthur, Robert S. and Venayagamoorthy, Subhas K. and Koseff, Jeffrey R. and Fringer, Oliver B.},

abstractNote = {We know that most commonly used models for turbulent mixing in the ocean rely on a background stratification against which turbulence must work to stir the fluid. While this background stratification is typically well defined in idealized numerical models, it is more difficult to capture in observations. Here, a potential discrepancy in ocean mixing estimates due to the chosen calculation of the background stratification is explored using direct numerical simulation data of breaking internal waves on slopes. There are two different methods for computing the buoyancy frequency$N$, one based on a three-dimensionally sorted density field (often used in numerical models) and the other based on locally sorted vertical density profiles (often used in the field), are used to quantify the effect of$N$on turbulence quantities. It is shown that how$N$is calculated changes not only the flux Richardson number$R_{f}$, which is often used to parameterize turbulent mixing, but also the turbulence activity number or the Gibson number$Gi$, leading to potential errors in estimates of the mixing efficiency using$Gi$-based parameterizations.},

doi = {10.1017/jfm.2017.679},

journal = {Journal of Fluid Mechanics},

number = ,

volume = 831,

place = {United States},

year = {2017},

month = {10}

}

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