# Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

## Abstract

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. In this study, we explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers $$0.05\lesssim Ri\lesssim 1$$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small $$Ri$$ the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger $$Ri$$ interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest $$Ri$$ but decreases rapidly as $$Ri$ increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. Finally, the distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.

- Authors:

- Universite de Lyon, ENS de Lyon, Universite Claude Bernard Lyon 1, CNRS (France)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1356145

- Report Number(s):
- LA-UR-17-20090

Journal ID: ISSN 0022-1120

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 815; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 58 GEOSCIENCES; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Earth Sciences; Planetary Sciences; turbulence, stratified, instability

### Citation Formats

```
Odier, Philippe, and Ecke, Robert E.
```*Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow*. United States: N. p., 2017.
Web. doi:10.1017/jfm.2017.48.

```
Odier, Philippe, & Ecke, Robert E.
```*Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow*. United States. doi:10.1017/jfm.2017.48.

```
Odier, Philippe, and Ecke, Robert E. Tue .
"Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow". United States.
doi:10.1017/jfm.2017.48. https://www.osti.gov/servlets/purl/1356145.
```

```
@article{osti_1356145,
```

title = {Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow},

author = {Odier, Philippe and Ecke, Robert E.},

abstractNote = {Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. In this study, we explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers $0.05\lesssim Ri\lesssim 1$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small $Ri$ the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger $Ri$ interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest $Ri$ but decreases rapidly as $Ri$ increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. Finally, the distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.},

doi = {10.1017/jfm.2017.48},

journal = {Journal of Fluid Mechanics},

number = ,

volume = 815,

place = {United States},

year = {Tue Feb 21 00:00:00 EST 2017},

month = {Tue Feb 21 00:00:00 EST 2017}

}