# Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

## Abstract

We report results on rotating stratified turbulence in the absence of forcing, with large-scale isotropic initial conditions, using direct numerical simulations computed on grids of up to $4096^3$ points. The Reynolds and Froude numbers are respectively equal to $$Re=5.4\times 10^4$$ and $Fr=0.0242$$. The ratio of the Brunt-V\"ais\"al\"a to the inertial wave frequency, $$N/f$, is taken to be equal to 5, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number $$R_B=ReFr^2=32$$, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the large-scale dynamics and confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation, and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow in the velocity and temperature fields, and a large-scale enhancement of energy is also observed, directly attributable to the effect of rotation.

- Authors:

- ORNL
- National Center for Atmospheric Research (NCAR)
- Universidad de Buenos Aires, Argentina

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1185644

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Fluids; Journal Volume: 27; Journal Issue: 5

- Country of Publication:
- United States

- Language:
- English

- Subject:
- turbulence; Bolgiano-Obukhov; direct numerical simulation; convective instabilities

### Citation Formats

```
Rosenberg, Duane L, Pouquet, Dr. Annick, Mininni, Dr. Pablo D., and Marino, Dr. Raffaele.
```*Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations*. United States: N. p., 2015.
Web. doi:10.1063/1.4921076.

```
Rosenberg, Duane L, Pouquet, Dr. Annick, Mininni, Dr. Pablo D., & Marino, Dr. Raffaele.
```*Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations*. United States. doi:10.1063/1.4921076.

```
Rosenberg, Duane L, Pouquet, Dr. Annick, Mininni, Dr. Pablo D., and Marino, Dr. Raffaele. Thu .
"Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations". United States.
doi:10.1063/1.4921076.
```

```
@article{osti_1185644,
```

title = {Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations},

author = {Rosenberg, Duane L and Pouquet, Dr. Annick and Mininni, Dr. Pablo D. and Marino, Dr. Raffaele},

abstractNote = {We report results on rotating stratified turbulence in the absence of forcing, with large-scale isotropic initial conditions, using direct numerical simulations computed on grids of up to $4096^3$ points. The Reynolds and Froude numbers are respectively equal to $Re=5.4\times 10^4$ and $Fr=0.0242$. The ratio of the Brunt-V\"ais\"al\"a to the inertial wave frequency, $N/f$, is taken to be equal to 5, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number $R_B=ReFr^2=32$, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the large-scale dynamics and confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation, and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow in the velocity and temperature fields, and a large-scale enhancement of energy is also observed, directly attributable to the effect of rotation.},

doi = {10.1063/1.4921076},

journal = {Physics of Fluids},

number = 5,

volume = 27,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}