### Lagrangian statistics in weakly forced two-dimensional turbulence

Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r

_{i}. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distributionmore »- Publication Date:

- Report Number(s):
- LA-UR-15-27458

Journal ID: ISSN 1054-1500

- Grant/Contract Number:
- AC52-06NA25396; W-7405-ENG-36

- Type:
- Accepted Manuscript

- Journal Name:
- Chaos (Woodbury, N. Y.)

- Additional Journal Information:
- Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 1; Journal ID: ISSN 1054-1500

- Publisher:
- American Institute of Physics (AIP)

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

- Sponsoring Org:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; planetary sciences; Lagrangian; turbulence

- OSTI Identifier:
- 1351187

- Alternate Identifier(s):
- OSTI ID: 1234931

```
Rivera, Michael K., and Ecke, Robert E..
```*Lagrangian statistics in weakly forced two-dimensional turbulence*. United States: N. p.,
Web. doi:10.1063/1.4937163.

```
Rivera, Michael K., & Ecke, Robert E..
```*Lagrangian statistics in weakly forced two-dimensional turbulence*. United States. doi:10.1063/1.4937163.

```
Rivera, Michael K., and Ecke, Robert E.. 2016.
"Lagrangian statistics in weakly forced two-dimensional turbulence". United States.
doi:10.1063/1.4937163. https://www.osti.gov/servlets/purl/1351187.
```

```
@article{osti_1351187,
```

title = {Lagrangian statistics in weakly forced two-dimensional turbulence},

author = {Rivera, Michael K. and Ecke, Robert E.},

abstractNote = {Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.},

doi = {10.1063/1.4937163},

journal = {Chaos (Woodbury, N. Y.)},

number = 1,

volume = 26,

place = {United States},

year = {2016},

month = {1}

}