# Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes

## Abstract

Studies of stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not addressed these measurements. Here we present numerical simulations that explain how the combined effect of spin-up and thermal boundary conditions enhances or hinders mixing of a fluid in a cylinder. The energy of the system is characterized by splitting the potential energy into diabatic and adiabatic components, and measurements of efficiency of mixing are based on both, the ratio of dissipation of available potential energy to forcing and variance of temperature. The numerical simulations of the Navier–Stokes equations for the problem with different sets of thermal boundary conditions at the horizontal walls helped shed some light on the physical mechanisms of mixing, for which a clear explanation was absent.

- Authors:

- Department of Mechanical Engineering, California State University, Los Angeles, Los Angeles, California 90032 (United States)
- SAP Americas Inc., Scottsdale, Arizona 85251 (United States)
- (United States)
- Dipartimento di Ingegneria Meccanica, Universita di Roma “Tor Vergata”, Via del Politecnico 1, 00133, Roma (Italy)
- (Netherlands)

- Publication Date:

- OSTI Identifier:
- 22311056

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Fluids (1994)

- Additional Journal Information:
- Journal Volume: 26; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-6631

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; COMPUTERIZED SIMULATION; CYLINDERS; EFFICIENCY; FLUIDS; MIXING; NAVIER-STOKES EQUATIONS; NONLINEAR PROBLEMS; POTENTIAL ENERGY; WALLS

### Citation Formats

```
Baghdasarian, Meline, Pacheco-Vega, Arturo, Pacheco, J. Rafael, E-mail: rpacheco@asu.edu, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, Environmental Fluid Dynamics Laboratories, Department of Civil Engineering and Geological Sciences, The University of Notre Dame, South Bend, Indiana 46556, Verzicco, Roberto, and PoF, University of Twente, 7500 AE Enschede.
```*Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes*. United States: N. p., 2014.
Web. doi:10.1063/1.4895435.

```
Baghdasarian, Meline, Pacheco-Vega, Arturo, Pacheco, J. Rafael, E-mail: rpacheco@asu.edu, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, Environmental Fluid Dynamics Laboratories, Department of Civil Engineering and Geological Sciences, The University of Notre Dame, South Bend, Indiana 46556, Verzicco, Roberto, & PoF, University of Twente, 7500 AE Enschede.
```*Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes*. United States. doi:10.1063/1.4895435.

```
Baghdasarian, Meline, Pacheco-Vega, Arturo, Pacheco, J. Rafael, E-mail: rpacheco@asu.edu, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, Environmental Fluid Dynamics Laboratories, Department of Civil Engineering and Geological Sciences, The University of Notre Dame, South Bend, Indiana 46556, Verzicco, Roberto, and PoF, University of Twente, 7500 AE Enschede. Mon .
"Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes". United States. doi:10.1063/1.4895435.
```

```
@article{osti_22311056,
```

title = {Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes},

author = {Baghdasarian, Meline and Pacheco-Vega, Arturo and Pacheco, J. Rafael, E-mail: rpacheco@asu.edu and School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287 and Environmental Fluid Dynamics Laboratories, Department of Civil Engineering and Geological Sciences, The University of Notre Dame, South Bend, Indiana 46556 and Verzicco, Roberto and PoF, University of Twente, 7500 AE Enschede},

abstractNote = {Studies of stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not addressed these measurements. Here we present numerical simulations that explain how the combined effect of spin-up and thermal boundary conditions enhances or hinders mixing of a fluid in a cylinder. The energy of the system is characterized by splitting the potential energy into diabatic and adiabatic components, and measurements of efficiency of mixing are based on both, the ratio of dissipation of available potential energy to forcing and variance of temperature. The numerical simulations of the Navier–Stokes equations for the problem with different sets of thermal boundary conditions at the horizontal walls helped shed some light on the physical mechanisms of mixing, for which a clear explanation was absent.},

doi = {10.1063/1.4895435},

journal = {Physics of Fluids (1994)},

issn = {1070-6631},

number = 9,

volume = 26,

place = {United States},

year = {2014},

month = {9}

}