### Abstract

The current work involves identification of coherent structures in rotating turbulent Rayleigh-Benard convection (RBC) in a moderately large aspect-ratio (8:8:1) rectangular enclosure. The enclosure is rotating about a vertical axis passing through its center of gravity. The incompressible Navier-Stokes and energy equations are solved in a rotating frame of reference and the resulting velocity and thermal fields are analyzed to educe coherent structures. The flow structures have been investigated at different nondimensional rotation rates ranging from ω=0 to 10_{4} for a fixed Rayleigh number Ra=10_{7} and Prandtl number Pr=0.01, keeping the Ra_{w}/Ta ratio constant at 10_{-3} in order to stringently maintain Boussinesq approximation as well as to attain experimentally realizable rotational Rayleigh numbers. Coherent structures in the flow domain have been sought using different identification techniques, namely large eddy simulation (LES) decomposition using top-hat filter, proper orthogonal decomposition (POD) considering larger energy modes, second invariant (Q) of the velocity gradient tensor, and regions of negative λ2, the second largest eigenvalue of the tensor S_{ik}S_{kj} +Ω_{ik}Ω_{kj}. It has been found that the coherent structures educed using POD or LES decomposition at low to moderate rotation (ω=10 to 10_{3}) show the formation of two to three large-scale rolls aligned along both horizontal directions. At higher-rotation rates corresponding to ω=10_{4}, there is a breakup of large-scale structures into multiple small-scale rolls having random spatial orientation. The thermal structures educed using both POD and large-scale LES decomposition at zero rotation show randomly rising and descending plumes that at Ω=10 coalesce to form a large cylindrical thermal plume in the core of the cavity. Further increase of rotation leads again to breakup of the cylindrical plume into multiple random plumes. Isosurfaces of Q and λ2 reveal elongated tubular roll-like structures mainly concentrated near the side-wall regions, though at higher rotation-rate (ω= 10_{4}) the density of tubular structures increases significantly. There is a strong similarity of results obtained by large-scale LES decomposition and results obtained using mean plus first mode of POD decomposition. The structures educed using Q and λ2 are different in shape compared to LES or POD educed structures.

Original language | English |
---|---|

Article number | 125105 |

Journal | Physics of Fluids |

Volume | 18 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2006 |

### Fingerprint

### Keywords

- Benard convection
- Boundary layer turbulence
- Confined flow
- Eigenvalues and eigenfunctions
- Gravity waves
- Navier-Stokes equations
- Rotational flow

### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*18*(12), [125105]. https://doi.org/10.1063/1.2404939

**Investigation of coherent structures in rotating Rayleigh-Benard convection.** / Husain, A.; Baig, M. F.; Varshney, H.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 18, no. 12, 125105. https://doi.org/10.1063/1.2404939

}

TY - JOUR

T1 - Investigation of coherent structures in rotating Rayleigh-Benard convection

AU - Husain, A.

AU - Baig, M. F.

AU - Varshney, H.

PY - 2006/12

Y1 - 2006/12

N2 - The current work involves identification of coherent structures in rotating turbulent Rayleigh-Benard convection (RBC) in a moderately large aspect-ratio (8:8:1) rectangular enclosure. The enclosure is rotating about a vertical axis passing through its center of gravity. The incompressible Navier-Stokes and energy equations are solved in a rotating frame of reference and the resulting velocity and thermal fields are analyzed to educe coherent structures. The flow structures have been investigated at different nondimensional rotation rates ranging from ω=0 to 104 for a fixed Rayleigh number Ra=107 and Prandtl number Pr=0.01, keeping the Raw/Ta ratio constant at 10-3 in order to stringently maintain Boussinesq approximation as well as to attain experimentally realizable rotational Rayleigh numbers. Coherent structures in the flow domain have been sought using different identification techniques, namely large eddy simulation (LES) decomposition using top-hat filter, proper orthogonal decomposition (POD) considering larger energy modes, second invariant (Q) of the velocity gradient tensor, and regions of negative λ2, the second largest eigenvalue of the tensor SikSkj +ΩikΩkj. It has been found that the coherent structures educed using POD or LES decomposition at low to moderate rotation (ω=10 to 103) show the formation of two to three large-scale rolls aligned along both horizontal directions. At higher-rotation rates corresponding to ω=104, there is a breakup of large-scale structures into multiple small-scale rolls having random spatial orientation. The thermal structures educed using both POD and large-scale LES decomposition at zero rotation show randomly rising and descending plumes that at Ω=10 coalesce to form a large cylindrical thermal plume in the core of the cavity. Further increase of rotation leads again to breakup of the cylindrical plume into multiple random plumes. Isosurfaces of Q and λ2 reveal elongated tubular roll-like structures mainly concentrated near the side-wall regions, though at higher rotation-rate (ω= 104) the density of tubular structures increases significantly. There is a strong similarity of results obtained by large-scale LES decomposition and results obtained using mean plus first mode of POD decomposition. The structures educed using Q and λ2 are different in shape compared to LES or POD educed structures.

AB - The current work involves identification of coherent structures in rotating turbulent Rayleigh-Benard convection (RBC) in a moderately large aspect-ratio (8:8:1) rectangular enclosure. The enclosure is rotating about a vertical axis passing through its center of gravity. The incompressible Navier-Stokes and energy equations are solved in a rotating frame of reference and the resulting velocity and thermal fields are analyzed to educe coherent structures. The flow structures have been investigated at different nondimensional rotation rates ranging from ω=0 to 104 for a fixed Rayleigh number Ra=107 and Prandtl number Pr=0.01, keeping the Raw/Ta ratio constant at 10-3 in order to stringently maintain Boussinesq approximation as well as to attain experimentally realizable rotational Rayleigh numbers. Coherent structures in the flow domain have been sought using different identification techniques, namely large eddy simulation (LES) decomposition using top-hat filter, proper orthogonal decomposition (POD) considering larger energy modes, second invariant (Q) of the velocity gradient tensor, and regions of negative λ2, the second largest eigenvalue of the tensor SikSkj +ΩikΩkj. It has been found that the coherent structures educed using POD or LES decomposition at low to moderate rotation (ω=10 to 103) show the formation of two to three large-scale rolls aligned along both horizontal directions. At higher-rotation rates corresponding to ω=104, there is a breakup of large-scale structures into multiple small-scale rolls having random spatial orientation. The thermal structures educed using both POD and large-scale LES decomposition at zero rotation show randomly rising and descending plumes that at Ω=10 coalesce to form a large cylindrical thermal plume in the core of the cavity. Further increase of rotation leads again to breakup of the cylindrical plume into multiple random plumes. Isosurfaces of Q and λ2 reveal elongated tubular roll-like structures mainly concentrated near the side-wall regions, though at higher rotation-rate (ω= 104) the density of tubular structures increases significantly. There is a strong similarity of results obtained by large-scale LES decomposition and results obtained using mean plus first mode of POD decomposition. The structures educed using Q and λ2 are different in shape compared to LES or POD educed structures.

KW - Benard convection

KW - Boundary layer turbulence

KW - Confined flow

KW - Eigenvalues and eigenfunctions

KW - Gravity waves

KW - Navier-Stokes equations

KW - Rotational flow

UR - http://www.scopus.com/inward/record.url?scp=33846096284&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846096284&partnerID=8YFLogxK

U2 - 10.1063/1.2404939

DO - 10.1063/1.2404939

M3 - Article

VL - 18

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 12

M1 - 125105

ER -