Model of a truncated fast rotating flow at infinite Reynolds number
The purpose of this study is to examine the strongly rotating limit of a turbulent flowtheoretically and numerically. The goal is to verify the predictions of asymptotic theories. Given the limitations of experimental and dissipative numerical approaches to this problem, we use classical equilibrium...
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| Format: | Article |
| Language: | en_US |
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American Institute of Physics (AIP)
2014
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| Online Access: | http://hdl.handle.net/1721.1/86391 https://orcid.org/0000-0001-6025-457X |
| _version_ | 1826209544670281728 |
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| author | Bourouiba, Lydia |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Bourouiba, Lydia |
| author_sort | Bourouiba, Lydia |
| collection | MIT |
| description | The purpose of this study is to examine the strongly rotating limit of a turbulent flowtheoretically and numerically. The goal is to verify the predictions of asymptotic theories. Given the limitations of experimental and dissipative numerical approaches to this problem, we use classical equilibrium statistical mechanics. We apply the statistical mechanics approach to the inviscid truncated model of strongly rotating turbulence (in the small Rossby number range) and derive the theoretical spectra of the decoupled model. We use numerical simulations to complement these derivations and examine the relaxation to equilibrium of the inviscid unforced truncated rotating turbulent system for different sets of initial conditions. We separate our discussion into two time domains: the discussion of the decoupled phase with time below a threshold time t[subscript ⋆], for which a new set of invariants S are identified, and the coupled phase with a time beyond t[subscript ⋆], for which the quantities S are no longer invariants. We obtain a numerical evaluation of t[subscript ⋆] which is coherent with the theoretical asymptotic expansions. We examine if the quantities S play a constraining role on the coupled dynamics beyond t > t[subscript ⋆]. We find that the theoretical statistical predictions in the decoupled phase capture the horizontal dynamics of the flow. In the coupled phase, the invariants S are found to still play a constraining role on the short-timescale horizontal dynamics of the flow. These results are discussed in the larger context of previous rotating turbulence studies. |
| first_indexed | 2024-09-23T14:24:10Z |
| format | Article |
| id | mit-1721.1/86391 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:24:10Z |
| publishDate | 2014 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/863912022-10-01T21:06:18Z Model of a truncated fast rotating flow at infinite Reynolds number Bourouiba, Lydia Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Bourouiba, Lydia Bourouiba, Lydia The purpose of this study is to examine the strongly rotating limit of a turbulent flowtheoretically and numerically. The goal is to verify the predictions of asymptotic theories. Given the limitations of experimental and dissipative numerical approaches to this problem, we use classical equilibrium statistical mechanics. We apply the statistical mechanics approach to the inviscid truncated model of strongly rotating turbulence (in the small Rossby number range) and derive the theoretical spectra of the decoupled model. We use numerical simulations to complement these derivations and examine the relaxation to equilibrium of the inviscid unforced truncated rotating turbulent system for different sets of initial conditions. We separate our discussion into two time domains: the discussion of the decoupled phase with time below a threshold time t[subscript ⋆], for which a new set of invariants S are identified, and the coupled phase with a time beyond t[subscript ⋆], for which the quantities S are no longer invariants. We obtain a numerical evaluation of t[subscript ⋆] which is coherent with the theoretical asymptotic expansions. We examine if the quantities S play a constraining role on the coupled dynamics beyond t > t[subscript ⋆]. We find that the theoretical statistical predictions in the decoupled phase capture the horizontal dynamics of the flow. In the coupled phase, the invariants S are found to still play a constraining role on the short-timescale horizontal dynamics of the flow. These results are discussed in the larger context of previous rotating turbulence studies. 2014-05-02T19:17:57Z 2014-05-02T19:17:57Z 2008-07 2007-10 Article http://purl.org/eprint/type/JournalArticle 10706631 1089-7666 http://hdl.handle.net/1721.1/86391 Bourouiba, L. “Model of a Truncated Fast Rotating Flow at Infinite Reynolds Number.” Physics of Fluids 20, no. 7 (2008): 075112. © 2008 American Institute of Physics https://orcid.org/0000-0001-6025-457X en_US http://dx.doi.org/10.1063/1.2958319 Physics of Fluids Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Physics (AIP) Bourouiba |
| spellingShingle | Bourouiba, Lydia Model of a truncated fast rotating flow at infinite Reynolds number |
| title | Model of a truncated fast rotating flow at infinite Reynolds number |
| title_full | Model of a truncated fast rotating flow at infinite Reynolds number |
| title_fullStr | Model of a truncated fast rotating flow at infinite Reynolds number |
| title_full_unstemmed | Model of a truncated fast rotating flow at infinite Reynolds number |
| title_short | Model of a truncated fast rotating flow at infinite Reynolds number |
| title_sort | model of a truncated fast rotating flow at infinite reynolds number |
| url | http://hdl.handle.net/1721.1/86391 https://orcid.org/0000-0001-6025-457X |
| work_keys_str_mv | AT bourouibalydia modelofatruncatedfastrotatingflowatinfinitereynoldsnumber |