Scaling Analysis of Time-Reversal Asymmetries in Fully Developed Turbulence
In fully developed turbulence, there is a flux of energy from large to small scales in the inertial range until the dissipation at small scales. It is associated with irreversibility, i.e., a breaking of the time reversal symmetry. Such turbulent flows are characterized by scaling properties, and we...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/8/630 |
| _version_ | 1797584723452624896 |
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| author | François G. Schmitt |
| author_facet | François G. Schmitt |
| author_sort | François G. Schmitt |
| collection | DOAJ |
| description | In fully developed turbulence, there is a flux of energy from large to small scales in the inertial range until the dissipation at small scales. It is associated with irreversibility, i.e., a breaking of the time reversal symmetry. Such turbulent flows are characterized by scaling properties, and we consider here how irreversibility depends on the scale. Indicators of time-reversal symmetry for time series are tested involving triple correlations in a non-symmetric way. These indicators are built so that they are zero for a time-reversal symmetric time series, and a departure from zero is an indicator of irreversibility. We study these indicators applied to two fully developed turbulence time series, from flume tank and wind tunnel databases. It is found that irreversibility occurs in the inertial range and has scaling properties with slopes close to one. A maximum value is found around the injection scale. This confirms that the irreversibility is associated with the turbulent cascade in the inertial range and shows that the irreversibility is maximal at the injection scale, the largest scale of the turbulent cascade. |
| first_indexed | 2024-03-10T23:55:42Z |
| format | Article |
| id | doaj.art-ce7f48f9f11e484f9043c80f921a2d55 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T23:55:42Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-ce7f48f9f11e484f9043c80f921a2d552023-11-19T01:11:53ZengMDPI AGFractal and Fractional2504-31102023-08-017863010.3390/fractalfract7080630Scaling Analysis of Time-Reversal Asymmetries in Fully Developed TurbulenceFrançois G. Schmitt0Laboratoire d’Océanologie et de Géosciences, CNRS, University Littoral Cote d’Opale, University Lille, UMR 8187, LOG, F 62930 Wimereux, FranceIn fully developed turbulence, there is a flux of energy from large to small scales in the inertial range until the dissipation at small scales. It is associated with irreversibility, i.e., a breaking of the time reversal symmetry. Such turbulent flows are characterized by scaling properties, and we consider here how irreversibility depends on the scale. Indicators of time-reversal symmetry for time series are tested involving triple correlations in a non-symmetric way. These indicators are built so that they are zero for a time-reversal symmetric time series, and a departure from zero is an indicator of irreversibility. We study these indicators applied to two fully developed turbulence time series, from flume tank and wind tunnel databases. It is found that irreversibility occurs in the inertial range and has scaling properties with slopes close to one. A maximum value is found around the injection scale. This confirms that the irreversibility is associated with the turbulent cascade in the inertial range and shows that the irreversibility is maximal at the injection scale, the largest scale of the turbulent cascade.https://www.mdpi.com/2504-3110/7/8/630turbulencescalingirreversibilitytime-reversal symmetryinertial range |
| spellingShingle | François G. Schmitt Scaling Analysis of Time-Reversal Asymmetries in Fully Developed Turbulence Fractal and Fractional turbulence scaling irreversibility time-reversal symmetry inertial range |
| title | Scaling Analysis of Time-Reversal Asymmetries in Fully Developed Turbulence |
| title_full | Scaling Analysis of Time-Reversal Asymmetries in Fully Developed Turbulence |
| title_fullStr | Scaling Analysis of Time-Reversal Asymmetries in Fully Developed Turbulence |
| title_full_unstemmed | Scaling Analysis of Time-Reversal Asymmetries in Fully Developed Turbulence |
| title_short | Scaling Analysis of Time-Reversal Asymmetries in Fully Developed Turbulence |
| title_sort | scaling analysis of time reversal asymmetries in fully developed turbulence |
| topic | turbulence scaling irreversibility time-reversal symmetry inertial range |
| url | https://www.mdpi.com/2504-3110/7/8/630 |
| work_keys_str_mv | AT francoisgschmitt scalinganalysisoftimereversalasymmetriesinfullydevelopedturbulence |