Irreversible energy extraction from negative-temperature two-dimensional turbulence
| Autor: | Yohei Onuki |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Physical Review E. 106 |
| ISSN: | 2470-0053 2470-0045 |
| DOI: | 10.1103/physreve.106.064131 |
| Popis: | The formation and transition of patterns observed in various geophysical turbulent flows are commonly explained in terms of statistical mechanics. This study aims to extend the range of such a statistical mechanics theory by introducing a perhaps novel conceptual model. We consider an inviscid two-dimensional flow contained in a bounded domain, the shape of which is distorted by an externally imposed force. Unlike the usual fixed boundary cases, the flow energy within the domain is exchanged with the external system via pressure work through the moving lateral boundary. Concurrently, the flow field remains constrained by vorticity conservation. The vorticity equation expanded onto time-dependent Laplacian eigenfunctions and subsequently truncated at a finite number satisfies Liouville's theorem. Consequently, based on energy and enstrophy constraints, a grand-canonical ensemble (GCE) is defined with a negative or positive temperature. Beginning from the GCE, when the domain shape is distorted from one shape to another in a finite time, the Jarzynski equality is established. The pressure work performed on the system is thus related to the difference in the Helmholtz free energy. The direction of the inequality between the mean work and the free energy difference derived from the Jarzynski equality depends on the sign of the initial temperature. If the temperature is negative, the pressure work irreversibly extracts flow energy from the system. This result provides new insights into the unique thermodynamic characteristics of geophysical flows. 41 pages, 14 figures, submitted to Physical Review E |
| Databáze: | OpenAIRE |
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