[A-CG38] 海洋と大気の波動・渦・循環の力学

[ACG38-07] Irreversible energy extraction from negative temperature two-dimensional turbulence

*大貫 陽平¹ (1.九州大学応用力学研究所大気海洋環境研究センター海洋モデリング分野)

キーワード：二次元乱流、統計力学、ジャルジンスキー等式

Large-scale motions of the atmosphere and ocean are idealized as two-dimensional turbulence. Energy transfer and structure formation of two-dimensional turbulence have attracted attention for a long time, and many past studies have analyzed them within an open domain or surrounded by a fixed lateral boundary. In this study, to extend our understanding of two-dimensional turbulence, we consider a flow system in a bounded domain whose shape is distorted by an externally imposed force. Unlike fixed boundary cases, this system exchanges energy with the external system via pressure work through the moving boundary. At the same time, the flow field is still constrained by vorticity conservation. When the vorticity equation is expanded onto the Laplacian eigenfunctions and truncated at a finite number, it satisfies Liouville's theorem. Consequently, based on energy and enstrophy constraints, a grand-canonical ensemble (GCE) with the temperature either positive or negative sign is defined. Starting from GCE, when one distorts the domain from one to another in a finite time, the Jarzynski equality establishes. The pressure work exerted on the system is thus related to the difference in the Helmholtz free energy. The direction of the inequality derived from the Jarzynski equality depends on the sign of the initial temperature. For a negative-temperature state, the moving boundary irreversibly extracts turbulence energy from the system via pressure work. This peculiar result gives a new interpretation for the inter-scale energy transfer in geophysical flows.