Collective Dynamics of Vortex Clusters in Compact Fluid Domains: From Pair Interactions to a Quadrupole Description
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911591157465088 |
|---|---|
| author | KR, Aswathy Samanta, Rickmoy |
| author_facet | KR, Aswathy Samanta, Rickmoy |
| contents | Clusters of co-rotating vortices on compact fluid domains exhibit a simple collective dynamics, combining coherent global rotation with a slow breathing of the cluster size. In this work, we investigate an analytically tractable model of vortex interactions on a doubly periodic inviscid fluid domain, based on an exact representation in terms of the Schottky--Klein prime function and its $q$-representation. The two-vortex problem reduces to a single complex degree of freedom, from which explicit expressions for the orbital rotation frequency and dipole translation velocity are obtained. Building on this framework, we derive a small-cluster expansion that reveals a universal decomposition of the dynamics into planar interactions, isotropic torus corrections, and geometry-induced anisotropic modes. At leading order, the collective dynamics admits a description in terms of a single complex quadrupole moment: its real part governs corrections to the rotation rate, while its imaginary part controls the slow breathing of the cluster. These predictions are quantitatively confirmed by direct numerical simulations, establishing a reduced description of vortex clusters on the flat torus and compact fluid domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07373 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Collective Dynamics of Vortex Clusters in Compact Fluid Domains: From Pair Interactions to a Quadrupole Description KR, Aswathy Samanta, Rickmoy Fluid Dynamics Quantum Gases Soft Condensed Matter Mathematical Physics Clusters of co-rotating vortices on compact fluid domains exhibit a simple collective dynamics, combining coherent global rotation with a slow breathing of the cluster size. In this work, we investigate an analytically tractable model of vortex interactions on a doubly periodic inviscid fluid domain, based on an exact representation in terms of the Schottky--Klein prime function and its $q$-representation. The two-vortex problem reduces to a single complex degree of freedom, from which explicit expressions for the orbital rotation frequency and dipole translation velocity are obtained. Building on this framework, we derive a small-cluster expansion that reveals a universal decomposition of the dynamics into planar interactions, isotropic torus corrections, and geometry-induced anisotropic modes. At leading order, the collective dynamics admits a description in terms of a single complex quadrupole moment: its real part governs corrections to the rotation rate, while its imaginary part controls the slow breathing of the cluster. These predictions are quantitatively confirmed by direct numerical simulations, establishing a reduced description of vortex clusters on the flat torus and compact fluid domains. |
| title | Collective Dynamics of Vortex Clusters in Compact Fluid Domains: From Pair Interactions to a Quadrupole Description |
| topic | Fluid Dynamics Quantum Gases Soft Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2604.07373 |