Dissipative Vortex Binaries in Compact Fluid Domains with Geometric Corrections
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| Format: | Preprint |
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2026
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| author | R., Aswathy K. Samanta, Rickmoy |
| author_facet | R., Aswathy K. Samanta, Rickmoy |
| contents | We study a dissipative extension of vortex-binary motion in a doubly periodic fluid domain. The underlying conservative system admits an exact integrable reduction to a single complex relative coordinate. Dissipation is introduced via a minimal rotated-velocity (mutual-friction) term, as motivated by finite-temperature superfluid dynamics, converting the Hamiltonian evolution into a mixed symplectic--gradient flow with monotonic energy decay for quantized vortices. In the local regime, the dissipative binary remains analytically solvable and admits closed-form solutions, with systematic corrections arising from the toroidal geometry. Equal same-sign vortices execute outward spiraling motion, while equal opposite-sign pairs (dipoles) undergo finite-time collapse in the planar limit. On the torus, however, the dipole orientation is no longer invariant: the geometry induces a slow angular drift, even in regimes where planar dynamics would preserve alignment. For unequal opposite-sign pairs, dissipation induces coupled contraction and rotation, leading to a finite-time nonlinear chirp characterized by $\dotω\proptoω^2$, in contrast with electromagnetic and gravitational inspirals where $\dotω\propto ω^{3}$ and $\dotω\propto ω^{11/3}$. These results highlight the interplay between Hamiltonian structure, dissipation, and geometry in periodic fluid systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23857 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dissipative Vortex Binaries in Compact Fluid Domains with Geometric Corrections R., Aswathy K. Samanta, Rickmoy Fluid Dynamics Quantum Gases Soft Condensed Matter Mathematical Physics We study a dissipative extension of vortex-binary motion in a doubly periodic fluid domain. The underlying conservative system admits an exact integrable reduction to a single complex relative coordinate. Dissipation is introduced via a minimal rotated-velocity (mutual-friction) term, as motivated by finite-temperature superfluid dynamics, converting the Hamiltonian evolution into a mixed symplectic--gradient flow with monotonic energy decay for quantized vortices. In the local regime, the dissipative binary remains analytically solvable and admits closed-form solutions, with systematic corrections arising from the toroidal geometry. Equal same-sign vortices execute outward spiraling motion, while equal opposite-sign pairs (dipoles) undergo finite-time collapse in the planar limit. On the torus, however, the dipole orientation is no longer invariant: the geometry induces a slow angular drift, even in regimes where planar dynamics would preserve alignment. For unequal opposite-sign pairs, dissipation induces coupled contraction and rotation, leading to a finite-time nonlinear chirp characterized by $\dotω\proptoω^2$, in contrast with electromagnetic and gravitational inspirals where $\dotω\propto ω^{3}$ and $\dotω\propto ω^{11/3}$. These results highlight the interplay between Hamiltonian structure, dissipation, and geometry in periodic fluid systems. |
| title | Dissipative Vortex Binaries in Compact Fluid Domains with Geometric Corrections |
| topic | Fluid Dynamics Quantum Gases Soft Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2604.23857 |