Sign-Indefinite Helicity and the Structure of Weak Turbulence in Inertial and Non-Hermitian Waves
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917458308235264 |
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| author | Shapira, Shahaf Aharony Shavit, Michal |
| author_facet | Shapira, Shahaf Aharony Shavit, Michal |
| contents | We investigate how sign-indefinite quadratic invariants shape turbulent cascades in incompressible flows with broken time-reversal symmetry, where the dynamics supports strongly anisotropic dispersive waves. Focusing on rotating Euler flow and odd-viscous Euler flow, we isolate the wave component study the corresponding weak-turbulence kinetic equation. We show that helicity conservation substantially simplifies the kinetic equation. Fixing the energy flux by a natural gauge choice, we identify the turbulent spectrum as the unique scale-invariant solution that sustains a constant flux of energy from large to small scales. Under a mild approximation motivated by the accumulation of energy near slow modes, we compute the leading angular dependence and uncover an integrable singularity along the slow-mode curve, that agrees with previous results. We then demonstrate that helicity reorganizes cascade directions at the level of resonant triads. Although helicity is globally sign-indefinite, the helical decomposition splits it into sign-definite contributions on each polarization branch. Triads whose three legs lie on the same branch behave as if constrained by a sign-definite invariant and drive an upscale transfer of energy, producing systematic backscatter even when the net cascade is direct. In the helicity-definite limit (single-branch dynamics), the kinetic equation admits an additional scale-invariant solution associated with helicity transport. Finally, we validate the analytical predictions by numerically evaluating the collision integral in the strongly anisotropic limit, revealing a family of stationary solutions in that regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14181 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sign-Indefinite Helicity and the Structure of Weak Turbulence in Inertial and Non-Hermitian Waves Shapira, Shahaf Aharony Shavit, Michal Fluid Dynamics Soft Condensed Matter Statistical Mechanics We investigate how sign-indefinite quadratic invariants shape turbulent cascades in incompressible flows with broken time-reversal symmetry, where the dynamics supports strongly anisotropic dispersive waves. Focusing on rotating Euler flow and odd-viscous Euler flow, we isolate the wave component study the corresponding weak-turbulence kinetic equation. We show that helicity conservation substantially simplifies the kinetic equation. Fixing the energy flux by a natural gauge choice, we identify the turbulent spectrum as the unique scale-invariant solution that sustains a constant flux of energy from large to small scales. Under a mild approximation motivated by the accumulation of energy near slow modes, we compute the leading angular dependence and uncover an integrable singularity along the slow-mode curve, that agrees with previous results. We then demonstrate that helicity reorganizes cascade directions at the level of resonant triads. Although helicity is globally sign-indefinite, the helical decomposition splits it into sign-definite contributions on each polarization branch. Triads whose three legs lie on the same branch behave as if constrained by a sign-definite invariant and drive an upscale transfer of energy, producing systematic backscatter even when the net cascade is direct. In the helicity-definite limit (single-branch dynamics), the kinetic equation admits an additional scale-invariant solution associated with helicity transport. Finally, we validate the analytical predictions by numerically evaluating the collision integral in the strongly anisotropic limit, revealing a family of stationary solutions in that regime. |
| title | Sign-Indefinite Helicity and the Structure of Weak Turbulence in Inertial and Non-Hermitian Waves |
| topic | Fluid Dynamics Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2603.14181 |