Distinct transverse-response signatures of retained-spin, eliminated-spin, and polynomial Burnett-type surrogate closures
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| Format: | Preprint |
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2026
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| _version_ | 1866911622362038272 |
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| author | Tsuzuki, Satori |
| author_facet | Tsuzuki, Satori |
| contents | High-curvature observables in incompressible flows, including $k^4$-weighted spectra, can arise from explicit internal rotation, elimination of a fast spin variable, or polynomial higher-gradient closure. Building on a retained-spin micropolar closure derived separately from the Boltzmann--Curtiss equation, we show that these mechanisms are dynamically distinguishable in transverse linear response. In a fast-spin regime the retained-spin theory reduces to a one-field model with a rational $k$-dependent kernel whose low-$k$ expansion generates $k^4$ and $k^6$ terms, while preserving the large-$k$ roll-off of the eliminated degree of freedom. We compare four closures: incompressible Navier--Stokes, a polynomial Burnett-type surrogate, the explicit-spin micropolar theory, and the eliminated-spin rational-kernel theory. The explicit-spin theory has two poles, the eliminated-spin theory retains only the slow pole, and finite polynomial truncations fail qualitatively: a strict $k^4$ truncation becomes over-damped, while a matched $k^6$ truncation develops near-critical amplification and finite-$k$ instability. Many-particle event-driven simulations of perfectly rough spheres show that these observables are measurable and, in targeted campaigns, discriminating at the microscopic level: fixed-$k$ and multi-$k$ harmonic forcing resolve a finite spin-to-vorticity phase lag that strongly favors retained-spin dynamics over instantaneous adiabatic elimination, while the stronger-drive multi-$k$ vorticity response rejects a pure $k^2$ closure and favors the rational eliminated-spin kernel over a polynomial surrogate. Transverse response thus provides a practical diagnostic for separating retained rotational microphysics, eliminated-spin effective dynamics, and ordinary polynomial higher-gradient closures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00177 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distinct transverse-response signatures of retained-spin, eliminated-spin, and polynomial Burnett-type surrogate closures Tsuzuki, Satori Fluid Dynamics Mathematical Physics High-curvature observables in incompressible flows, including $k^4$-weighted spectra, can arise from explicit internal rotation, elimination of a fast spin variable, or polynomial higher-gradient closure. Building on a retained-spin micropolar closure derived separately from the Boltzmann--Curtiss equation, we show that these mechanisms are dynamically distinguishable in transverse linear response. In a fast-spin regime the retained-spin theory reduces to a one-field model with a rational $k$-dependent kernel whose low-$k$ expansion generates $k^4$ and $k^6$ terms, while preserving the large-$k$ roll-off of the eliminated degree of freedom. We compare four closures: incompressible Navier--Stokes, a polynomial Burnett-type surrogate, the explicit-spin micropolar theory, and the eliminated-spin rational-kernel theory. The explicit-spin theory has two poles, the eliminated-spin theory retains only the slow pole, and finite polynomial truncations fail qualitatively: a strict $k^4$ truncation becomes over-damped, while a matched $k^6$ truncation develops near-critical amplification and finite-$k$ instability. Many-particle event-driven simulations of perfectly rough spheres show that these observables are measurable and, in targeted campaigns, discriminating at the microscopic level: fixed-$k$ and multi-$k$ harmonic forcing resolve a finite spin-to-vorticity phase lag that strongly favors retained-spin dynamics over instantaneous adiabatic elimination, while the stronger-drive multi-$k$ vorticity response rejects a pure $k^2$ closure and favors the rational eliminated-spin kernel over a polynomial surrogate. Transverse response thus provides a practical diagnostic for separating retained rotational microphysics, eliminated-spin effective dynamics, and ordinary polynomial higher-gradient closures. |
| title | Distinct transverse-response signatures of retained-spin, eliminated-spin, and polynomial Burnett-type surrogate closures |
| topic | Fluid Dynamics Mathematical Physics |
| url | https://arxiv.org/abs/2604.00177 |