Distinct transverse-response signatures of retained-spin, eliminated-spin, and polynomial Burnett-type surrogate closures

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.