Demonstration of the rotational viscosity transfer across scales in Navier–Stokes turbulence

Mechanical effects that span multiple physical scales-such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions-play a critical role in real fluid systems. The spin angular momentum-conserving Navier-Stokes equations offer a theoretical framework for describing such multiscale fluid dynamics by decomposing total angular momentum into bulk and intrinsic spin components. However, this framework still assumes locally non-solid rotational flows, a condition that remains empirically unverified. This study addresses such unvalidated assumptions intrinsic to the model and extends it within the framework of turbulence hierarchy theory. The theory suggests that under certain conditions, small-scale structures may transfer to larger scales through the rotational viscosity. To verify this, we conducted spectral analyses of freely decaying two-dimensional turbulence initialized with a vortex-concentrated distribution. The results indicate that rotational viscosity exhibits interscale transfer behavior, revealing a new mechanism by which order can propagate from small to large scales in Navier-Stokes turbulence.