Abstract

This structured literature review synthesizes the concepts of rotational dynamics and vortical structures across three traditionally distinct physical domains: classical fluid mechanics, relativistic cosmology, and quantum optics. The review establishes a unifying Gradient Principle, whereby the core dynamic effects in all systems—from fluid flow to structured light—are governed by the spatial gradients of their fundamental fields.

Key findings show that in fluid dynamics, the topological invariant, helicity (H), is remarkably conserved even during topology-changing vortex reconnection events, demonstrating an efficient mechanism for the transfer of rotational energy across scales. In the gravitational realm, the Lense–Thirring effect (frame dragging) manifests in wave optics by intricately altering gravitational lensing caustics, transforming lensing into a high-precision tool capable of directly measuring the spin (angular momentum content) of compact cosmic objects. For structured light, the conserved Orbital Angular Momentum (OAM), derived from SO(3) spacetime symmetry, requires engaging unconventional electric-quadrupole (E2) moments—dependent on the electric field gradient—to achieve discriminatory chiroptical interactions characterized by a signature spin-OAM (σℓ) coupling.

The review highlights two major critical gaps driving ongoing debates: the lack of stringent observational constraints on late-time, large-scale cosmic vorticity, which challenges the strict homogeneity implied by the Cosmological Principle (CP) and CDM model; and the deficiency of a comprehensive non-equilibrium thermodynamic framework to rigorously explain the physical trigger for rotational spontaneous symmetry breaking across scales. Future high-value research trajectories include implementing Vorticity-Constrained Cosmology (VCC) techniques and developing E2-driven spectroscopic systems to exploit these gradient-based rotational sensitivities.

Rotational Dynamics and Vortical Structures in Interconnected Systems: A Structured Review from Fundamental Fluidity to Cosmic and Quantum Scales

I. Foundational Principles and Classical Vorticity Dynamics

The systematic study of rotational motion in physical systems requires a rigorous approach rooted in continuum mechanics, even when analyzing highly complex phenomena ranging from atmospheric storms to astrophysical magnetic fields. The conceptual foundation for this analysis rests on vorticity (), a field quantity that quantifies the local spin of a fluid element.

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