Optical Caustics as Probes of Turbulence and Flow Singularities

This work explores a conceptual and optical bridge between light caustics and turbulence, proposing a novel framework for investigating flow singularities within the Navier–Stokes equations. By treating turbulent velocity fields as dynamic refractive-index distributions, the propagation of light through such media produces caustic intensity patterns that encode the underlying flow’s spatiotemporal structure. The document outlines how caustic statistics—derived from ray mapping singularities and intensity fluctuations—can be correlated with turbulence metrics such as Kolmogorov scaling and intermittency exponents. This optical analogy suggests a new pathway toward detecting and characterizing near-singular regions in fluid motion through non-invasive optical observation, potentially offering experimental insight into the open problem of existence and smoothness in the Navier–Stokes framework.