Covariant Chu-Kovasznay Decomposition: Resolving Thermodynamic Ambiguity in Compressible Flows

TL;DR

The paper introduces the Covariant Chu--Kovasznay Decomposition (CCKD), a geometric framework that clarifies thermodynamic ambiguities in compressible flows by analyzing shock interactions as near-unitary scattering maps within an effective acoustic spacetime.

Contribution

It formulates a covariant geometric decomposition on effective acoustic spacetime, resolving thermodynamic ambiguities and characterizing shock interactions as isometric scattering processes.

Findings

Shock--turbulence interaction acts as a near-unitary scattering map.

Entropy fluctuations are geometrically blue-shifted into sound.

Information transfer is preserved in the fluctuation mapping, with practical loss due to noise and model mismatch.

Abstract

We establish the Covariant Chu--Kovasznay Decomposition (CCKD), a geometric framework that resolves thermodynamic ambiguity in compressible mode content by formulating the decomposition on the effective acoustic spacetime. Enforcing orthogonality in the covariant Chu energy norm, we show that shock--turbulence interaction, often treated as a scattering source, is, in the idealized linear, inviscid setting, a near-unitary (Chu-isometric) scattering map constrained by conservation of covariant Chu-energy flux. In the canonical Shu-Osher problem, CCKD characterizes the shock as a thermo-acoustic lens, mathematically demonstrating that the transfer of entropy fluctuations into sound follows a geometric blue-shift ($k_{\mathrm{out}}=\Lambda k_{\mathrm{in}}$) analogous to gravitational blue-shift. Thus, while the mean flow produces entropy across the shock, the fluctuation mapping is information-preserving on the retained subspace; practical information loss arises from noise, truncation, and model mismatch, not shock physics.