Variable-coefficient transport for sheared base flows

Develop the variable-coefficient transport theory for genuinely sheared base flows, replacing the finite-dimensional matrix-group description by Fourier integral operators and incorporating the changes in the dependent variable introduced by vorticity-, dilatation-, and related source reorganisations.

Background

The exact theory in the paper is restricted to spatially uniform, constant-coefficient effective media. In genuinely sheared flows, the propagation operators have variable coefficients, so the matrix-group transport used here must be replaced by a more general microlocal or Fourier-integral-operator framework. The authors also note that common reorganisations of acoustic analogies can change the dependent-variable map itself, requiring an extension of the fibre structure beyond operator transport alone.

References

Two remarks on scope. First, all exact computations below concern spatially uniform (constant-coefficient) effective media; genuinely sheared base flows, with variable coefficients, are outside the exact theory and are discussed as the principal open problem.

— A transport geometry of acoustic analogies:exact holonomy of source re-attribution and its observable consequences  (2608.12031 - Sharma, 12 Aug 2026) in Scope paragraph in Section 1; problem (4), Section 7.3 “Open problems”