Distributional acoustic analogy across a moving interface (${\partial }_i{\partial }_j{T}_{ij}+{\partial }_t(Q{\delta }_s)-{\partial }_i(L_i{\delta }_s)$)

Mass and momentum flux defects at a moving interface add surface acoustic monopole and acoustic dipole terms to Lighthill acoustic analogy. For a physical conservative fluid shock wave, the Rankine-Hugoniot conditions set both defects to zero; the shock still affects distributional derivatives of the Lighthill stress tensor. A discontinuity alone is not independent mass or force injection.