Energy transfer across scales in a non-ideal shock: the role of pressure-dilatation

In compressible flows, including turbulence, kinetic and internal energy budgets couple through two mechanisms. One is viscous dissipation which was proved in [1] to be confined to the smallest dissipation scale range. The second mechanism is pressure-dilatation, −P∇·u, which exchanges kinetic and internal energy via compression and rarefaction. It was shown in [2] that if the pressure-dilatation co-spectrum decays faster than k^-1, then mean pressure-dilatation exchanges mean kinetic and internal energy over a transitional “conversion” scale range of limited extent. Eyink & Drivas [3] proposed a mechanism they called ``pressure-dilatation defect,'' which can convert energy at arbitrarily small scales. Here, we examine these ideas in the context of a non-ideal shock and relate them to the shock structure.

[1] Aluie, H. et al. (2012), ApJ. Lett., doi: 10.1088/2041-8205/751/2/L29.

[2] Aluie, H. (2011), Phys. Rev. Lett., doi: 10.1103/PhysRevLett.106.174502.

[3] Eyink, G. & Drivas, T. (2018), Phys. Rev. X, doi: 10.1103/PhysRevX.8.011022.