Does dissipative anomaly hold for compressible turbulence?

We systematically study dissipative anomaly in compressible turbulence using a direct numerical simulations (DNS) database spanning a large parameter space, and show that the classical incompressible scaling does not hold for the total dissipation field. We assess the scaling for the solenoidal and dilatational parts separately. The solenoidal dissipation obeys the same scaling as incompressible turbulence when rescaled on solenoidal variables. We propose new scaling laws for total dissipation that predict the transition between regimes dominated by the solenoidal and dilatational components, and confirm them by the DNS data. An analysis of dilatational dissipation shows that dissipative anomaly may hold if properly scaled for certain regimes; on this empirical basis, we propose a new criterion for the energy cascade in the dilatational component.