Does dissipative anomaly hold for compressible turbulence?

We systematically study dissipative anomaly in compressible turbulence

using a 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.