The churning cauldron of turbulence burns energy in two distinct ways. Vortices, like whirlpools in a maelstrom, twist the fluid and rub layers against each other. Shock waves, like a sudden clap, abruptly compress the gas and turn motion into heat. For a long time it was thought that at very low viscosity the rate of these losses stops depending on it, a phenomenon known as the dissipative anomaly. But what happens when the flow moves faster than sound and compression becomes the dominant effect? It turns out there is not one anomaly but two.

Numerical simulations on grids with up to 2048³ points have shown that the normalized kinetic energy dissipation rate reaches a finite value at high Reynolds numbers. However, that value depends on the Mach number, the ratio of flow speed to sound speed. If the flow is subsonic or transonic (Mach number less than or about 1), dissipation approaches one constant. If the flow is highly supersonic (Mach number greater than 3), it approaches another. The data split into two branches, like a road forking at a mountain pass.

The geometry of these regions changes dramatically. At subsonic speeds, intense dissipation is spread across a network of shear layers with an effective dimension of about 2.5. At supersonic speeds, it concentrates in two-dimensional shock layers. The generation mechanisms also differ: at low Mach numbers, vortex stretching dominates; at high Mach numbers, it is the interaction of vortical and compressive motions within the shock layers. This is like how in one case energy is dissipated by the friction of many small gears, and in another by the sharp blow of a hammer.

Previously it was unclear whether the dissipative anomaly persists in compressible turbulence and how it depends on the Mach number. Now we see that the anomaly exists but splits into two branches. One branch corresponds to subsonic and transonic regimes, the other to highly supersonic ones. This difference is linked to a restructuring of the flow: from vortex tubes and fragmented shock waves to dominant shock layers. This result is important for building correct turbulence models in astrophysics, where supersonic flows are common, and in engineering calculations of high-speed flows.

The turbulence cauldron has no single recipe for burning energy. Vortices and shock waves, as two different mechanisms, lead to the same finish, energy loss, but along different roads. And these roads do not merge, even when viscosity becomes vanishingly small. The dissipative anomaly in compressible turbulence turns out to be double, and this changes our understanding of how energy leaves the flow.