Structure function of helicity in compressible homogeneous isotropic turbulence

In this paper, we investigate compressibility effects on helicity using structure functions and third-order relations. The helicity scaling law ${r}^{2/3}$ holds in compressible turbulence, as helicity remains unaffected by compressive components. A new third-order relation introduces pressure and divergence terms, which are crucial in the dissipative range and drive inverse helicity cascades in the inertial range, respectively. Our findings clarify the role of compressibility in interscale helical dynamics, providing insights for its application in compressible turbulence and future theoretical advancements.