Energy dissipation in high-resolution direct numerical simulations of compressible turbulence

Energy dissipation in compressible turbulence driven by solenoidal forcing is investigated using large-scale, high-resolution direct numerical simulations (DNS) in a periodic box. The simulations employ up to N³=8192³ grid points, achieving a maximum spatial resolution of η/Δx≈5.3, where η is the Kolmogorov length scale and Δx is the grid spacing. The Taylor microscale Reynolds number R_λ and turbulent Mach number M_t range from 100 to 300 and 0.1 to 0.6, respectively. The DNS results show that the dilatational component of the energy spectrum extends to higher wavenumbers with increasing M_t, indicating the development of smaller-scale turbulent structures, such as shocklets, in the flow field. Under conditions where such structures are pronounced—specifically at R_λ≈300 and M_t≈0.5—the ratio ε_d/ε_s of dilatational to solenoidal dissipation increases with η/Δx, suggesting that high-resolution DNS can accurately capture dilatational dissipation associated with shocklets. Moreover, ε_d/ε_s is observed to scale as M_t^α, ​where the exponent α depends on R_λ. At R_λ≈300, a fit over the range M_t≈0.3 to 0.5 yields α=6.1, which exceeds the value predicted by EDQNM theory and previous numerical studies (α=5) for moderate to high M_t.