Is k −2 scaling sustained in shock–bubble interaction? A spectral and modal perspective

Abstract

Shock–bubble interaction constitutes a canonical problem in compressible turbulence, governed by the interplay of compressive and vortical dynamics. Numerical simulations are employed to examine light (He) and heavy (R22) bubbles using dynamic mode decomposition and Favre-weighted turbulent kinetic energy spectra. The flow initially displays steep, shock-dominated spectra consistent with Burgers-type scaling. Following shock passage, the light bubble generates coherent jet-driven vortices and a hierarchical energy cascade, producing departures from k−2 scaling. In contrast, the heavy bubble suppresses large-scale coherence and dissipates energy rapidly. These findings highlight that spectral evolution is dictated by the competition among baroclinic vorticity generation, compressibility, and shear-driven turbulence. Although the numerical analysis clarifies the persistence of k−2 spectral scaling in shock–bubble interactions, its applicability is limited by the two-dimensional inviscid framework adopted for incident shocks at Mach 1.22 and Mach 1.8. Extrapolation to fully three-dimensional flows requires caution, as additional dissipative and vortical mechanisms may modify the scaling behavior.