A compressible linear theory of Richtmyer–Meshkov unstable interfaces propagating along cylindrical tubes

We develop a linear compressible theory for Richtmyer–Meshkov unstable interfaces propagating along cylindrical tubes. In contrast to classical planar periodic systems, the cylindrical geometry introduces non-periodic boundary conditions and produces distinct features in interface morphology and growth dynamics. Using a complete eigenfunction expansion based on Bessel modes, we derive the linear evolution equations for arbitrary initial interface shapes and study the growth rates and mode amplitudes. The analysis reveals qualitatively new fingering patterns, including substructures associated with each fundamental mode, which is a feature absent in periodic geometries. We also identify a universal scaling relation that collapses the growth rates and amplitudes of all cylindrical-tube fundamental modes onto a single curve and provides a direct mapping to the two-dimensional periodic case. The results of this study form a key step toward a comprehensive quantitative nonlinear theory of Richtmyer–Meshkov unstable interfaces between compressible fluids of arbitrary density ratios in cylindrical geometries from early to late times.