Theoretical Description of Instability Waves in the Flow on a Rotating Disk Part 1. False-Expansion Method Applied to Linear Stability Equations

摘要

Linear stability characteristics of rotating-disk flow are governed by partial differential equations, because variation of basic-flow velocities with the radial distance yields non-parallel terms. A new method of small-parameter expansion is proposed to decompose the original stability equations into a sequence of ordinary differential systems. The lowest-order approximation poses an eigenvalue problem, whose solutions establish a complex dispersion relation connecting complex frequency, complex wavenumbers and local Reynolds number.