text: The derivation of the Rayleigh–Kuo criterion was first written down by Hsiao-Lan Kuo in his paper called <nowiki/>dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere  from 1949. This derivation is repeated and simplified below.
  First, the assumptions made by Hsiao-Lan Kuo are discussed. Second, the Rayleigh equation is derived in order continue to derive the Rayleigh–Kuo criterion. By integrating this equation and filling in the boundary conditions, the Kuo criterion can be obtained.