Modulated rotating waves and triadic resonances in spherical fluid systems: The case of magnetized spherical Couette flow

The paper derives the azimuthal–frequency triad rules by multiplying the rotating-wave and Floquet-mode phases to obtain m2 = m0 + m1 and ω2 = ω0 + ω1 (its Eq. (7)), and discusses the trivial RW case (its Eq. (6)) . It then uses associated-Legendre/spherical-harmonic product rules to characterize latitudinal coupling and parity (its Eq. (14) and footnote on m+l parity) . The candidate solution reproduces exactly this mechanism: (a) the phase-product argument for (m,ω) addition, (b) Gaunt/Wigner selection rules for L with M = m1 + m2, and (c) the equatorial parity rule for poloidal modes. The small differences are expository (Legendre vs. Gaunt presentation); the core logic and conclusions coincide.