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We discuss properties of oscillatory convective modes in low-mass red giants,and compare them with observed properties of the long secondary periods (LSPs)of semi-regular red giant variables. Oscillatory convective modes are verynonadiabatic g$^{-}$ modes and they are present in luminous stars, such as redgiants with $\log L/{\rm L}_\odot \ga 3$. Finite amplitudes for these modes areconfined to the outermost nonadiabatic layers, where the radiative energy fluxis more important than the convective energy flux. The periods of oscillatoryconvection modes increase with luminosity, and the growth times are comparableto the oscillation periods. The LSPs of red giants in the Large MagellanicCloud (LMC) are observed to lie on a distinct period-luminosity sequence calledsequence D. This sequence D period-luminosity relation is roughly consistentwith the predictions for dipole oscillatory convective modes in AGB models ifwe adopt a mixing length of 1.2 pressure scale height ($\alpha = 1.2$).However, the effective temperature of the red-giant sequence of the LMC isconsistent to models with $\alpha=1.9$, which predict periods too short by afactor of two.

Oscillatory convective modes in red giants: a possible explanation of the long secondary periods