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 very nonadiabatic g ^ { - } modes and they are present in luminous stars , such as red giants with \log L / { L } _ { \odot } \ga 3 . Finite amplitudes for these modes are confined to the outermost nonadiabatic layers , where the radiative energy flux is more important than the convective energy flux . The periods of oscillatory convection modes increase with luminosity , and the growth times are comparable to the oscillation periods . The LSPs of red giants in the Large Magellanic Cloud ( LMC ) are observed to lie on a distinct period-luminosity sequence called sequence D. This sequence D period-luminosity relation is roughly consistent with the predictions for dipole oscillatory convective modes in AGB models if we 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 is consistent to models with \alpha = 1.9 , which predict periods too short by a factor of two .