The influence of convective heating on baroclinic instability in the presence of surface sensible heat and moisture fluxes is investigated. Following previous numerical work, a two-dimensional continuous model on an f plane incorporates diabatic heating effects due to cumulus convection and surface sensible heat flux using parameterizations based on a wave-induced unstable boundary layer and associated moist convective destabilization. The temperature-damping effect of surface sensible heat flux is assumed to decrease exponentially with height, and the vertical distribution of convective heating uses a prescribed profile. The atmosphere is assumed to overlie an oceanic surface. In this configuration, convective heating occurs in the wave’s cold sector.

General forms of the dispersion relation and eigenfunction are derived analytically. Results show that the most unstable wave is modified by the effect of convective latent heating. With weak convection, the wave’s structure does not change much, while the wave’s energy generation is hampered by the negative contribution of convection. In the presence of moderate convective heating, although the wave’s energy generation is decreased by convection, the wave adjusts its structure to minimize the negative effect of convection and retain growth. In the region with strong convective heating, convective heating significantly changes the wave’s temperature structure. Above and below the strong heating region, the wave structure still retains some features of the Eady mode. The results have bearing on how the structure of oceanic storms may be altered by convection.