Entrainment of dry moat air with low equivalent potential temperature laterally into the eyewall and rainbands is a unique turbulent process in the inner-core region of a tropical cyclone (TC). By analyzing in-situ aircraft measurements collected by the reconnaissance flights that penetrated the eyewalls and rainbands of Hurricanes Rita (2005), Patricia (2015), Harvey (2017), and Michael (2018), as well as numerical simulations of Hurricanes Patricia (2015) and Michael (2018), we show that the moat air entrained into the eyewall and rainbands meets the instability criterion, and therefore, sinks unstably as a convective downdraft. The resultant positive buoyancy fluxes are an important source for the turbulent kinetic energy (TKE) in the eyewall and rainband clouds. This mechanism of TKE generation via lateral entrainment instability should be included in the TKE-type turbulent mixing schemes for a better representation of turbulent transport processes in numerical forecasts of TCs.