Temporal Linear Stability of a Convective Atmospheric Parcel With an Affine Velocity Field

In this article, we study the temporal linear stability of some class of convective atmospheric parcels, assuming an input affine velocity profile. The purpose is to compare the results to those obtained in our previous studies [1]. The assumption of an affine velocity profile led to the establishment of a satisfying base flow since the pressure is hydrostatic and the vertical gradient of the density is decreasing. Subsequently, the disturbance of our basic flow allowed us to obtain dispersion relations whose resolutions have given eigenfrequencies. Numerical analysis of these eigenfrequencies has shown that apparent gravity is not a destabilizing parameter, unlike the real gravity intensity and the entrainment rate, which are destabilizing parameters for the atmospheric cell in full ascent in the atmospheric boundary layer.