This dissertation reports on two semi-independent studies of rotating atmospheric convection. The first is an analytical investigation of the linear stability and structure of convection in a mean circular shear. The study is intended to complement the classical theoretical work of Asai and to extend the Lilly and Davies-Jones Beltrami solutions to consider the effects of buoyancy on disturbance helicity. The method of normal modes is used to analyze the Boussinesq equations with periodic lateral boundary conditions and free-slip, rigid vertical boundary conditions. The most unstable modes are found to be transverse to the shear vector at the channel center. At small Richardson numbers, the most unstable modes are highly helical with helicity obtained from the mean flow, but disturbance helicity decreases rapidly for Richardson numbers greater than unity. The second study is a numerical investigation of the formation of vertical vortices in the convective boundary layer. In Nature, these vortices are typically made visible by the presence of dust or other particulates. Observations indicate that such vortices may be occurring, even in the absence of visible tracers. If boundary layer vertical vortices are therefore ubiquitous in the atmosphere, they may play an important role in boundary layer transports and evolution. However, these convective vertical vortices have not often been pointed out in laboratory or numerical simulations. Large-eddy simulations of convection, in the absence of imposed mean wind or other sources of angular momentum, are performed for the purpose of investigating boundary layer vertical vortex formation. The simulations are designed to resolve boundary layer convective cells and embedded smaller-scale horizontal circulations. Simulated vertical vortices form rather readily at the vertices of polygonal convective rings, where updrafts are locally maximized. Although they have larger horizontal scale, these vortices have vertical structure similar to observed dust devils. The results indicate that boundary layer vertical vortices can form in the absence of surface or temperature inhomogeneities or imposed sources of angular momentum. In at least one case that is examined, the boundary layer height is elevated in the vicinity of a vortex. Possible mechanisms for vertical vortex formation are discussed.