A Model for Cumulus Cloud Tilt and the Effect of Vertical Shear

Developing a tractable understanding of the interaction between cumulus cloud tilt and vertical shear, both due to synoptic background winds and neighboring cumulus clouds in a cloud field, is crucial to expanding the theory associated with squall line development and tradewind cumuli climatological feedbacks.  Although these interactions are multifaceted, we focus on the dynamic interplay between vertical shear and the cloud-scale flow. To perform this investigation, we implement the Kinematic Representation of Neutrally-buoyant Updraft Tori (KRoNUT) model to represent cloud-scale motions. Unlike previous formulations of the KRoNUT model, we introduce a new tilting parameters into the functional form of the flow. Using a moment closure technique, we then solve for the Dynamics of Neutrally-buoyant Updraft Tori (DoNUT) equations, a coupled non-linear system of ordinary differential equations which govern the temporal evolution of the parameters describing the intensity and geometry of a cloud-scale flow. Using this technique, we analytically and numerically compare the DoNUT equations with and without tilt to determine how the tilting associated with various forms of vertical shear influences the life cycle of a cumulus cloud. When considering the processes of turbulent diffusion and self-advection, we find that tilting alters the nature of a cloud’s steady state circulation. In turn, clouds have the potential to evolve to larger horizontal extents. However, we also find that tilting contributes strongly to enervation and thus the weakening of a cloud’s maximum vertical velocity and a shortening of its life cycle. These impacts are maximized at tilting angles of plus or minus 45 degrees from the vertical axis.