The Influence of a Capping Inversion on the Dynamic and. Convective Instability of a Boundary Layer Model with Shear

The dynamic instability and the kinematics of a multi-layer, shear model of a convective boundary layer are analyzed. Important features of the model include a capping temperature inversion that may or may not be accompanied by a wind discontinuity, a surface-based superadiabatic layer, and a statically stable upper atmosphere. It is shown that the capping inversion can result in a relatively narrow band of dynamically unstable wavenumbers that depend upon shear layer thickness, implying a strong selection of scale in growing disturbances. The influence of the various model parameters upon selection of the most unstable scales is shown and their corresponding propagation velocities are calculated. A simple form of the model is also used to examine the characteristics of the convectively unstable modes. It is found that two-dimensional disturbances aligned transverse to the wind shear are most dynamically unstable, whereas two-dimensional disturbances parallel to the wind shear are most convectively unstable. The vorticity and general kinematics of the disturbances are affected in an important way by the presence of a critical level within the height range occupied by the disturbance.