Boussinesq dynamics at a cloud edge: Theory and simulation

A consequence of air becoming increasingly less dense with altitude is that the vertical displacement of air against gravity results in up and down oscillatory motion -- much like the restoring force of a spring trying to maintain its equilibrium. This gravity-driven buoyancy effect is what sustains the vertical atmospheric motions known as gravity waves. Just as density decreases with height, the atmosphere is also stratified in its other thermodynamic properties. It becomes lower in pressure and generally cooler with height. When air is displaced vertically, with respect to this stratification, it alters the local thermodynamic state. Additionally, when moisture is included it can exist in either its vapour phase or as suspended liquid water droplets, the latter of which defines the presence of cloud. Altering the moist thermodynamic state can lead to the condensation and evaporation of water. In this way, gravity waves can impact the formation and dynamics of cloud. In this thesis, a simplified model is developed extending the classical Boussinesq approximation for gravity waves to include the effects of vapour-liquid phase change. The result is a mathematical framework that couples the fluid dynamics of gravity waves to the thermodynamics of moisture giving a theory that describes the geometrical evolution of cloud. From this model a particular wave-cloud interaction is identified which has a gravity wave trapped in the clear region below a cloud layer. This is commonly known as a waveguide or wave duct. In this setting, vertical motions of the wave lead to the phase change of water at the cloud-edge boundary resulting in a newly identified mechanism for wave propagation on the edge of cloud. This dynamical solution is constructed within the full physics numerical model ``cm1.'' This represents a first analytically derived moist dynamical solution realized within a numerical weather model. A quantitative comparison of the cm1 computed and approximate Boussinesq solutions show a high degree of agreement in the dynamics. This validates that the moist physics of cm1 are true to the Boussinesq dynamical analysis and illustrates that the cloud-trapped wave-duct solution is achievable in idealized atmospheric conditions.