The role of inner-core and boundary layer dynamics on tropical cyclone structure and intensification - Slocum, Christopher J., author; Schubert, Wayne H., advisor; DeMaria, Mark, advisor; Schumacher, Russ S., committee member; Randall, David A., committee member; Kirby, Michael, committee member; Fiorino, Michael, committee member (Colorado State University. Libraries, 2018)
Inner-core and boundary layer dynamics play a vital role in the tropical cyclone life cycle. This study makes use of analytical solutions and numerical models to gain insight into the role of dynamical processes involved with the incipient, rapidly intensifying, and eyewall replacement stages. A simplified, axisymmetric, one-layer, analytical model of tropical cyclone intensification is developed. Rather than formulating the model with the gradient balance approximation, the model uses the wave-vortex approximation, an assumption to the kinetic energy of the system, which limits its use to flows with small Froude numbers. Through filtering the inertia-gravity waves and adding a mass sink so that potential vorticity is not conserved in the system, the model is solved and provides analytical, time-evolving solutions that provide insight into long incubation periods prior to rapid intensification, potential vorticity tower development without frictional effects, and storm evolution in time through the maximum tangential velocity, total energy phase space. To understand the applicability of the forced, balance model for tropical cyclone intensification, the model is compared to a model using gradient balance. The comparison shows that the model based on the wave-vortex approximation is appropriate for fluids with flow speeds indicative of the external vertical normal mode in which case the deviation to the fluid depth is small. To understand another aspect of the inner-core dynamics that influence the radial location of the mass sink associated with the eyewall convection in the tropical cyclone, boundary-layer dynamics are considered. Motivated by abrupt jumps in the horizontal wind fields observed in flight-level aircraft reconnaissance data collected in Hurricanes Allen (1980) and Hugo (1989), an axisymmetric, f-plane slab boundary layer numerical model with a prescribed pressure forcing is developed. From this model, two simple analytic models are formulated in addition to two local, steady-state models. These models allow for the role of shock dynamics in the tropical cyclone boundary layer to be assessed. Two local models are also developed to evaluate the role of the nonlinear terms in the full numerical slab model. The local models adequately describe the boundary layer winds outside of the eyewall region. If a storm is weak or broad, the local models can explain a portion of the structure that develops in the eyewall region. This result shows that, to capture the hyperbolic nature of the eyewall region, the nonlinear terms are needed. The nonlinear response allows for the boundary-layer Ekman pumping to shift radially inward into the region of high inertial stability. The results from the local models and full numerical model also show that as the vortex wind field broadens, the convergence associated with the primary eyewall decays and that a secondary maximum displaced radially outward forms, a feature indicative of the formation of a secondary eyewall.