Browsing by Author "Schubert, Wayne H., advisor"
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Item Open Access A theory of topographically bound balanced motions and application to atmospheric low-level jets(Colorado State University. Libraries, 2011) Silvers, Levi Glenn, author; Schubert, Wayne H., advisor; Randall, David A., committee member; Thompson, David W. J., committee member; Eykholt, Richard E., committee memberThe response of a stratified fluid to forcing from the lower boundary is studied both analytically and numerically. The lower boundary forces a flow field through orographic obstacles and potential vorticity anomalies. It is argued that these mechanisms contribute to the maintenance of low-level jets that are observed regularly in the vicinity of the Rocky Mountains and the Andes. Low-level jets function as one of the primary mechanisms through which topography and surface heating influence regional and global climates. On the ƒ-plane a horizontal transform of the governing equation for potential vorticity leads to a vertical structure equation that is solved using Green's functions. On the sphere a vertical transform of this system leads to a horizontal structure equation that is solved using spheroidal harmonics. These analytic solutions lead to a conceptually simple picture of the fluid response to forcing. However, these derivations only lead to closed analytic solutions for the case of an isentropic lower boundary. When the lower boundary is not isentropic a massless layer must be included in the domain and the solution is then found iteratively. For the cases including a massless layer the system is approximated using finite differences and solved with an over-relaxation procedure. Solutions are presented for the geostrophically balanced, steady response of the fluid to three idealized lower boundaries. An isentropic ridge is studied to determine the role non-heated orography plays on the wind field. Then a flat heated lower boundary and a non-isentropic ridge are studied. The cases with a heated lower surface result in a cyclonic wind field that is anchored over the topography. Observations show a prominent cyclonic wind field centered on both the Rocky Mountains and the Andes. The idealized cases studied in this work allow for the examination of fluid systems analogous to the Great Plains low-level jet and the South American LLJ. Both the mean behavior of these jets and their variability have important climatological and economic impacts on the plains regions of North and South America. One of the purposes of this work is to interpret particular low-level jet systems as part of the orographically bound, balanced motion associated with the potential vorticity anomalies produced by solar heating. This research proposes the jets on opposite sides of the mountains to be a single response to potential vorticity forcing that is the result of radiative heating on the Rockies and the Andes. The orographically bound circulations can also impact monsoon circulations. Although the importance of heated orography to LLJs has tended to be downplayed in the literature, it is shown here to be a significant component in the maintenance of LLJs.Item Open Access Balanced and transient aspects of the intertropical convergence zone(Colorado State University. Libraries, 2015) Gonzalez, Alex O., author; Schubert, Wayne H., advisor; Maloney, Eric D., committee member; Birner, Thomas, committee member; Estep, Donald J., committee memberThe Intertropical Convergence Zone (ITCZ) is one of the primary drivers of tropical circulations and because of its interactions with the extratropics, contributes significantly to Earth's general circulation. This dissertation investigates dynamical aspects of the ITCZ using a variety of analytical and numerical models. In the first chapter, we learn that deep and shallow balanced Hadley circulations are forced by deep diabatic heating and Ekman pumping at the top of the boundary layer, respectively. Also, when the ITCZ is located off of the equator there is an inherent asymmetry between the winter and summer Hadley cells due to the anisotropic nature of the inertial stability. The second study examines shallow and deep vertical motions over the eastern Pacific Ocean (80°W--150°W) using the Year of Tropical Convection reanalysis (YOTC). Vertical motions in the eastern Pacific tend to be bimodal, with both shallow and deep vertical motions occurring throughout the year. Shallow vertical motions are typically narrow and restricted to low latitudes (ITCZ-like) while deep vertical motions tend to be broad and are located poleward of shallow regimes, except during El Niño conditions. The study of balanced Hadley circulations is also extended to investigate the role of transient aspects of the Hadley circulation. The solutions illustrate that inertia-gravity wave packets emanate from the ITCZ and bounce off a spectrum of turning latitudes when the ITCZ is switched on at various rates. These equatorially trapped wave packets cause the Hadley cells to pulsate with periods of 1--3 days. In the last part of this dissertation, we focus on boundary layer aspects of the formation of the ITCZ. Since the ITCZ boundary layer is a region of significant meridional convergence, meridional advection should not be neglected. Using a zonally symmetric slab boundary layer model, shock-like structures appear in the form of near discontinuities in the horizontal winds and near singularities in the vorticity and Ekman pumping after 1--2 days. The numerical model also agrees well with dynamical fields in YOTC while adding important details about the boundary layer pumping and vorticity. In closing, we believe that the ITCZ is a highly transient region vital to the general circulation of the atmosphere, and many of its features can be explained by dry dynamics.Item Open Access Deep and shallow overturning circulations in the tropical atmosphere(Colorado State University. Libraries, 2013) Rojas, Gabriela Mora, author; Schubert, Wayne H., advisor; Birner, Thomas, committee member; DeMaria, Mark, committee member; Maloney, Eric D., committee member; Trumbo, Craig W., committee memberThis dissertation examines the dynamics of zonally symmetric, deep and shallow overturning circulations in the tropical atmosphere. The dynamics are discussed in the context of idealized analytical solutions of the equatorial β-plane version of the Eliassen meridional circulation equation that arises in balanced models of the Hadley circulation. This elliptic equation for the meridional circulation has been solved analytically by first performing a vertical normal mode transform that converts the partial differential equation into a system of ordinary differential equations for the meridional structures of all the vertical modes. These meridional structure equations can be solved via the Green's function, which can be expressed in terms of parabolic cylinder functions of half-integer order. The analytical solutions take simple forms in two special cases: (1) Forcing by deep diabatic heating that projects only onto the first internal mode in the absence of Ekman pumping; (2) Forcing by Ekman pumping in the absence of any diabatic heating. Case (1) leads to deep overturning circulations, while case (2) leads to shallow overturning circulations. Both circulations show a marked asymmetry between the winter hemisphere and summer hemisphere overturning cells. This asymmetry is due to the basic anisotropy introduced by the spatially varying inertial stability coefficient in the Eliassen meridional circulation equation. A simple physical interpretation is that fluid parcels forced near the equator to overturn by diabatic and frictional processes tend to move much more easily in the horizontal direction because the resistance to horizontal motion (i.e. inertial stability) is so much less than the resistance to vertical motion (i.e., static stability).Item Open Access Diabatic and frictional forcing effects on the structure and intensity of tropical cyclones(Colorado State University. Libraries, 2013) Slocum, Christopher J., author; Schubert, Wayne H., advisor; DeMaria, Mark, advisor; Schumacher, Russ S., committee member; Kirby, Michael J., committee member; Fiorino, Michael, committee memberTropical cyclone intensity forecasting skill has slowed in improvement for both dynamical and statistical-dynamical forecasting methods in comparison to gains seen in track forecasting skill. Also, forecast skill related to rapid intensification, e.g. a 30 kt or greater increase in intensity within a 24-hour period, still remains poor. In order to make advances and gain a greater understanding, the processes that affect intensity change, especially rapid intensification, need further study. This work evaluates the roles of diabatic and frictional forcing on the structure and intensity of tropical cyclones. To assess the diabatic forcing effects on intensity change in tropical cyclones, this study develops applications of Eliassen's balanced vortex model to obtain one-dimensional solutions to the geopotential tendency and two-dimensional solutions to the transverse circulation. The one-dimensional balanced solutions are found with dynamical model outputs as well as aircraft reconnaissance combined with diabatic heating derived from microwave rainfall rate retrievals. This work uses solutions from both datasets to make short-range intensity predictions. The results show that for the one-dimensional solutions, the tangential tendency does not match the dynamical model or aircraft wind tendencies. To relax the assumptions of the one-dimensional solutions to the geopotential tendency, solutions for idealized vortices are examined by finding two-dimensional solutions to the transverse circulation. The two-dimensional solutions allow for evaluation of the axisymmetric structure of the vortex on the (r, z)-plane without setting the baroclinicity to zero and the static stability to a constant value. While the sensitivity of tangential wind tendency to diabatic forcing and the region of high inertial stability is more realistic in the two-dimensional results, the solutions still neglect the influence of friction from the boundary layer. To understand further the role of frictional forcing in the boundary layer, two analytical slab models developed in this study provide insight into recent work that demonstrates how dry dynamics plays a role in determining eyewall location and size, how potential vorticity rings develop, and how an outer concentric eyewall forms through boundary layer "shock-like" structures. The analytical models show that when horizontal diffusion is neglected, the u(∂u/∂r) term in the radial equation of motion and the u[ƒ + (∂v/∂r) + (v/r)] term in the tangential equation of motion develop discontinuities in the radial and tangential wind, with associated singularities in the boundary layer pumping and the boundary layer vorticity. The analytical models provide insight into the boundary layer processes that are responsible for determining the location of the eyewall and the associated diabatic heating that ultimately impacts the intensity of the tropical cyclone. This work shows that future research linking the roles of frictional forcing in the boundary layer to the diabatic forcing aloft while using a balanced model will be important for gaining insight into forcing effects on tropical cyclone intensity.Item Open Access Forecasting of Atlantic tropical cyclones using a kilo-member ensemble(Colorado State University. Libraries, 2004) Vigh, Jonathan L., author; Schubert, Wayne H., advisor; DeMaria, Mark, committee member; Gray, William M., committee member; Taylor, Gerald D., committee memberThe past 30 years have witnessed steady improvements in the skill of tropical cyclone track forecasts. These increases have been largely driven by improved numerical weather prediction models and increased surveillance of the storm environment through aircraft reconnaissance and satellite remote sensing. The skill of deterministic track forecasts from full-physics models is gradually approaching the theoretical limit of predictability that arises due to the atmosphere's chaotic nature and limitations in determining the initial state. To make further progress, it is necessary to treat the uncertainty of the initial condition. One practical approach is to sample this uncertainty by perturbing the initial state. The resulting suite of forecasts that result from integrating such perturbations is known as an ensemble. This thesis describes the design, implementation, and evaluation of a semi-operational ensemble forecasting system using an efficient multigrid barotropic vorticity equation model (MBAR). Five perturbation classes are used to simulate uncertainties in the storm environment and vortex structure. Uncertainties in the storm environment are simulated by using the background environmental flow evolutions provided by the NCEP Global Forecasting System (GFS) ensemble forecasts. Several deep layer-mean wind averages account for uncertainty in the depth of the storm steering layer. Uncertainties in the decomposition of the tropical atmosphere's vertical modes are simulated by varying the model equivalent phase speed. Finally, uncertainties in the vortex structure are simulated by varying the vortex size and storm motion vector. Each perturbation in a given class is cross-multiplied with all other perturbations of other classes to obtain an ensemble with 1980 members. One of the fundamental questions addressed by this research is whether such cross-multiplication increases the degrees of freedom in the ensemble. The ensemble is run for 294 cases from the 2001-2003 Atlantic hurricane seasons. Theory dictates that a properly-perturbed ensemble should, on average, be more accurate than any single ensemble member, but it was found that the kilo-ensemble mean forecast did not demonstrate substantial improvement over the control forecast. However, the ensemble mean did show substantial skill relative to the five-day climatology and persistence model (CLP5) throughout the 120-h forecast period. The ensemble mean spread (the mean distance of the individual members from the ensemble mean), x-bias, and y-bias statistics are also evaluated. Probabilistic interpretations are valid with an ensemble of this size, so cumulative strike probabilities are calculated explicitly from the kilo-ensemble output. In a related possibilistic interpretation, the ensemble can be looked upon as mapping out the subspace of all possible storm tracks, so the reliability of this ensemble envelope is examined. Finally, if the ensemble can accurately simulate the uncertainties in the dynamical system, then there should be a positive relationship between ensemble mean spread and the error of the ensemble mean forecast. A strong relationship allows useful forecasts of forecast skill to be made at the time of the forecast. The kilo-member ensemble was found to have a weak spread-error relationship that peaks at 60 h.Item Open Access Formation of the hurricane eye(Colorado State University. Libraries, 2010) Vigh, Jonathan L., author; Schubert, Wayne H., advisor; Cotton, William R., 1940-, committee member; Ito, Takamitsu, committee member; DeMaria, Mark, committee member; Krueger, David A., committee memberThis dissertation consists of three distinct studies which investigate aspects of eye formation. The first study reviews eye phenomenon in a variety of vortices ranging from simple vortices to the menagerie of geophysical vortices, emphasizing similarities and differences to the eyes formed in hurricanes. The hurricane eye is found to be a paradoxical structure imposed by conservation of angular momentum and the boundaries of the vortex. A comprehensive definition for hurricane eye formation is proposed and various eye formation mechanisms are summarized. The next study presents a simple theoretical argument to isolate the conditions under which a tropical cyclone can rapidly develop a warm-core thermal structure and subsequently approach a steady state. The theoretical argument is based on the balanced vortex model and, in particular, on the associated transverse circulation equation and the geopotential tendency equation. The transverse circulation and the temperature tendency in a tropical vortex depend not only on the diabatic forcing, but also on the spatial distributions of the static stability, the baroclinity, and the inertial stability. The vortex response to diabatic heating depends critically on whether the heating occurs in the low inertial stability region outside the radius of maximum wind or in the high inertial stability region inside the radius of maximum wind. This result suggests that rapid intensification is favored for storms which have at least some of the eyewall convection inside the radius of maximum wind. The development of an eye partially removes diabatic heating from the high inertial stability region of the storm center, yet rapid intensification may continue if the eyewall heating continues to become more efficient. As the warm core matures and static stability increases over the inner core, conditions there become less favorable for deep upright convection and the storm tends to approach a steady state. The final study characterizes the kinematic and thermodynamic changes that occur before, during, and after the initial eye formations of a broad set of Atlantic tropical cyclones. To obtain the requisite structure and intensity parameters, a new data set has been synthesized from the Vortex Data Messages transmitted by routine aircraft reconnaissance from 1989-2008. Intensity ranges are determined for the times when the eye/eyewall structure first appears in aircraft radar and infrared satellite imagery. The mean intensity at which an eye is first observed in both aircraft or satellite imagery is found to be 58 kt, somewhat lower than reported in previous studies. Changes about the time of eye formation are examined for intensity, the radius of maximum winds, the minimum Rossby radius of deformation, eye temperature and dew point temperature depression. Storms are found to intensify most rapidly near the time of eye formation, especially when a persistent eye is observed in infrared satellite imagery. Many storms which are forming eyes are found to undergo a substantial and rapid contraction in the radius of maximum winds during the 24-h period before the eye is observed; once the eye is present, this contraction slows or ceases. Strong warming at lower levels (850 or 700 hpa) of the eye is not observed to correlate well with the time in which the eye is first observed. Finally, observations suggest that the dynamical heating efficiency of the resulting eyewall increases even as the physical scale of the efficient heating region decreases. This allows the storm to continue intensifying even though the total inner core diabatic heating may decrease. The answer to why some storms fail to form eyes may shed light on whether eye formation is a stochastic process involving constructive and destructive mesoscale interactions -- or whether it is a manifold attractor of the system sometimes stymied by an unfavorable environment.Item Open Access Simple analytical solutions for potential vorticity intrusions(Colorado State University. Libraries, 2012) Masarik, Matthew Thomas, author; Schubert, Wayne H., advisor; Eykholt, Richard E., committee member; Maloney, Eric D., committee member; Randall, David A., committee memberUsing potential temperature (θ) as the vertical coordinate, we derive analytical solutions of the potential vorticity (PV) invertibility principle for the case in which the flow is y-independent and an isolated PV anomaly is confined within an ellipse in the (x, θ)-plane. The solutions aid in understanding the dynamics of low latitude PV intrusions whose associated cloud patterns are often referred to as moisture bursts, or tropical plumes and whose flow patterns are often referred to as tropical upper tropospheric troughs (TUTTs). The solutions illustrate the phenomenon of isentropic upglide below an upper tropospheric positive anomaly in PV. They also quantify how the partitioning of PV between vorticity and static stability depends on the shape and strength of the PV anomaly. The solutions also apply to the problem of determining the balanced flow induced by a surface temperature anomaly, which is equivalent to a very thin layer of infinite PV at the surface. Reanalysis data is consulted as a check on the solutions. Finally, a numerical model is constructed where approximations made in the analytical theory can be examined.Item Open Access Spectral methods for limited area models(Colorado State University. Libraries, 1984) Fulton, Scott R., author; Schubert, Wayne H., advisor; Taylor, Gerald D., committee member; Krueger, David A., committee member; Stevens, Duane E., committee member; Johnson, Richard H. (Richard Harlan), committee memberThis study investigates the usefulness of Chebyshev spectral methods in limited area atmospheric modeling. Basic concepts of spectral methods and properties of Chebyshev polynomials are reviewed. Chebyshev spectral methods are illustrated by applying them to the linear advection equation in one dimension. Numerical results demonstrate the high accuracy obtained compared to finite difference methods. The nonlinear shallow water equations on a bounded domain in two dimensions are then considered as a more realistic prototype model. Characteristic boundary conditions based on Reimann invariants are developed, and contrasted with wall conditions and boundary conditions based on the assumption of balanced flow. Chebyshev tau and collocation methods are developed for this model. Results from one-dimensional tests show the superiority of the characteristic conditions in most situations. Results from two-dimensional tests are also presented. Comparison of the tau and collocation methods shows that each has its own advantages and both are practical. Time differencing schemes for Chebyshev spectral methods are studied. The stability condition obtained with explicit time differencing, often thought to be "severe", is shown to be less severe than the corresponding condition for finite difference methods. Numerical results and asymptotic estimates show that time steps may in fact be limited by accuracy rather than stability, in which case simple explicit time differencing is practical and efficient. Two modified explicit schemes are reviewed, and implicit time differencing is also discussed. A Chebyshev spectral method is also used to solve the vertical structure problem associated with vertical normal mode transforms in a hydrostatic atmosphere. Numerical results demonstrate the accuracy of the method, and illustrate the aliasing which can occur unless the vertical levels at which data is supplied are carefully chosen. Vertical transforms of observed forcings of tropical wind and mass fields are presented. The results of this study indicate that Chebyshev spectral methods are a practical alternative to finite difference methods for limited area modeling, especially when high accuracy is desired. Spectral methods require less storage than finite difference methods, are more efficient when high enough accuracy is desired, and are at least as easy to program.Item Open Access Steady-state circulations forced by diabatic heating and wind stress in the intertropical convergence zone(Colorado State University. Libraries, 2011) Gonzalez, Alex Omar, author; Schubert, Wayne H., advisor; Maloney, Eric D., committee member; Estep, Don J., committee memberA number of studies have shown the importance of using idealized models to gain insight into large-scale atmospheric circulations in the tropics, especially when investigating phenomena that are not well understood. The recent discovery of the Shallow Meridional Circulation (SMC) in the tropical East Pacific and West Africa is a perfect example of a phenomenon that is not well understood (Zhang et al., 2004). The vertical structure of the SMC is similar to the Hadley circulation, but its return flow is located at the top of the boundary layer. The current theory of the SMC is entirely different dynamically than the Hadley circulation because it has been thought of as a large-scale "sea-breeze" circulation rather a geostrophic balance in the meridional momentum equation. The SMC is a vital aspect of the general circulation since it can transport more moisture than the traditional deep Hadley circulation. Climate models often misrepresent the SMC, making many model simulations incomplete (Zhang et al. 2004; Nolan et al. 2007). We aim to better understand the dynamics near the Intertropical Convergence Zone (ITCZ) that involve both deep and shallow circulations using a steady-state linearized model on the equatorial β-plane that is solved analytically. The model is forced by prescribed diabatic heating and boundary layer wind stress curl. The circulations that arise from deep diabatic heating profiles suggest that both the Hadley and Walker circulations are always present, with the Hadley circulation being more prevalent as the deep heating is elongated in the zonal direction, similar to the ITCZ in the East Pacific. The Hadley circulation strengthens because the horizontal surface convergence increases in the meridional direction. Also, the zonal and meridional surface wind anomalies enhance as the deep heating is displaced farther from the equator. The surface wind field associated with this deep heating also forces a significant wind stress curl north of the equator. The atmosphere responds to the wind stress curl by opposing the initial dynamical fields, and generating Ekman pumping in the boundary layer. For example, the surface consists of anomalous negative vorticity in a region that previously contained positively vorticity. This is often referred to as spin down. The Ekman pumping in the boundary layer forces shallow circulations when the frictional forcing is zonally-elongated and sufficiently displaced off of the equator. This shallow circulation makes sense in the East Pacific, where the ITCZ is always north of the equator and is often zonally-elongated. There are two SMCs that develop, one north of the Ekman pumping, and the other to its south. The cross-equatorial SMC is shallower and is stretched in the meridional direction compared to the SMC north of the Ekman pumping since the Rossby length is very large near the equator. It turns out that the frictional forcing does not provide enough vertical or meridional motion to be seen when deep diabatic heating is also present using our simple model. Since the ITCZ is a transient phenomenon and the frictional forcing is more steady, there are days where this Ekman pumping can be seen when deep convection is suppressed. Future research should concentrate on better understanding the effect of the wind stress and surface temperatures on the buildup of subsequent convection using idealized models.Item Open Access The effects of environmental flow on the internal dynamics of tropical cyclones(Colorado State University. Libraries, 2012) Williams, Gabriel Jason, author; Schubert, Wayne H., advisor; Dangelmayr, Gerhard, committee member; Maloney, Eric D., committee member; van den Heever, Sue, committee memberThis dissertation focuses on two projects that examine the interaction between the internal dynamics of tropical cyclones and the large-scale environmental flow using a hierarchy of numerical model simulations. Diabatic heating from deep moist convection in the hurricane eyewall produces a towering annular structure of elevated potential vorticity (PV) called a hollow PV tower. For the first project, the three-dimensional rearrangement of hurricane-like hollow PV towers is examined in an idealized framework. For the adiabatic PV tower in the absence of environmental flow, barotropic instability causes air parcels with high PV to be mixed into the eye preferentially at lower levels, where unstable PV wave growth rates are the largest. When the diabatic forcing is included, diabatic PV production accompanies the inward mixing at low levels, and similarly diabatic PV destruction accompanies the outflow at upper-levels. The largest variation in PV is produced when the diabatic forcing is placed within the radius of maximum winds (RMW) due to its ability to efficiently extract kinetic energy from the specified heating source. For the adiabatic PV tower in vertical shear, the initial response of the vortex to the vertical shear is to tilt downshear and rotate cyclonically about the mid-level center. The cyclonic precession of the vortex around the center demonstrates the existence of an azimuthal wavenumber-1 quasimode that prevents the vertical alignment of the vortex. When the effects of diabatic forcing are included, the increase in inertial stability causes the resonant damping of the quasimode to become more efficient, leading to the emission of sheared vortex Rossby waves (VRWs) and vortex alignment. Generally, it is shown that the vortex response to vertical shear depends sensitively on the Rossby deformation radius, Rossby penetration depth, and the vortex beta Rossby number of the vortex. For the second project, we examine the development of shock-like structures in the tropical cyclone boundary layer for a stationary and slowly moving tropical cyclone. Using a two-dimensional slab boundary layer model and a three-dimensional boundary layer model, we show that both boundary layer models approximate the nonlinear viscous Burgers' equation in the tropical cyclone boundary layer. For the stationary tropical cyclone, radial inflow creates a circular shock near the surface while vertical mixing communicates the shock throughout the boundary layer. The peak Ekman pumping occurs at a height of 600 m, which is also the location of maximum turbulent transport, consistent with Hurricane Hugo (1989). For a moving TC, the asymmetry in the frictional drag causes an asymmetry in the boundary layer response. As the translation speed of the TC increases, the nonlinear asymmetric advective interactions amplify, leading to an anticyclonic spiral in the vertical velocity field and pronounced inflow in the right-front quadrant of the storm.Item Open Access The role of inner-core and boundary layer dynamics on tropical cyclone structure and intensification(Colorado State University. Libraries, 2018) 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 memberInner-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.