[1] This paper presents high horizontal resolution solutions of an axisymmetric, constant depth, slab boundary layer model designed to simulate the radial inflow and boundary layer pumping of a hurricane. Shock-like structures of increasing intensity appear for category 1-5 hurricanes. For example, in the category 3 case, the u @u=@r ð Þ term in the radial equation of motion produces a shock-like structure in the radial wind, i.e., near the radius of maximum tangential wind the boundary layer radial inflow decreases from approximately 22 m s 21 to zero over a radial distance of a few kilometers. Associated with this large convergence is a spike in the radial distribution of boundary layer pumping, with updrafts larger than 22 m s 21 at a height of 1000 m. Based on these model results, it is argued that observed hurricane updrafts of this magnitude so close to the ocean surface are attributable to the dry dynamics of the frictional boundary layer rather than moist convective dynamics. The shock-like structure in the boundary layer radial wind also has important consequences for the evolution of the tangential wind and the vertical component of vorticity. On the inner side of the shock the tangential wind tendency is essentially zero, while on the outer side of the shock the tangential wind tendency is large due to the large radial inflow there. The result is the development of a U-shaped tangential wind profile and the development of a thin region of large vorticity. In many respects, the model solutions resemble the remarkable structures observed in the boundary layer of Hurricane Hugo (1989).

The effects of vortex translation and radial vortex structure in the distribution of boundary layer winds in the inner core of mature tropical cyclones are examined using a high-resolution slab model and a multilevel model. It is shown that the structure and magnitude of the wind field (and the corresponding secondary circulation) depends sensitively on the radial gradient of the gradient wind field above the boundary layer. Furthermore, it is shown that vortex translation creates low wave number asymmetries in the wind field that rotate anticyclonically with height. A budget analysis of the steady state wind field for both models was also performed in this study. Although the agradient force drives the evolution of the boundary layer wind field for both models, it is shown that the manner in which the boundary layer flow responds to this force differs between the two model representations. In particular, the inner core boundary layer flow in the slab model is dominated by the effects of horizontal advection and horizontal diffusion, leading to the development of shock structures in the model. Conversely, the inner core boundary layer flow in the multilevel model is primarily influenced by the effects of vertical advection and vertical diffusion, which eliminates shock structures in this model. These results further indicate that special care is required to ensure that qualitative applications from slab models are not unduly affected by the neglect of vertical advection.

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This paper presents numerical solutions and idealized analytical solutions of axisymmetric, f -plane models of the tropical cyclone boundary layer. In the numerical model, the boundary layer radial and tangential flow is forced by a specified pressure field, which can also be interpreted as a specified gradient balanced tangential wind field vgr(r) or vorticity field ζgr(r). When the specified ζgr(r) field is changed from one that is radially concentrated in the inner core to one that is radially spread, the quasi-steady-state boundary layer flow transitions from a single eyewall shock-like structure to a double eyewall shock-like structure. To better understand these structures, analytical solutions are presented for two simplified versions of the model. In the simplified analytical models, which do not include horizontal diffusion, the u(∂u/∂r) term in the radial equation of motion and the u[f + (∂v/∂r) + (v/r)] term in the tangential equation of motion produce discontinuities in the radial and tangential wind, with associated singularities in the boundary layer pumping and the boundary layer vorticity. In the numerical model, which does include horizontal diffusion, the radial and tangential wind structures are not true discontinuities, but are shock-like, with wind changes of 20 or 30 m s −1 over a radial distance of a few kilometers. When double shocks form, the outer shock can control the strength of the inner shock, an effect that likely plays an important role in concentric eyewall cycles.