## 1. Introduction

[2] The red curves in Figure 1 show aircraft data from a low level (434 m average height), southwest to northeast radial penetration of Hurricane Hugo on 15 September 1989 (see *Marks et al*. [2008] and *Zhang et al*. [2011] for detailed discussions). As the aircraft flew inward through the lower portion of the eyewall, the tangential wind increased from 50 m s^{−1} near *r* = 22 km to a maximum of 88 m s^{−1} just inside *r* = 10 km. Near the inner edge of the eyewall there were multiple updraft-downdraft couplets (the strongest updraft just exceeding 20 m s^{−1}), with associated oscillations of the radial and tangential velocity components and a very rapid 60 m s^{−1} change in tangential velocity near 7 km radius. After ascending in the eye, the aircraft departed the eye to the northeast (2682 m average height), obtaining the horizontal and vertical velocity data shown by the blue curves in Figure 1. The extreme horizontal wind shears and large vertical velocities observed at 434 m in the southwest sector were not observed at 2682 m in the northeast sector. Since these extreme structures in the boundary layer wind field occur under a region of high radar reflectivity, it is natural to attribute them to moist convective dynamics. For example, the large updrafts could be attributed to nonhydrostatic vertical accelerations associated with latent heat release, and the large potential vorticity at *r* = 7 km could be attributed to the diabatic source term in the potential vorticity equation. However, the purpose of the present paper is to explore the possibility that the type of behavior seen in Figure 1 can be explained by nonlinear effects that occur in a simple dry model of the hurricane boundary layer. In the following analysis we shall interpret the blue tangential wind curve in Figure 1 as an inviscid, axisymmetric gradient balanced flow whose associated radial pressure gradient is also felt in the frictional boundary layer below. We then interpret the red tangential wind curve as an axisymmetric frictional boundary layer flow (driven by the same radial pressure gradient) that is supergradient inside km and subgradient outside this radius. The subgradient/supergradient nature of the boundary layer flow is closely related to the magnitude of the term in the radial equation of motion. We shall also argue that this term is responsible for the shock-like structure that occurs near *r* = 7 km.

[3] As a theoretical basis for the above arguments we shall use the axisymmetric, primitive equation version of the slab boundary layer model used in many studies of the hurricane boundary layer. For further discussion of the model and its application to many aspects of tropical cyclone dynamics, the reader is referred to *Ooyama* [1969a, 1969b], *Anthes* [1971], *Chow* [1971], *Yamasaki* [1977], *Shapiro* [1983], *Emanuel* [1997], *Smith* [2003], *Smith and Vogl* [2008], *Smith and Montgomery* [2008, 2010], *Smith et al*. [2008], *Smith and Thomsen* [2010], and *Kepert* [2010a, 2010b]. The emphasis here is on interpreting the observations shown in Figure 1 in terms of “Burgers' shock-like” structures that emerge from the fact that the radial boundary layer equation contains an embedded Burgers' equation. An excellent general mathematical discussion of Burgers' shock effects can be found in the book by *Whitham* [1974], which includes a review of the original work by *Burgers* [1948], *Hopf* [1950], and *Cole* [1951].

[4] This paper is organized in the following way. Section 2 presents the governing set of partial differential equations (PDEs) for the slab model. Section 3 discusses the shock-like structures that appear in the model solutions. Section 4 gives some reinterpretations of other low-level aircraft data and of previously published nonhydrostatic, moist model simulations. Section 5 contains some concluding remarks on shock-like structures in more general settings such as translating vortices.