The Dynamics of Boundary Layer Jets within the Tropical Cyclone Core. Part I: Linear Theory

Abstract

Observations of wind profiles within the tropical cyclone boundary layer have until recently been quite rare. The recent massive increase in observations due to the operational implementation of the global positioning system dropwindsonde has emphasised that a low-level wind speed maximum is a common feature of the tropical cyclone boundary layer. Here is proposed a mechanism for producing such a maximum, whereby strong inward advection of angular momentum generates the supergradient flow. The processes that maintain the necessary inflow against the outward acceleration resulting from gradient wind imbalance are identified as being (i) vertical diffusion, (ii) vertical advection, and (iii) horizontal advection. Two complementary tools are used to diagnose the properties and dynamics of the jet. The first, presented here, is a linear analytical model of the boundary layer flow in a translating tropical cyclone. It is an extension of the classical Ekman boundary layer model, as well as of earlier work on stationary vortex boundary layers. This simplifies the vertical diffusion, omits the vertical advection, and linearizes the horizontal advection. The solution is shown to have three components, a symmetric one due to the cyclone, and two asymmetric ones that result from the interaction of the moving cyclone with the earth's surface. The asymmetric components are shown to be equivalent to a frictionally stalled inertia wave. It is argued that an Ekman-type model may be appropriate in tropical cyclones since diurnal effects are weak or absent, turbulence is dominantly shear-generated, and baroclinicity is weak. The jet is similar to the supergeostrophic flow found at the top of the classical Ekman spiral. It is only a few percent supergradient in the linear model, although it is shown that the neglect of vertical advection substantially reduces the strength. The jet height scales as (2K/I)1/2, where K is the turbulent diffusivity and I the inertial stability, modulated by a function of a dimensionless parameter. It is typically several hundreds of meters in the cyclone core, and increases with radius. In a moving storm, the jet is most supergradient?several times stronger than in a stationary storm?at the eyewall to the left and front of the storm (in the Northern Hemisphere), as well as extending into a significant area around to the left of the storm. It is, however, much less marked to the right, where the strongest near-surface winds are found. The factor for reducing upper winds to a near-surface equivalent, which is frequently used in operational work, is shown to have a substantial spatial variability. Larger values are found near the eye, due to the symmetric component of the solution. There is also a marked overall increase from right to left of the storm in the Northern Hemisphere. The second tool used to diagnose the jet, to be presented in Part II of this paper, is a high-resolution, dry, hydrostatic, numerical model using the full set of primitive equations. It therefore includes those terms omitted in the linear model, and will be seen to produce a markedly stronger jet, more consistent with the observations.