The Dynamics of Boundary Layer Jets within the Tropical Cyclone Core. Part II: Nonlinear Enhancement

Abstract

Observations of wind profiles within the tropical cyclone boundary layer until recently have been quite rare. However, the recent spate of observations from the GPS dropsonde have confirmed that a low-level wind speed maximum is a common feature of the tropical cyclone boundary layer. In Part I, a mechanism for producing such a maximum was proposed, whereby strong inward advection of angular momentum generates the supergradient flow. The processes that maintain the necessary inflow against the outward acceleration due to gradient wind imbalance were identified as being (i) vertical diffusion, (ii) vertical advection, and (iii) horizontal advection, and a linear analytical model of the boundary layer flow in a translating tropical cyclone was presented and used to diagnose the properties of the jet and the near-surface flow. A significant shortcoming was that the jet was too weak, which was argued to be due to the neglect of vertical advection. Here, a high-resolution, dry, hydrostatic, numerical model using the full primitive equations and driven by an imposed pressure gradient representative of a tropical cyclone is presented. It relaxes the constraint of linearity from Part I, includes the full advection terms, and produces a markedly stronger jet, more consistent with the observations. It is shown that the vertical advection of inflow is of major importance in jet dynamics, and that its neglect was the main reason that the linear model produced too weak a jet. It is shown that the jet in a stationary storm is between 10% and 25% supergradient, depending on the particular characteristics of the storm. The height scale (2K/I) 1/2 , where K is the turbulent diffusivity and I the inertial stability, obtained in Part I, is shown to fit the numerical model results well. This is typically several hundreds of meters in the cyclone core, and increases with radius. In the case of a moving Northern Hemisphere storm, it is found that the jet is most supergradient-several times stronger than in a stationary storm-at the eyewall to the left and front of the storm, 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 winds are found. This asymmetry is in good agreement with that found in Part I, and is dominated by the wavenumber 1 response forced by the asymmetric friction. 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 an overall increase from right to left of the storm in the Northern Hemisphere, again consistent with the results in Part I.

Slab- and height-resolving models of the tropical cyclone boundary layer. Part I: Comparing the simulations

“…Compared with the higher-order closure used by Kepert and Wang (2001), the mixing-length closure does not produce a decrease in diffusivity near and above the boundarylayer top. Simulations with the two closures are compared in section 3.1, along with a discussion of the reasons for preferring the mixing-length closure for this study and the sensitivity to l ∞ .…”

“…Continuous models, including the height-resolving model here, generally display a layer of outflow above the inflow in the cyclone core in which the ascending supergradient flow smoothly returns to gradient balance (Rosenthal, 1962;Eliassen and Lystad, 1977;Kepert and Wang, 2001;Montgomery, et al, 2001). The gradual return to balance implies that any definition of the boundary-layer top will necessarily be somewhat arbitrary.…”

“…The threedimensional model will be that of Kepert and Wang (2001), with the turbulence and surface-flux parametrizations simplified to be more consistent with those typically used in slab models.…”

Slab- and height-resolving models of the tropical cyclone boundary layer. Part II: Why the simulations differ

“…One model, called the height-resolving model, solves the full three-dimensional equations of motion, with suitable parametrizations of the surface drag and turbulent fluxes (Kepert and Wang, 2001). The second model, the slab model, vertically averages the equations through the specified boundary-layer depth before solving them (Shapiro, 1983;Smith and Vogl, 2008).…”

Sensitivity of tropical‐cyclone intensification to perturbations in the surface drag coefficient

“…Indeed, this idea is central to Emanuel's (1986) formulation of a steady-state hurricane model, to its time-dependent extension (Emanuel, 1997(Emanuel, , 2012, and to his theory for the potential intensity of hurricanes (Bister and Emanuel, 1998, and references). More recently, theoretical and observational studies have shown that the maximum tangential wind speed occurs near the top of, but still within, the strong boundary-layer inflow associated with frictional convergence (Braun and Tao, 2000;Zhang et al, 2001;Kepert and Wang, 2001;Montgomery et al, 2006;Kepert, 2006aKepert, , 2006bSmith et al, 2009;Sanger, 2011;Zhang et al, 2012).…”