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 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 super-gradient 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 II: Why the simulations differ

“…Following some experimentation, and guided by the arguments of Rosenthal (1962), Kepert (2001) and Kepert and Wang (2001), the Ekman spiral was chosen in the form…”

“…The unknowns u m (r) and v m (r) describe the structure of the spiral and will be determined from the momentum-budget equations. Note that this form follows from the semi-slip surface boundary condition (Rosenthal, 1962;Eliassen and Lystad, 1977;Kepert, 2001) appropriate for turbulent boundary layers, rather than the more usual no-slip condition seen in many textbooks. In particular, u and v are non-zero at z = 0.…”

“…Examination of solutions to the model reveals that the inflow depth is close to 2.5δ, so simulations with constant δ will take δ = 320 m for comparison with the h = 800 m used for the slab model. However, the height-resolving model results show a marked variation in inflow-layer depth with radius (Kepert and Wang, 2001), and scaling arguments (Rosenthal, 1962;Eliassen and Lystad, 1977;Kepert, 2001) suggest that the boundary-layer height varies with radius as I −1/2 , where I = [(f + v g /r + ∂v g /∂r)(f + 2v g /r)] 1/2 is the inertial stability. Thus results for δ = 1200 m at radius 500 km and varying as I −1/2 , which gives inflow depths in reasonable agreement with those from the height-resolving model, will also be presented.…”

“…Note also that a similar but more severe surface-stress inconsistency occurs in slab models, where the surface stress is in the direction of the boundarylayer mean wind. There is unlikely to be a universal choice for u and v profiles with two unknowns that avoids this issue, since the boundary-layer structure is sensitive to the storm radial profile of the gradient wind (Kepert, 2001;Kepert and Wang, 2001;Kepert, 2006a,b). (One could use a no-slip surface boundary condition, but that changes the whole nature of the problem and is inconsistent with the quest for reasonably accurate solutions.)…”

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

“…] 1/2 is the inertial stability (Rosenthal, 1962;Eliassen and Lystad, 1977;Kepert, 2001). The maximum inflow of 11 m s −1 is at 60 m height and 60 km radius, or 1.5 times the RMW.…”