On the Applicability of Linear, Axisymmetric Dynamics in Intensifying and Mature Tropical Cyclones

Abstract

Abstract:The applicability of linearized axisymmetric dynamics to the intensification and structure change of tropical cyclones is investigated. The study is motivated by recent work that presented axisymmetric solutions to the linearized, non-hydrostatic, vortex-anelastic equations of motion (the so-called 3DVPAS model). The work called into question the importance of a recently proposed nonlinear, system-scale boundary-layer spinup mechanism both in intensifying storms and in mature storms undergoing secondary eyewall formation. The issue is examined using a three-dimensional mesoscale simulation of an intensifying tropical cyclone, alongside the linear 3DVPAS model. Solutions to the linear model, for imposed eddy forcing terms derived from the mesoscale simulation, are shown to be valid only for short times (t < 1 h) in the inner-core region of the vortex. At later times, the neglected nonlinear terms become significant and the linear results invalid. It follows that the linear results cannot be used to describe all aspects of the tropical cyclone dynamics at later times. In particular, they cannot be used (a) to dismiss the importance of the nonlinear boundary-layer spinup mechanism, nor (b) to isolate the separate effects of diabatic heating from those of friction, within the nonlinear boundary layer at least. Such separation depends on the linear superposition principle, which fails whenever nonlinearity is important. Similar caveats apply to the use of another linear model, the traditional Sawyer-Eliassen balance model. Its applicability is limited not only by linearity, but also by its assumption of strictly balanced motion. Both are incompatible with nonlinear spinup.

The role of heating and cooling associated with ice processes on tropical cyclogenesis and intensification

“…¶¶It is important to note that, despite statements in the literature to the contrary by Stern et al (), the forcing of the secondary circulation by radial and vertical gradients of diabatic heating cannot be completely isolated from forcing by boundary‐layer friction, because the boundary layer in the inner‐core region is intrinsically nonlinear (see e.g. Vogl and Smith, ; Smith and Montgomery, ; Montgomery and Smith ). Nevertheless, friction by itself would generate radial outflow above the boundary layer: only diabatic heating can induce inflow both within and above the boundary layer and only then at radii outside the heating.…”

The generation of kinetic energy in tropical cyclones revisited

“…The result is a net production of kinetic energy, dominated by the contribution from the inflow region.” While this view is broadly supported by the calculations presented herein, the calculations provide a sharper view of the net production of kinetic energy, indicating a region of significant kinetic energy generation accompanying inflow throughout the lower troposphere above the boundary layer, as well as significant regions where kinetic energy is consumed as air flows outwards, against the radial pressure gradient force, above the boundary layer. Indeed, the generation above the boundary layer is a manifestation of spin up by the classical mechanism articulated by Ooyama (), while the generation within the boundary layer, highlighted by Anthes, is a manifestation of the nonlinear boundary layer spin up mechanism articulated by Smith and Vogl (), Smith et al (), Smith and Montgomery () and Montgomery and Smith ().…”

Dynamics of tilted atmospheric vortices under asymmetric diabatic heating

“…Transforming (5) to the vortex-centered coordinates from Sect. 3.2 using (19) and defining U ≡ δ ∂ X/∂t and u rel = u r e r + u θ e θ we find…”

“…As Smith and Montgomery [20] point out in their review article, intricate interactions of boundary layer processes, moist thermodynamics, multiscale stochastic deep convection, and the vortex-scale fluid dynamics produce the observed, sometimes extremely rapid intensification of incipient hurricanes. They also emphasize that, despite the deep insights that have been gained in many studies of idealized axisymmetric flow models [6,18,19,37], asymmetries of vortex structure, convection patterns, and boundary layer structure have been observed to be important for vortex intensification in real-life situations, see, e.g., recent work by Callaghan [2], Rios-Berrios [34] and references therein.…”