Forced, Balanced Model of Tropical Cyclone Intensification

Abstract

A simplified, axisymmetric, one-layer model of tropical cyclone intensification is presented. The model is based on the Salmon wave-vortex approximation, which can describe flows with low Froude number and arbitrary Rossby number. After introducing an additional approximation designed to filter propagating inertia-gravity waves, the problem is reduced to the prediction of potential vorticity (PV) and the inversion of this PV to obtain the balanced wind and mass fields. This PV prediction/inversion problem is solved analytically for two types of forcing: a two-region model in which there is nonzero forcing in the cyclone core and zero forcing in the far-field and a three-region model in which there is nonzero forcing in both the cyclone core and the eyewall, with zero forcing in the far-field. The solutions of the two-region model provide insight into why tropical cyclones can have long incubation times before rapid intensification and how the size of the mature vortex can be influenced by the size of the initial vortex. The solutions of the three-region model provide insight into the formation of hollow PV structures and the inward movement of angular momentum surfaces across the radius of maximum wind.

Forced, Balanced, Axisymmetric Shallow Water Model for Understanding Short-Term Tropical Cyclone Intensity and Wind Structure Changes

“…The nonlinearity of TC invertibility principles creates some challenges to obtaining wellbehaved numerical solutions. A recent example of a TC model that uses PV prediction and inversion is the work in [33], the authors of which obtained analytic solutions to the shallow water equations using the wave-vortex approximation to understand the intensification of TCs.…”

“…The model is based upon the forced, balanced, axisymmetric equations in a barotropic framework. Motivated by the works in [13,33], the evolution of the TC vortex in the minimal model is dependent on the radial structure of tangential velocity (or equivalently, inertial stability) and the diabatic heating rate. After describing the model, we will first demonstrate its usefulness in understanding TC evolution in an idealized framework.…”

Evolution, propagation and interactions with topography of hurricane-like vortices in a moist-convective rotating shallow-water model

“…It can be included in shallow-water models in the simplest way as a sink in the mass equation, e.g. Schubert et al (2016), following the seminal ideas of Matsuno (1966) and Gill (1982b). A more systematic, although following the same philosophy, method to include moisture, condensation, and related latent heat release was applied in the moist-convective rotating shallow-water (mcRSW) model, respectively, in one-and two-layer versions in Bouchut et al (2009) and Lambaerts et al (2011).…”

“…Switching to shallow-water models (Hendricks et al. 2014; Lahaye & Zeitlin 2016; Schubert, Slocum & Taft 2016) allows us to include inertia–gravity waves and related radiative instabilities in the picture. Let us emphasize that instabilities of TC could be captured already in the adiabatic, ‘dry’ models (Schubert et al.…”

“…For example, 2-D Euler equations were used in Schubert et al (1999), Kossin & Schubert (2001) and Menelaou, Yau & Martinez (2012) to explain the formation of so-called meso-vortices in the vicinity of the TC cores. Switching to shallow-water models (Hendricks et al 2014;Lahaye & Zeitlin 2016;Schubert, Slocum & Taft 2016) allows us to include inertia-gravity waves and related radiative instabilities in the picture. Let us emphasize that instabilities of TC could be captured already in the adiabatic, 'dry' models (Schubert et al 1999).…”