Inertial motions in analytical vortex models

• Published in: Journal of the atmospheric sciences 1989-12, Vol.46 (23), p.3605-3610
• Main Authors: SNOW, J. T, LUND, D. E
• Format: Article
• Language: English
• Subjects: Convection, turbulence, diffusion. Boundary layer structure and dynamics; Earth, ocean, space; Exact sciences and technology; External geophysics; Meteorology
• ISSN: 0022-4928; 1520-0469
• DOI: 10.1175/1520-0469(1989)046<3605:IMIAVM>2.0.CO;2

As an aid to interpreting velocity fields produced in numerical studies of vortices, the authors present analytic results obtained from investigating inertial flow fields induced beneath simple vortex models. The analysis considers the horizontal motion of a ring of fluid driven by an imbalance between pressure-gradient and centrifugal forces. It is directly analogous to the vertical motion of a parcel driven by buoyancy. A basic state flow field boxing a steady tangential velocity distribution is given by an equation of inertial motion for stagnant inner flow, solidly rotating inner flow and potential outer flow. The solutions of the governing equation for the outer flow, the inner flow including stagnant core and solid relating core are presented. The coupling existing between the inflow layer and the corner region is modeled by joining the inflow solution to a corner solution by matching radial and tangential compounds of velocity at r=1. The results are a logical extension of the classical Rankine combed and stagnant core vortex models often used to describe qualitatively tornadoes and hurricanes. In relation to the analogy of buoyant convection, a perturbed ring (or ``parcel'') in the outer flow appears now ``unstable'' in the sense of being ``positively buoyant''; the angular momentum of the outer flow defines a neutral stability curve. The core provides a stable capping layer; because of inertia, rings overshoot their equilibrium level. The inertial oscillations are analogs to Brunt-Vaisala oscillations. The super-cyclostrophic region is one of negative buoyancy. Thus the horizontal flow within the inflow layer and corner region beneath the simple vortex models considered is highly analogous to one-dimensional buoyant convection impinging on a stable capping layer.