Atmospheric vortex stability under vertical shear

Abstract

The dynamics of atmospheric vortices play a great role in many environmental flow phenomena. When vortices experience vertical shear they persist, even intensify, or weaken, up to the point that they fade away. Identifying the parameters and conditions that lead to the respective scenarios is key to understanding the evolution of vortical flows in the atmosphere. Various temporal and spatial scales are involved and pose new challenges that simulations can help to resolve. We consider a numerical approach with the flow solver EULAG that has been successfully applied to a plethora of environmental systems, addressing the multi-scale behavior of the flow. A series of tests for two-dimensional setups is conducted first, borrowed from Klein (2009) and Kadioglu et al. (2008) to double-check EULAG's performance on concentrated vortical flows. A first application is the numerical implementation of precessing quasi-modes of three-dimensional atmospheric vortices. Their core structure and centerline change under environmental shear and are of particular interest for the overall evolution in time. Averaged measures are implemented in the code to extract these quantities from data without suffering from numerical oscillations. In a simple model an incipient hurricane is described by an axisymmetric, Gaussian vorticity profile, parameters are the radius of maximum wind and the corresponding wind speed. Modeling the hurricane on a finite grid requires zero velocity at the boundary, imitating an infinite domain, which we enforce with an appropriate mollifier. Instead of inducing shear flow we displace the vortex centerline initially, giving rise to a subsequent realignment phase of the vortex. Thereafter, the problem at hand is implemented and different initial shapes of the vortex centerline are discussed. Theoretical predictions lead us to an Eigenmode of the precession that is as well covered in the numerical experiment. Furthermore, the underlying model is supplemented with a diabatic heat source utilizing EULAG's design. Our choice of the heating term is based on the nonlinear matched asymptotic analysis for vortices with large tilt by Paeschke et al. (2012). Ultimately, our numerical study supports the asymptotic hurricane model and provides room for enhancement.