Intensification of tilted atmospheric vortices by asymmetric diabatic heating

P\"aschke et al. (JFM, 701, 137--170 (2012)) studied the nonlinear dynamics of strongly tilted vortices subject to asymmetric diabatic heating by asymptotic methods. They found, i.a., that an azimuthal Fourier mode 1 heating pattern can intensify or attenuate such a vortex depending on the relative orientation of tilt and heating asymmetries. The theory originally addressed the gradient wind regime which, asymptotically speaking, corresponds to vortex Rossby numbers of order O(1) in the limit. Formally, this restricts the appicability of the theory to rather weak vortices in the near equatorial region. It is shown below that said theory is, in contrast, uniformly valid for vanishing Coriolis parameter and thus applicable to vortices up to hurricane strength. The paper's main contribution is a series of three-dimensional numerical simulations which fully support the analytical predictions.Comment: 22 pages, 11 figure

An Interactive Approach for Identifying Structure Definitions

Our ability to grasp and understand complex phenomena is essentially based on recognizing structures and relating these to each other. For example, any meteorological description of a weather condition and explanation of its evolution recurs to meteorological structures, such as convection and circulation structures, cloud fields and rain fronts. All of these are spatiotemporal structures, defined by time-dependent patterns in the underlying fields. Typically, such a structure is defined by a verbal description that corresponds to the more or less uniform, often somewhat vague mental images of the experts. However, a precise, formal definition of the structures or, more generally, concepts is often desirable, e.g., to enable automated data analysis or the development of phenomenological models. Here, we present a systematic approach and an interactive tool to obtain formal definitions of spatiotemporal structures. The tool enables experts to evaluate and compare different structure definitions on the basis of data sets with time-dependent fields that contain the respective structure. Since structure definitions are typically parameterized, an essential part is to identify parameter ranges that lead to desired structures in all time steps. In addition, it is important to allow a quantitative assessment of the resulting structures simultaneously. We demonstrate the use of the tool by applying it to two meteorological examples: finding structure definitions for vortex cores and center lines of temporarily evolving tropical cyclones. Ideally, structure definitions should be objective and applicable to as many data sets as possible. However, finding such definitions, e.g., for the common atmospheric structures in meteorology, can only be a long-term goal. The proposed procedure, together with the presented tool, is just a first systematic approach aiming at facilitating this long and arduous way. Keywords: Visual data analysis; Coherent and persistent structures; Atmospheric vortices; Tropical storms;

Feuchte-induzierte Dynamik von Tropischen Wirbelstürmen

The following dissertation examines the asymptotic model, initially derived and pub- lished by Päschke et al. (2012), that describes the tropospheric flow above the boundary layer of a strongly tilted tropical cyclone (TC)-like vortex in vertical wind shear and under the influence of diabatic heating. Beginning with re-deriving the reduced model equations following essential steps of Päschke et al.’s (2012) asymptotic analysis, we show a straight-forward extension that accounts for smaller storms in the not originally anticipated cyclostrophic regime. In a next step we conduct analytical examinations of the leading-order equations that govern the motion of a TC-like vortex. Based on these findings, we make statements about the energetics and structural changes of the TC in the context of intensity changes due to symmetric and asymmetric diabatic heating. Furthermore, we analyze the structural properties of the equations that allow us to construct an adapted numerical scheme to efficiently and robustly solve the asymptotic equations by means of finite-volume methods. Special attention is paid to the semi-implicit second-order time integration of the coupled system. The remaining part of this dissertation is dedicated to presenting the results of numerical experiments that examine mechanisms, either in isolated or combined fashion, that, as we suggest, play a crucial role in the context of rapid intensification (RI) and rapid weakening (RW). These experiments are conducted based on both, the asymptotic model equations and the full three-dimensional equations of atmospheric fluid dynamics, to make statements about the validity and accuracy of the reduced model equations. We present possible pathways of intensity changes that are based on a combined interaction of external wind shear and symmetric-asymmetric diabatic heating. It is found particularly interesting how diabatic heating interacts with the storms structure causing both, intensity and structural changes. Implications towards the applicability of the asymptotic theory in the context of the open research question of RI/RW are discussed as a final contribution of this dissertation.Die vorliegende Arbeit untersucht das asymptotische Model, welches in seiner ursprüng- lichen Form von Päschke u. a. (2012) hergeleitet und veröffentlicht wurde. Es beschreibt die troposphärische Strömung eines stark geneigten tropischen Wirbelsturms oberhalb der planetaren Grenzschicht unter den Einflüssen von vertikaler Windscherung und diabatischer Wärmefreisetzung. Wir beginnen mit der Herleitung der reduzierten Modellgleichungen, wobei wir im Wesentlichen den Ausführungen von Päschke u. a. (2012) folgen. Dabei zeigen wir eine Erweiterung auf, die es zulässt, das reduzierte Modell auch auf Stürme mit kleinerer räumlicher Ausdehnung anzuwenden, die sich im ursprünglich nicht berücksichtigten zy- klostrophischen Regime befinden. Im Folgenden stellen wir analytische Untersuchungen der Gleichungen an, die als Resultat der asymptotischen Betrachtungen die Bewegung eines tropischen Sturms in führender Ordnung beschreiben. Darauf aufbauend treffen wir Aussagen über die Energiebilanz und die Veränderungen der Struktur des Strö- mungsfeldes im Zusammenhang von Intensitätsveränderungen, die durch symmetrische und asymmetrische Wärmefreisetzung hervorgerufen werden. Des Weiteren gehen wir auf die analytische Struktur der Gleichungen ein, was es uns erlaubt ein adaptiertes numerisches Schema zu konstruieren, das mithilfe von Finite-Volumen-Verfahren die asymptotischen Gleichungen effizient und robust integriert. Wir legen dabei besonderes Augenmerk auf die gekoppelte, semi-implizite Zeitintegration zweiter Ordnung. Der verbleibende Teil dieser Arbeit wird numerischen Experimenten sowie der Darstellung und Interpretation der Ergebnisse gewidmet. Dabei werden Mechanismen, die im Zusammenhang mit rapider Verstärkung oder Abschwächung stehen und die Einfluss auf die Wirbelstruktur haben, sowohl isoliert als auch in kombinierter Weise untersucht. Die Experimente werden mithilfe der numerischen Implementierung der asymptotischen Gleichungen untersucht, sowie anhand von dreidimensionalen Referenz- lösungen der Gleichungen der atmosphärischen Fluiddynamik. Wir zeigen mögliche Wege zur Intensitätsveränderung auf, die auf Interaktionen des Wirbels mit der Sche- rung des externen Windfeldes und einer Kombination aus symmetrisch-asymmetrischer diabatischer Wärmefreisetzungen zurückzuführen sind. Von großem Interesse ist dabei die Interaktion der asymmetrische Komponente der Wärmefreisetzung mit der Sturm- struktur, die wiederum die Intensität und Struktur selbst beeinflusst. Rückschlüsse in Bezug auf die Anwendbarkeit der asymptotischen Theorie im Zusammenhang mit rapider Verstärkung/Abschwächung werden als abschließender Beitrag dieser Arbeit gezogen

Dynamics of tilted atmospheric vortices under asymmetric diabatic heating

Päschke et al. (J Fluid Mech, 2012) studied the nonlinear dynamics of strongly tilted vortices subject to asymmetric diabatic heating by asymptotic methods. They found, inter alia, that an azimuthal Fourier mode 1 heating pattern can intensify or attenuate such a vortex depending on the relative orientation of the tilt and the heating asymmetries. The theory originally addressed the gradient wind regime which, asymptotically speaking, corresponds to vortex Rossby numbers of order unity in the limit. Formally, this restricts the applicability of the theory to rather weak vortices. It is shown below that said theory is, in contrast, uniformly valid for vanishing Coriolis parameter and thus applicable to vortices up to low hurricane strengths. An extended discussion of the asymptotics as regards their physical interpretation and their implications for the overall vortex dynamics is also provided in this context. The paper’s second contribution is a series of three-dimensional numerical simulations examining the effect of different orientations of dipolar diabatic heating on idealized tropical cyclones. Comparisons with numerical solutions of the asymptotic equations yield evidence that supports the original theoretical predictions of Päschke et al. In addition, the influence of asymmetric diabatic heating on the time evolution of the vortex centerline is further analyzed, and a steering mechanism that depends on the orientation of the heating dipole is revealed. Finally, the steering mechanism is traced back to the correlation of dipolar perturbations of potential temperature, induced by the vortex tilt, and vertical velocity, for which diabatic heating not necessarily needs to be responsible, but which may have other origins

Definition, detection and trackingof persistent structures in atmospheric flows

Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" - to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence. Johannes von Lindheim, Abhishek Harikrishnan, Tom Dörffel, Rupert Klein, Peter Koltai, Natalia Mikula, Annette Müller, Peter Névir, George Pacey, Robert Polzin, Nikki Vercautere