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.
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.
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.
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, of the 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.
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