Vortex criteria can be objectivized by unsteadiness minimization

Theisel, Holger; Hadwiger, Markus; Rautek, Peter; Theußl, Thomas; Günther, Tobias

doi:10.1063/5.0063817

Cited by 8 publications

(4 citation statements)

References 18 publications

(83 reference statements)

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“…We now discuss the following objectivized Eulerian scalar fields: the deformation kinetic energy E d (x), the deformation enstrophy E d (x), and the deformation helicity H d (x) defined in (29). We calculate them for the classic ABC velocity field [56], given by…”

Section: Objectivized Eulerian Fields In 3dmentioning

confidence: 99%

“…Using a simple counterexample, Haller [28] also shows that even under a correct implementation, v * (x, t) would not be objective, irrespective of the measure of unsteadiness chosen. Theisel et al [29] continue to claim objectivity of v * (x, t), but their argument uses the pull-back, as opposed to the inverse, of the nonlinear transformation v ↦ → v * when computing v * ↦ → v. This is incorrect, given that velocity fields are non-objective precisely because they do not transform under the push-forward and pull-back of frame changes.…”

Section: Introductionmentioning

confidence: 99%

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The Objective Deformation Component of a Velocity Field

Kaszás¹,

Pedergnana

Haller³

2022

Preprint

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According to a fundamental axiom of continuum mechanics, material response should be objective, i.e., indifferent to the observer. In the context of geophysical fluid dynamics, fluid-transporting vortices must satisfy this axiom and hence different observers should come to the same conclusion about the location and size of these vortices. As a consequence, only objectively defined extraction methods can provide reliable results for material vortices.As velocity fields are inherently non-objective, they render most Eulerian flow-feature detection non-objective. To resolve this issue, &#160;we discuss a general decomposition of a velocity field into an objective deformation component and a rigid-body component. We obtain this decomposition as a solution of a physically motivated extremum problem for the closest rigid-body velocity of a general velocity field.This extremum problem turns out to have a unique, &#160;physically interpretable, &#160;closed-form solution. Subtracting this solution from the velocity field then gives an objective deformation velocity field that is also physically observable. As a consequence, all common Eulerian feature detection schemes, as well as the momentum, energy, vorticity, enstrophy, and helicity of the flow, become objective when computed from the deformation velocity component. We illustrate the use of this deformation velocity field on several velocity data sets.

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Section: Objectivized Eulerian Fields In 3dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Objective Deformation Component of a Velocity Field

Kaszás¹,

Pedergnana

Haller³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Data visualization, together with flow research, has contributed a great deal to this. There is not enough space here, to sketch the nearly half‐century‐long research thread; instead we refer to the current state of research [THR∗21] and the papers cited therein. In recent work [vLHD∗21], a formal approach to the definition and persistence of meteorological structures has been taken.…”

Section: Related Workmentioning

confidence: 99%

An Interactive Approach for Identifying Structure Definitions

Mikula

Dörffel

Baum

et al. 2022

Computer Graphics Forum

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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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“…Data visualization, together with flow research, has contributed a great deal to this. There is not enough space here, to sketch the nearly half-century-long research thread; instead we refer to the current state of research (Theisel et al, 2021) and the papers cited therein. In recent work (von Lindheim et al, 2021), a formal approach to the definition and persistence of meteorological structures has been taken.…”

Section: Related Workmentioning

confidence: 99%

An Interactive Approach for Identifying Structure Definitions

Mikula¹,

Dörffel²,

Baum³

et al. 2021

Preprint

View full text Add to dashboard Cite

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.

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Vortex criteria can be objectivized by unsteadiness minimization

Cited by 8 publications

References 18 publications

The Objective Deformation Component of a Velocity Field

The Objective Deformation Component of a Velocity Field

An Interactive Approach for Identifying Structure Definitions

An Interactive Approach for Identifying Structure Definitions

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