Vortex criteria can be objectivized by unsteadiness minimization

@article{Theisel2021VortexCC,
  title={Vortex criteria can be objectivized by unsteadiness minimization},
  author={Holger Theisel and Markus Hadwiger and Peter Rautek and Thomas Theu{\ss}l and Tobias G{\"u}nther},
  journal={Physics of Fluids},
  year={2021}
}
Reference frame optimization is a generic framework to calculate a spatially-varying observer field that views an unsteady fluid flow in a reference frame that is as-steady-as-possible. In this paper, we show that the optimized vector field is objective, i.e., it is independent of the initial Euclidean transformation of the observer. To check objectivity, the optimized velocity vectors and the coordinates in which they are defined must both be connected by an Euclidean transformation. In this… Expand

Figures from this paper

References

SHOWING 1-10 OF 22 REFERENCES
Can vortex criteria be objectivized?
  • G. Haller
  • Mathematics
  • Journal of Fluid Mechanics
  • 2020
Abstract Several procedures have been proposed to modify non-objective (observer-dependent) local vortex criteria so that they become objective. These modifications are only justifiable if they areExpand
Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows
TLDR
This work develops a general mathematical framework for the objective computation of observer fields for curved spaces, relative to which other computed measures become objective, and develops the case of unsteady 2D geophysical flows given on spheres, such as the Earth. Expand
Generic objective vortices for flow visualization
TLDR
This paper proves that in the optimal frame, all local vortex extraction methods that are based on velocity and its derivatives become objective, and demonstrates the approach with objective counterparts to λ2, vorticity and Sujudi-Haimes. Expand
Vector Field Topology of Time-Dependent Flows in a Steady Reference Frame
TLDR
This work builds up on recent work on vortex extraction to define a time-dependent vector field topology for 2D and 3D flows and compares and discusses the relationships with existing local and integration-based topology extraction methods, showing for instance that separatrices seeded from saddles in the optimal frame align with the Integration-based streakline vector fieldTopology. Expand
Objective Vortex Corelines of Finite-sized Objects in Fluid Flows
TLDR
It is demonstrated in this paper that the objective detection of an inertial vortex coreline can be reduced in 2D to a critical point search in2D and in a number of 2D and 3D vector fields. Expand
An objective version of the Rortex vector for vortex identification
Vortices are a ubiquitous natural phenomenon, and their structure, shape, and characteristics should be independent of the observer, which implies that the vortex identification method or vortexExpand
Time-Dependent Flow seen through Approximate Observer Killing Fields
TLDR
This work compute a time-dependent observer velocity field that describes the motion of a continuous field of observers adapted to the input flow, corresponding to almost-rigid motion, and proves that theinput flow perceived by the observer field is objective, which makes derived flow features, such as vortices, objective as well. Expand
The State of the Art in Vortex Extraction
TLDR
An overview over the advances that have been made in the analysis of vortices in the last 40 years is provided, providing sufficient background on differential vector field calculus, extraction techniques like critical point search and the parallel vectors operator, and the notion of reference frame invariance is introduced. Expand
An objective definition of a vortex
  • G. Haller
  • Physics
  • Journal of Fluid Mechanics
  • 2005
The most widely used definitions of a vortex are not objective: they identify different structures as vortices in frames that rotate relative to each other. Yet a frame-independent vortex definitionExpand
The Dilemma of Defining a Vortex
The problem of defining a vortex in a real fluid is discussed. The definition and identification of a vortex in unsteady motions is difficult since streamlines and pathlines are not invariant withExpand
...
1
2
3
...