Journal ArticleDOI
A general classification of three-dimensional flow fields
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TLDR
In this paper, the geometry of solution trajectories for three first-order coupled linear differential equations can be related and classified using three matrix invariants for elementary three-dimensional flow patterns defined by instantaneous streamlines for flow at and away from no slip boundaries for both compressible and incompressible flow.Abstract:
The geometry of solution trajectories for three first‐order coupled linear differential equations can be related and classified using three matrix invariants. This provides a generalized approach to the classification of elementary three‐dimensional flow patterns defined by instantaneous streamlines for flow at and away from no‐slip boundaries for both compressible and incompressible flow. Although the attention of this paper is on the velocity field and its associated deformation tensor, the results are valid for any smooth three‐dimensional vector field. For example, there may be situations where it is appropriate to work in terms of the vorticity field or pressure gradient field. In any case, it is expected that the results presented here will be of use in the interpretation of complex flow field data.read more
Citations
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Journal ArticleDOI
Identifying 3‐D Vortex Structures At/Around the Magnetopause Using a Tetrahedral Satellite Configuration
TL;DR: In this article, the 3D magnetic vortex structures were identified by using various vortex identification criteria as follows: (i) the first criterion is Q•criterion that defines vortices as regions in which the vorticity energy prevails over other energies; (ii) the second criterion is the λ2−criterion is related to the minus eigenvalue of the Hessian matrix of the pressure terms; and (iii) the third criterion called the geometrical line-type method requires the existence of a Galilean-invariant vortex core inside the four
Journal ArticleDOI
Numerical simulation of turbulent thermal boundary layer and generation mechanisms of hairpin vortex
TL;DR: In this article, three-dimensional flow fields are computed along a ribbed flat-plate by direct numerical simulation and the detailed bypass transition process and its generation mechanisms are discussed and analyzed.
Book ChapterDOI
To Boldly Show What No One Has Seen Before: A Dashboard for Visualizing Multi-objective Landscapes
TL;DR: In this paper, the authors present a single R-package (moPLOT) for visualizing the decision and objective space of continuous multi-objective optimization problems (MOPs).
Journal ArticleDOI
A vortex axis and vortex core border grid adaptation algorithm
TL;DR: In this paper, a vortex flow structure adaptation algorithm is presented for local grid refinement at vortex axes positions and associated vortex core border locations, which is particularly designed for vortex axis detection and determination.
Book ChapterDOI
On the Applicability of Topological Methods for Complex Flow Data
TL;DR: The applicability of topological methods for creating expressive, feature revealing visualizations of 3D vector fields is studied and how to overcome this problem for a certain class of flow fields by removing the ambient part of the flow is shown.
References
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Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Book
Differential Equations, Dynamical Systems, and Linear Algebra
Morris W. Hirsch,Steve Smale +1 more
TL;DR: In this article, the structure theory of linear operators on finite-dimensional vector spaces has been studied and a self-contained treatment of that subject is given, along with a discussion of the relations between dynamical systems and certain fields outside pure mathematics.
Journal ArticleDOI
Direct simulation of a turbulent boundary layer up to R sub theta = 1410
TL;DR: In this paper, the turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub tta = 1410.