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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Wavelet Filtering to Extract Coherent Vortices from Altimetric Data
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Flow dynamics of a pitching foil by eulerian and lagrangian viewpoints
Chien Chou Tseng,Hou An Hu +1 more
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Density effects on turbulent boundary layer structure: From the atmosphere to hypersonic flow
TL;DR: In this article, the effects of density gradients on turbulent boundary layer statistics and structure using Particle Image Velocimetry (PIV) measurements were obtained in conjunction with the mean temperature profile in low Reynolds number facility over smooth and rough surfaces.
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Stretching and shearing contamination analysis for Liutex and other vortex identification methods
TL;DR: Liutex is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation as discussed by the authors. But, in the real flow, shearing and stretching do not contribute to fluid rotation, and the contamination effects of stretching and shearing of traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations.
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.
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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.