Journal ArticleDOI
A general classification of three-dimensional flow fields
Reads0
Chats0
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
More filters
Journal ArticleDOI
Preferential concentration of particles by turbulence
Kyle D. Squires,John K. Eaton +1 more
TL;DR: In this paper, a direct numerical simulation of isotropic turbulence was used to investigate the effect of turbulence on the concentration fields of heavy particles, and it was shown that the particles collect preferentially in regions of low vorticity and high strain rate.
Journal ArticleDOI
On the relationships between local vortex identification schemes
TL;DR: In this paper, a new measure of spiralling compactness of material orbits in vortices is introduced and using this measure a new local vortex identification criterion and requirements for a vortex core are proposed.
Journal ArticleDOI
Distinguished material surfaces and coherent structures in three-dimensional fluid flows
TL;DR: In this article, the authors prove the existence of finite-time attracting and repelling material surfaces and lines in three-dimensional unsteady flows and characterize coherent structures as local maximizers of the largest finite time Lyapunov exponent field computed directly from particle paths.
Journal ArticleDOI
Lagrangian Coherent Structures
TL;DR: The Lagrangian coherent structures (LCSs) as discussed by the authors are a skeleton of material surfaces, which can be used to shape the initial conditions of particle trajectories and frame, quantify, and forecast key aspects of material transport.
Journal ArticleDOI
An objective definition of a vortex
TL;DR: In this article, the authors define a vortex as a set of fluid trajectories along which the strain acceleration tensor is indefinite over directions of zero strain, and they show using examples how this vortex criterion outperforms earlier frame-dependent criteria.
References
More filters
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.