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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Characterizing three-dimensional features of vortex surfaces in the flow past a finite plate
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Density effects on post-shock turbulence structure and dynamics
TL;DR: In this paper, the effect of density variations on the turbulence structure and flow topology was studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods.
Journal ArticleDOI
Lattice Boltzmann model capable of mesoscopic vorticity computation.
TL;DR: This paper designs a multiple-relaxation time LB model on a three-dimensional 27-discrete-velocity (D3Q27) lattice and shows, with enough degrees of freedom and appropriate modifications, the mesoscopic vorticity computation can be achieved in LBM.
Journal ArticleDOI
Volume integrals of the QA-RA invariants of the velocity gradient tensor in incompressible flows
TL;DR: In this paper, the second and third invariants of the velocity gradient tensor Aij over an incompressible flow domain are shown to vanish for certain combinations of boundary conditions used in a large variety of direct numerical simulations of turbulent flows.
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.