Journal ArticleDOI
A general classification of three-dimensional flow fields
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
Galilean invariance of Omega vortex identification method
TL;DR: In this paper, Liu et al. proved the Galilean invariance of the omega vortex identification method and several examples are presented to verify the conclusion, which is the same as the result in this paper.
Journal ArticleDOI
Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations ii. global asymptotic behavior of time discretizations ∗
Helen C. Yee,P. K. Sweby +1 more
TL;DR: It is shown how “numerical” basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DCs).
Journal ArticleDOI
Direct numerical simulation of shock wavy-wall interaction: analysis of cellular shock structures and flow patterns
TL;DR: In this article, the reflection on a wavy wall of a planar shock propagating at Mach number 1.5 in air is simulated in a two-dimensional geometry by solving the fully compressible Navier-Stokes equations.
Journal ArticleDOI
Superfluid spherical Couette flow
TL;DR: In this paper, the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) equation was solved numerically for an He-II-like superfluid contained in a differentially rotating spherical shell, generalizing previous simulations of viscous spherical Couette flow (SCF) and superfluid Taylor-Couette flow.
Journal ArticleDOI
Objective Omega vortex identification method
TL;DR: In this paper, Liu et al. presented an objective vortex identification method by using the definitions of the net spin tensor and net vorticity vector, and the examples are presented to verify the vortex structures will still retain in a moving reference frame.
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.