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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Dissertation
Large-Eddy Simulation for Computing the Flow Around Vehicles
TL;DR: In this paper, the feasibility of the use of large-eddy simulation (LES) in external vehicle aerodynamics is investigated, and it is found that making LES of the flow around simplified car-like shapes at lower Reynolds numbers can increase our knowledge of flow around a car.
Journal ArticleDOI
Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem
TL;DR: In this paper, an enstrophy-based nonlinear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented, using the Taylor-Green vortex (TGV) problem as an example.
Journal ArticleDOI
Principal coordinates and principal velocity gradient tensor decomposition
TL;DR: In this paper, the principal coordinate and principal decomposition are introduced to solve the problems of Helmholtz decomposition and Cauchy-Stokes tensor decomposition for fluid kinematics.
Journal ArticleDOI
Toward vortex identification based on local pressure-minimum criterion in compressible and variable density flows
Jie Yao,Fazle Hussain +1 more
TL;DR: In this article, a dynamical vortex definition is proposed for studying vortex dynamics in highly compressible and strongly varying density flows, and the definition is used to define a vortex model.
Journal ArticleDOI
Simulation and study of stratified flows around finite bodies
V. A. Gushchin,P. V. Matyushin +1 more
TL;DR: In this article, the Navier-Stokes equations in the Boussinesq approximation are described by the spatial vortex structure of the flows past a sphere and a square cylinder of diameter d moving horizontally at the velocity U in a linearly density-stratified viscous incompressible fluid.
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.