scholarly journals Vortex Interactions Subjected to Deformation Flows: A Review

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 14 ◽  
Author(s):  
Konstantin Koshel ◽  
Eugene Ryzhov ◽  
Xavier Carton
Keyword(s):  
Review Paper ◽  
Point Vortex ◽  
Passive Scalar ◽  
Dynamical System Theory ◽  
Single Vortex ◽  
Vortex Interactions ◽  
Rotational Components ◽  
Coherent Vortices ◽  
Numerical And Analytical Methods ◽  
Submerged Obstacles

Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.

scholarly journals Vortex Interactions Subjected to Deformation Flows: A Review

2018 ◽  
Author(s):  
Konstantin V. Koshel ◽  
Eugene A. Ryzhov ◽  
Xavier J. Carton
Keyword(s):  
Review Paper ◽  
Point Vortex ◽  
Passive Scalar ◽  
Dynamical System Theory ◽  
Single Vortex ◽  
Vortex Interactions ◽  
Rotational Components ◽  
Coherent Vortices ◽  
Numerical And Analytical Methods ◽  
Submerged Obstacles

Deformation flows are flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets), various fixed obstacles (submerged obstacles, continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

Sound generation by shock–vortex interactions

1999 ◽  
Vol 380 ◽  
pp. 81-116 ◽  
Author(s):  
OSAMU INOUE ◽  
YUJI HATTORI
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Early Stage ◽  
Near Field ◽  
Time Integration ◽  
Flow Fields ◽  
Navier Stokes ◽  
Single Vortex ◽  
Vortex Interactions ◽  
Reflected Shock

Two-dimensional, unsteady, compressible flow fields produced by the interactions between a single vortex or a pair of vortices and a shock wave are simulated numerically. The Navier–Stokes equations are solved by a finite difference method. The sixth-order-accurate compact Padé scheme is used for spatial derivatives, together with the fourth-order-accurate Runge–Kutta scheme for time integration. The detailed mechanics of the flow fields at an early stage of the interactions and the basic nature of the near-field sound generated by the interactions are studied. The results for both a single vortex and a pair of vortices suggest that the generation and the nature of sounds are closely related to the generation of reflected shock waves. The flow field differs significantly when the pair of vortices moves in the same direction as the shock wave than when opposite to it.

scholarly journals Network-theoretic approach to sparsified discrete vortex dynamics

2015 ◽  
Vol 768 ◽  
pp. 549-571 ◽  
Author(s):  
Aditya G. Nair ◽  
Kunihiko Taira
Keyword(s):  
Vortex Dynamics ◽  
Point Vortex ◽  
Spectral Graph Theory ◽  
Theoretic Approach ◽  
Dynamics Model ◽  
Discrete Vortex ◽  
Sparse Graphs ◽  
Graph Representations ◽  
Vortex Interactions ◽  
Two Dimensional Flow

We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters interacting amongst themselves. We also evaluate the performance of sparsification with increasing number of point vortices. The sparsified-dynamics model developed with spectral graph theory requires a reduced number of vortex-to-vortex interactions but agrees well with the full nonlinear dynamics. Furthermore, the sparsified model derived from the sparse graphs conserves the invariants of discrete vortex dynamics. We highlight the similarities and differences between the present sparsified-dynamics model and reduced-order models.

Streamwise vortices and transition to turbulence

1994 ◽  
Vol 264 ◽  
pp. 185-212 ◽  
Author(s):  
James M. Hamilton ◽  
Frederick H. Abernathy
Keyword(s):  
Streamwise Velocity ◽  
Transition To Turbulence ◽  
Streamwise Vortices ◽  
Single Vortex ◽  
Transitional Flows ◽  
Vortex Interactions ◽  
Crossflow Velocity ◽  
Series Of Experiments ◽  
Made In

A series of experiments was conducted to determine the conditions under which streamwise vortices can cause transition to turbulence in shear flows. A specially designed obstacle was used to produce a single vortex in a water-table flow, and the design of this obstacle is discussed. Laser-Doppler velocimetry measurements of the streamwise and crossflow velocity fields were made in transitional and non-transitional flows, and flow visualization was also used. It was found that strong vortices (vortices with large circulation) lead to turbulence while weaker vortices do not. Determination of a critical value of vortex strength for transition, however, was complicated by ambiguities in calculating the vortex circulation. The profiles of streamwise velocity were found to be inflexional for both transitional and non-transitional flows. Transition in single-vortex and multi-vortex flows was compared, and no qualitative differences were observed, suggesting no significant vortex interactions affecting transition.

Vorticity and passive-scalar dynamics in two-dimensional turbulence

1987 ◽  
Vol 183 ◽  
pp. 379-397 ◽  
Author(s):  
Armando Babiano ◽  
Claude Basdevant ◽  
Bernard Legras ◽  
Robert Sadourny
Keyword(s):  
Similarity Theory ◽  
Physical Space ◽  
Passive Scalar ◽  
Inertial Range ◽  
Flow Dynamics ◽  
Two Dimensional ◽  
Closure Model ◽  
Coherent Vortices ◽  
Vorticity Transport ◽  
Kolmogorov Theory

The dynamics of vorticity in two-dimensional turbulence is studied by means of semi-direct numerical simulations, in parallel with passive-scalar dynamics. It is shown that a passive scalar forced and dissipated in the same conditions as vorticity, has a quite different behaviour. The passive scalar obeys the similarity theory à la Kolmogorov, while the enstrophy spectrum is much steeper, owing to a hierarchy of strong coherent vortices. The condensation of vorticity into such vortices depends critically both on the existence of an energy invariant (intimately related to the feedback of vorticity transport on velocity, absent in passive-scalar dynamics, and neglected in the Kolmogorov theory of the enstrophy inertial range); and on the localness of flow dynamics in physical space (again not considered by the Kolmogorov theory, and not accessible to closure model simulations). When space localness is artificially destroyed, the enstrophy spectrum again obeys a k−1 law like a passive scalar. In the wavenumber range accessible to our experiments, two-dimensional turbulence can be described as a hierarchy of strong coherent vortices superimposed on a weak vorticity continuum which behaves like a passive scalar.

Vorticity dynamics in a breaking internal gravity wave. Part 2. Vortex interactions and transition to turbulence

1998 ◽  
Vol 367 ◽  
pp. 47-65 ◽  
Author(s):  
DAVID C. FRITTS ◽  
STEVE ARENDT ◽  
ØYVIND ANDREASSEN
Keyword(s):  
Gravity Wave ◽  
Internal Gravity Wave ◽  
Companion Paper ◽  
Transition To Turbulence ◽  
Single Vortex ◽  
Vortex Sheets ◽  
Initial Formation ◽  
Vortex Interactions ◽  
Vorticity Dynamics ◽  
Vortex Tubes

A companion paper (Part 1) employed a three-dimensional numerical simulation to examine the vorticity dynamics of the initial instabilities of a breaking internal gravity wave in a stratified, sheared, compressible fluid. The present paper describes the vorticity dynamics that drive this flow to smaller-scale, increasingly isotropic motions at later times. Following the initial formation of discrete and intertwined vortex loops, the most important interactions are the self-interactions of single vortex tubes and the mutual interactions of multiple vortex tubes in close proximity. The initial formation of vortex tubes from the roll-up of localized vortex sheets gives the vortex tubes axial variations with both axisymmetric and azimuthal-wavenumber-2 components. The axisymmetric variations excite axisymmetric twist waves or Kelvin vortex waves which propagate along the tubes, drive axial flows, deplete the tubes' cores, and fragment the tubes. The azimuthal-wavenumber-2 variations excite m=2 twist waves on the vortex tubes, which undergo strong amplification and unravel single vortex tubes into pairs of intertwined helical tubes; the vortex tubes then burst or fragment. Reconnection often occurs among the remnants of such vortex fragmentation. A common mutual interaction is that of orthogonal vortex tubes, which causes mutual stretching and leads to long-lived structures. Such an interaction also sometimes creates an m=1 twist wave having an approximately steady helical form as well as a preferred sense of helicity. Interactions among parallel vortex tubes are less common, but include vortex pairing. Finally, the intensification and roll-up of weaker vortex sheets into new tubes occurs throughout the evolution. All of these vortex interactions result in a rapid cascade of energy and enstrophy toward smaller scales of motion.

scholarly journals Quantification of the Local Heat Release Rate During Flame-Vortex Interactions at Different Lewis Numbers and Equivalence Ratios

2014 ◽  
Vol 16 (2-3) ◽  
pp. 195
Author(s):  
J.A. Denev ◽  
I. Naydenova ◽  
H. Bockhorn
Keyword(s):  
Heat Release ◽  
Flame Front ◽  
Heat Release Rate ◽  
Release Rate ◽  
Lewis Number ◽  
Local Heat ◽  
Flame Extinction ◽  
Single Vortex ◽  
Vortex Interactions ◽  
Polarisation Effect

<p>The present work aims at the detailed understanding of the local processes in premixed combustion of hydrogen, methane and propane flames at unsteady conditions. The methodology consists of the analysis of simulations of two-dimensional flame-vortex interactions as well as statistical data obtained from threedimensional Direct Numerical Simulations (DNS) of the flame front interacting with a set of vortexes. Special attention is given to the relationship between the Lewis number (<em>Le</em>) of the fuel and the flame front stretch in terms of both curvature and strain rate. A large single vortex bends the flame front thus creating both positive and negative curvatures, which in turn enhance the heat release rate in some locations of the flame front and decrease it in others. The resulting effect is called “polarisation effect”. The occurrence and the strength of the polarisation effect of curvature are tightly bound up with the Lewis number of the fuel. The polarisation effect is quantified by the ratio of maximum to minimum heat release rates along the flame front, which defines the Polarisation Effect Number (PEN). The more the Lewis number of a fuel deviates from unity, the stronger the polarisation effect is. Strong polarisation effects lead finally to local flame extinction. This is demonstrated for hydrogen flames with<em> Le</em> = 0.29 (lean) and Le = 2.2 (rich) as well as for artificially designed cases with <em>Le</em> = 0.1 and <em>Le</em> = 10.0. Therefore, flame extinction can occur for both thermodiffusively stable and unstable flames. It is shown that choosing an appropriate mixture of real fuels with different Lewis numbers, the homogeneity of the heat release rate along the flame front could be considerably enhanced. This relatively uniform heat release rate is not sensitive to curvature, which consequently decreases the occurrence of local extinction.</p><p> </p>

scholarly journals Wave–vortex interactions, remote recoil, the Aharonov–Bohm effect and the Craik–Leibovich equation

2019 ◽  
Vol 881 ◽  
pp. 182-217 ◽  
Author(s):  
Michael Edgeworth McIntyre
Keyword(s):  
Exceptional Case ◽  
Quantum Fluids ◽  
Single Vortex ◽  
Wave Refraction ◽  
Vortex Interactions ◽  
The Third ◽  
Refraction Effect ◽  
Rotating Shallow Water ◽  
Anti Stokes ◽  
Aharonov Bohm

Three examples of non-dissipative yet cumulative interaction between a single wavetrain and a single vortex are analysed, with a focus on effective recoil forces, local and remote. Local recoil occurs when the wavetrain overlaps the vortex core. All three examples comply with the pseudomomentum rule. The first two examples are two-dimensional and non-rotating (shallow water or gas dynamical). The third is rotating, with deep-water gravity waves inducing an Ursell ‘anti-Stokes flow’. The Froude or Mach number, and the Rossby number in the third example, are assumed small. Remote recoil is all or part of the interaction in all three examples, except in one special limiting case. That case is found only within a severely restricted parameter regime and is the only case in which, exceptionally, the effective recoil force can be regarded as purely local and identifiable with the celebrated Craik–Leibovich vortex force – which corresponds, in the quantum fluids literature, to the Iordanskii force due to a phonon current incident on a vortex. Another peculiarity of that exceptional case is that the only significant wave refraction effect is the Aharonov–Bohm topological phase jump.

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