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.

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.

A SEMI-ANALYTICAL METHOD FOR A FLOW OF NON-VISCOUS FLUID AROUND AN AIRFOIL WITH A SHARP TRAILING EDGE

2021 ◽  
pp. 4-10
Author(s):  
Alexey A. Bondarchuk ◽  
Mezhlum A. Sumbatyan
Keyword(s):  
Viscous Fluid ◽  
Analytical Method ◽  
Velocity Vector ◽  
Point Vortex ◽  
Two Dimensional ◽  
Double Layer Potential ◽  
Boundary Contour ◽  
Trailing Edge ◽  
Layer Potential ◽  
Two Dimensional Flow

In the present work we propose a method to study a two-dimensional flow of non-viscous fluid around an airfoil with a sharp trailing edge, by the double-layer potential theory. The circulation of velocity vector is modeled by the potential of a point vortex whose center is located inside the boundary contour. The magnitude of the circulation is defined on the basis of the Joukowski-Chaplygin postulate. There are presented some results for a Joukowski rudde, as well as for the airfoil in the form of a pair of interacting circles. It is performed a comparison of the circulation with its theoretical value.

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.

Co-rotating stationary states and vertical alignment of geostrophic vortices with thin cores

1998 ◽  
Vol 357 ◽  
pp. 321-349 ◽  
Author(s):  
GEORGI G. SUTYRIN ◽  
JAMES C. McWILLIAMS ◽  
R. SARAVANAN
Keyword(s):  
Potential Vorticity ◽  
Numerical Solutions ◽  
Pair Interaction ◽  
Evolutionary Stage ◽  
Stationary States ◽  
Rotating Fluid ◽  
Dynamics Model ◽  
Vertical Alignment ◽  
Vortex Interactions ◽  
Strong Vortex

We investigate the evolution of nearby like-sign vortices whose centres are at different vertical levels in a stably stratified rotating fluid. We employ two differently singularized representations of the potential vorticity distribution in the quasi-geostrophic equations (QG), in order to elucidate the pair-interaction behaviour previously seen in non-singular QG numerical solutions. The first is an analytically tractable conservative (Hamiltonian) elliptical-moment model (EM) for thin-core vortices, which exhibits a regime of very strong horizontal elongation of a vortex in response to the strain induced by its partner. We interpret this as an early evolutionary stage towards the irreversible dissipative merger and alignment interactions. This interpretation is strengthened by weakly dissipative numerical solutions of a thin-core contour-dynamics model (CD), which exhibit even further progress towards the completion of these vortex interactions in the same regime.In the EM model we classify the co-rotating stationary states which exist always for vertically offset thin-core vortices. However, the mutual strain field among the vortices cannot be balanced by co-rotation in a weakly elongated stationary state for a certain class of neighbouring, but substantially non-aligned, vortex configurations, and our interpretive assumption is that such configurations will rapidly evolve in non-singular QG solutions towards a more aligned configuration through significantly non-conservative reorganizations of the potential vorticity field. Both the EM and CD models show qualitatively similar regime boundaries between evolutions with weakly and strongly deformed vortices. In particular, there is a fairly close correspondence between the occurrence of strong vortex elongation in the EM solutions and significant filamentation and splitting in the CD solutions.

Interplay between signaling network design and swarm dynamics

2016 ◽  
Vol 4 (2) ◽  
pp. 244-265 ◽  
Author(s):  
ANDRÉ SEKUNDA ◽  
MOHAMMAD KOMAREJI ◽  
ROLAND BOUFFANAIS
Keyword(s):  
Network Design ◽  
Information Transfer ◽  
Network Models ◽  
Signaling Network ◽  
Spectral Graph Theory ◽  
Theoretic Approach ◽  
Collective Behaviors ◽  
Global Consensus ◽  
Swarm Dynamics ◽  
The Impact

AbstractDistributed information transfer is of paramount importance to the effectiveness of dynamic collective behaviors, especially when a swarm is confronted with complex environmental circumstances. Recently, the signaling network of interaction underlying such effective information transfers has been revealed in the particular case of bird flocks governed by a topological interaction. Such biological systems are known to be evolutionary optimized, but are also constrained by the very nature of the signaling mechanisms—owing to intrinsic limitations in sensory modalities—enabling communication among individuals. Here, we propose that artificial swarm design can be tackled from the angle of signaling network design. To this aim, we use different network models to investigate the impact of some network structural properties on the effectiveness of a specific emergent swarming behavior, namely global consensus. Two new network models are introduced, which together with the well-known Watts–Strogatz model form the basis for an analysis of the relationship between clustering, shortest path and speed to consensus. A network-theoretic approach combined with spectral graph theory tools are used to propose some signaling network design principles. Eventually, one key design principle—a concomitant reduction in clustering and connecting path—is successfully tested on simulations of swarms of self-propelled particles.

LES investigation on vortex dynamics of transient sheet/cloud cavitating flow using different vortex identification methods

2020 ◽  
pp. 2150111
Author(s):  
Shuheng Qu ◽  
Jinping Li ◽  
Huaiyu Cheng ◽  
Bin Ji
Keyword(s):  
Vortex Dynamics ◽  
Cavitating Flow ◽  
Vortex Identification ◽  
Cavitation Model ◽  
Identification Methods ◽  
Vortex Interactions ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Lift And Drag ◽  
Criterion Method

The sheet/cloud cavitating flow always contains complex multiscale vortex structures generated by the cavity cloud shedding and collapsing. In this study, the transient sheet/cloud cavitating flow around a Clark-Y hydrofoil is numerically investigated using the Large Eddy Simulation (LES) method coupled with the Zwart–Gerber–Belamri (ZGB) cavitation model. The simulation accurately reproduces the unsteady cavitation evolution process, and the predicted time-averaged lift and drag coefficients, total vapor volume variation and velocity distribution agree fairly well with the experimental measurements. The cavitation vortex dynamics are studied in detail with different vortex identification methods including the vorticity method, the [Formula: see text]-criterion method, the [Formula: see text] method, the [Formula: see text] method and the Liutex method. The vortex identification ability of the different methods in the transient sheet/cloud cavitating flow is also discussed. Generally, the Liutex method combines the advantages of the other methods and can accurately identify both the vortex position and strength. Further analysis of cavitation-vortex interactions demonstrates that the cavity cloud shedding and collapsing have a pronounced influence on the vortex structure.

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