Influence of a wall on the three-dimensional dynamics of a vortex pair

2017 ◽  
Vol 817 ◽  
pp. 339-373 ◽  
Author(s):  
Daniel J. Asselin ◽  
C. H. K. Williamson
Keyword(s):  
Ground Plane ◽  
Rebound Effect ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Vortex Rings ◽  
Wave Instability ◽  
Long Wave ◽  
Wall Interaction ◽  
Secondary Vortices ◽  
Crow Instability

In this paper, we are interested in perturbed vortices under the influence of a wall or ground plane. Such flows have relevance to aircraft wakes in ground effect, to ship hull junction flows, to fundamental studies of turbulent structures close to a ground plane and to vortex generator flows, among others. In particular, we study the vortex dynamics of a descending vortex pair, which is unstable to a long-wave instability (Crow, AIAA J., vol. 8 (12), 1970, pp. 2172–2179), as it interacts with a horizontal ground plane. Flow separation on the wall generates opposite-sign secondary vortices which in turn induce the ‘rebound’ effect, whereby the primary vortices rise up away from the wall. Even small perturbations in the vortices can cause significant topological changes in the flow, ultimately generating an array of vortex rings which rise up from the wall in a three-dimensional ‘rebound’ effect. The resulting vortex dynamics is almost unrecognizable when compared with the classical Crow instability. If the vortices are generated below a critical height over a horizontal ground plane, the long-wave instability is inhibited by the wall. We then observe two modes of vortex–wall interaction. For small initial heights, the primary vortices are close together, enabling the secondary vortices to interact with each other, forming vertically oriented vortex rings in what we call a ‘vertical rings mode’. In the ‘horizontal rings mode’, for larger initial heights, the Crow instability develops further before wall interaction; the peak locations are farther apart and the troughs closer together upon reaching the wall. The proximity of the troughs to each other and the wall increases vorticity cancellation, leading to a strong axial pressure gradient and axial flow. Ultimately, we find a series of small horizontal vortex rings which ‘rebound’ from the wall. Both modes comprise two small vortex rings in each instability wavelength, distinct from Crow instability vortex rings, only one of which is formed per wavelength. The phenomena observed here are not limited to the above perturbed vortex pairs. For example, remarkably similar phenomena are found where vortex rings impinge obliquely with a wall.

Direct numerical simulations of the Crow instability and subsequent vortex reconnection in a stratified fluid

2001 ◽  
Vol 426 ◽  
pp. 1-45 ◽  
Author(s):  
J. F. GARTEN ◽  
J. WERNE ◽  
D. C. FRITTS ◽  
S. ARENDT
Keyword(s):  
Growth Rate ◽  
Numerical Model ◽  
Time Scale ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Direct Numerical Simulations ◽  
Reversal Effect ◽  
Vortex Reconnection ◽  
Vertically Propagating ◽  
Crow Instability

The evolution of a vertically propagating three-dimensional vortex pair in ambient stratification is studied with a three-dimensional numerical model. We consider a range of Reynolds (Re) and Froude (Fr) numbers, and initialize the vortex pair in a configuration that promotes growth of the Crow instability (Crow 1970). The growth rate of the instability is Re dependent, and we present a method for extending Crow's model to predict this dependence. We also find that relatively strong ambient stratification (Fr [les ] 2) further alters the growth of the instability via advection by baroclinically produced vorticity. For all of our cases with Fr [ges ] 1 (including our unstratified cases where Fr → ∞), the instability leads to vortex reconnection and formation of a vortex ring. A larger Re delays the commencement of the reconnection, but it proceeds more rapidly once it does commence. We compute a reconnection time scale (tR), and find that tR ∼ 1/Re, in agreement with a model formulated by Shelley et al. (1993). We also discuss a deformative/diffusive effect (related to yet distinct from the curvature reversal effect discussed by Melander & Hussain 1989) which prevents complete reconnection. Ambient stratification (in the range Fr [ges ] 1) accelerates the reconnection and reduces tR by an amount roughly proportional to 1/Fr. For some Fr, stratification effects overwhelm the deformative effect, and complete reconnection results.

scholarly journals A short wave instability caused by the approach of a vortex pair to a ground plane

2010 ◽  
Vol 22 (9) ◽  
pp. 091106 ◽  
Author(s):  
D. M. Harris ◽  
V. A. Miller ◽  
C. H. K. Williamson
Keyword(s):  
Ground Plane ◽  
Vortex Pair ◽  
Short Wave ◽  
Wave Instability

Instability of secondary vortices generated by a vortex pair in ground effect

2012 ◽  
Vol 700 ◽  
pp. 148-186 ◽  
Author(s):  
D. M. Harris ◽  
C. H. K. Williamson
Keyword(s):  
Ground Plane ◽  
Point Vortex ◽  
Vortex Pair ◽  
Ground Effect ◽  
Secondary Vortex ◽  
Primary Vortex ◽  
Single Vortex ◽  
Displacement Mode ◽  
Instability Modes ◽  
Secondary Vortices

AbstractIn this work, we investigate the approach of a descending vortex pair to a horizontal ground plane. As in previous studies, the primary vortices exhibit a ‘rebound’, due to the separation of secondary opposite-sign vortices underneath each primary vortex. On each side of the flow, the weaker secondary vortex can become three-dimensionally unstable, as it advects around the stronger primary vortex. It has been suggested in several recent numerical simulations that elliptic instability is the origin of such waviness in the secondary vortices. In the present research, we employ a technique whereby the primary vortices are visualized separately from the secondary vortices; in fact, we are able to mark the secondary vortex separation, often leaving the primary vortices invisible. We find that the vortices are bent as a whole in a Crow-type ‘displacement’ mode, and, by keeping the primary vortices invisible, we are able to see both sides of the flow simultaneously, showing that the instability perturbations on the secondary vortices are antisymmetric. Triggered by previous research on four-vortex aircraft wake flows, we analyse one half of the flow as an unequal-strength counter-rotating pair, noting that it is essential to take into account the angular velocity of the weak vortex around the stronger primary vortex in the analysis. In contrast with previous results for the vortex–ground interaction, we find that the measured secondary vortex wavelength corresponds well with the displacement bending mode, similar to the Crow-type instability. We have analysed the elliptic instability modes, by employing the approximate dispersion relation of Le Dizés & Laporte (J. Fluid Mech., vol. 471, 2002, p. 169) in our problem, finding that the experimental wavelength is distinctly longer than predicted for the higher-order elliptic modes. Finally, we observe that the secondary vortices deform into a distinct waviness along their lengths, and this places two rows of highly stretched vertical segments of the vortices in between the horizontal primary vortices. The two rows of alternating-sign vortices translate towards each other and ultimately merge into a single vortex row. A simple point vortex row model is able to predict trajectories of such vortex rows, and the net result of the model’s ‘orbital’ or ‘passing’ modes is to bring like-sign vortices, from each secondary vortex row, close to each other, such that merging may ensue in the experiments.

Three-dimensional long-wave instability of unidirectional spatially periodic viscous flows

1996 ◽  
Vol 325 ◽  
pp. 283-301 ◽  
Author(s):  
Y. S. Khazan ◽  
A. A. Nepomnyashchy
Keyword(s):  
Asymptotic Expansions ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Oscillatory Instability ◽  
Wave Instability ◽  
Periodic Flows ◽  
Long Wave ◽  
Spatially Periodic ◽  
New Type

The long-wave instability of unidirectional spatially periodic flows is investigated by means of asymptotic expansions. It is shown that the wavevector of the most dangerous disturbances is generally inclined to the direction of the basic stream. A new type of long-wave oscillatory instability is discovered, and a comparison with results of previous investigations is performed.

Crow instability: nonlinear response to the linear optimal perturbation

2016 ◽  
Vol 795 ◽  
pp. 652-670 ◽  
Author(s):  
Holly G. Johnson ◽  
Vincent Brion ◽  
Laurent Jacquin
Keyword(s):  
Nonlinear Response ◽  
Linear Growth ◽  
Vortex Pair ◽  
Periodic Oscillation ◽  
Vortex Rings ◽  
Optimal Perturbation ◽  
Evolution Stage ◽  
Counter Rotating Vortex Pair ◽  
Crow Instability ◽  
Loss Of Coherence

The potential for anticipated destruction of a counter-rotating vortex pair using the linear optimal perturbation of the Crow instability is assessed. Direct numerical simulation is used to study the development of the Crow instability and the subsequent evolution of the flow up to 30 characteristic times at a circulation-based Reynolds number of 1000. The conventional development of the instability leads to multiple contortions of the vortices including the linear growth of sinusoidal deformation, vortex linking and the formation of vortex rings. A new evolution stage is identified, succeeding this well-established sequence: the vortex rings undergo periodic oscillation. Two complete periods are simulated during which the vortical system is hardly altered, thereby demonstrating the extraordinary resilience of the vortices. The possibility of preventing these dynamics using the linear optimal perturbation of the Crow instability, the adjoint mode, is analysed. By appropriately setting the forcing amplitude, the lifetime of the vortices until their loss of coherence is reduced to approximately 13 characteristic times, which is less than half that of the natural Crow behaviour observed with infinitesimal forcing. The dynamics of the flow induced by the linear optimal perturbation that enable this result are connected to processes already known to efficiently alter vortical flows, in particular transient growth and four-vortex dynamics.

scholarly journals Three-Dimensional Imaging of Terahertz Circular SAR with Sparse Linear Array

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2477 ◽  
Author(s):  
Jubo Hao ◽  
Jin Li ◽  
Yiming Pi
Keyword(s):  
3D Imaging ◽  
Linear Array ◽  
Ground Plane ◽  
Three Dimensional ◽  
Terahertz Waves ◽  
Recovery Method ◽  
Imaging Algorithm ◽  
Imaging Geometry ◽  
Imaging Results ◽  
Sparse Linear Array

Due to the non-contact detection ability of radar and the harmlessness of terahertz waves to the human body, three-dimensional (3D) imaging using terahertz synthetic aperture radar (SAR) is an efficient method of security detection in public areas. To achieve high-resolution and all aspect imaging, circular trajectory movement of radar and linear sensor array along the height direction were used in this study. However, the short wavelength of terahertz waves makes it practically impossible for the hardware to satisfy the half-wavelength spacing condition to avoid grating lobes. To solve this problem, a sparse linear array model based on the equivalent phase center principle was established. With the designed imaging geometry and corresponding echo signal model, a 3D imaging algorithm was derived. Firstly, the phase-preserving algorithm was adopted to obtain the 2D image of the ground plane for each sensor. Secondly, the sparse recovery method was applied to accomplish the scattering coefficient reconstruction along the height direction. After reconstruction of all the range-azimuth cells was accomplished, the final 3D image was obtained. Numerical simulations and experiments using terahertz radar were performed. The imaging results verify the effectiveness of the 3D imaging algorithm for the proposed model and validate the feasibility of terahertz radar applied in security detection.

scholarly journals Single and multiple vortex rings in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics

2017 ◽  
Vol 95 (4) ◽  
Author(s):  
Wenlong Wang ◽  
R. N. Bisset ◽  
C. Ticknor ◽  
R. Carretero-González ◽  
D. J. Frantzeskakis ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Vortex Rings ◽  
Bose Einstein

Side-Wall Effect on the Long-Wave Instability in Kolmogorov Flow

1998 ◽  
Vol 67 (5) ◽  
pp. 1597-1602 ◽  
Author(s):  
Hiroaki Fukuta ◽  
Youichi Murakami
Keyword(s):  
Side Wall ◽  
Wall Effect ◽  
Wave Instability ◽  
Kolmogorov Flow ◽  
Long Wave
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