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We report on numerical studies of the DC vortex transport properties, including V(1) curves and vortex trajectories, in triangular pinning arrays of triangular blind antidots. The asymmetric geometry of the pinning sites produces ...
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We report on numerical studies of the DC vortex transport properties, including V(1) curves and vortex trajectories, in triangular pinning arrays of triangular blind antidots. The asymmetric geometry of the pinning sites produces a significant influence on the vortex motion depending on the direction of the applied Lorentz force F-L. (C) 2003 Elsevier Science B.V. All rights reserved. [References: 4]
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Point vortex systems that include vortices with constant coordinate functions are largely unexplored, even though they have reasonable physical interpretations in the geophysical context. Here, we investigate the dynamical aspects...
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Point vortex systems that include vortices with constant coordinate functions are largely unexplored, even though they have reasonable physical interpretations in the geophysical context. Here, we investigate the dynamical aspects of the restricted three-vortex problem when one of the point vortices is assumed to be fixed at a location in the plane. The motion of the passive tracer is explored from a rotating frame of reference within which the free vortex with non-zero circulation remains stationary. By using basic dynamical system theory, it is shown that the vortex motion is always bounded, and any configuration of the three vortices must go through at least one collinear state. The present analysis reveals that any non-relative equilibrium solution of the vortex system either has periodic inter-vortex distances or it will asymptotically converge to a relative equilibrium configuration. The initial conditions required for different types of motion are explained in detail by exploiting the Hamiltonian structure of the problem. The underlying effects of a fixed vortex on the motion of vortices are also explored.
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The dynamics of coherent structures forming in a turbulent shallow mixing layer (ML) between two parallel streams advancing in a constant-depth, open channel is investigated using three-dimensional, time-accurate simulations. The ...
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The dynamics of coherent structures forming in a turbulent shallow mixing layer (ML) between two parallel streams advancing in a constant-depth, open channel is investigated using three-dimensional, time-accurate simulations. The large channel length to flow depth ratio (L-x/H = 400-800) allows characterization of the spatial evolution of shallow MLs until the mean velocity difference between the two streams becomes less than 3% of the initial value at the end of the splitter plate. Away from the ML origin, the dynamics and coherence of the Kelvin-Helmholtz (KH) billows are affected by the destabilizing effect of the mean shear between the two streams and by the stabilizing effect of the bed friction. A linear decay of the entrainment coefficient a with the bed-friction factor, S, applies only over the region where merging of neighbouring KH billows is still observed (transition to quasi-equilibrium regime). At larger distances from the origin, where the billows are severely stretched in the streamwise direction before being destroyed, the rates of increase of the ML width, delta, and centreline shift, l(cy), become very small and alpha is exponentially decaying with increasing S toward zero (quasi-equilibrium regime). During the initial stages of the quasi-equilibrium regime where the KH vortices are severely stretched, the ML assumes an undulatory shape in horizontal planes. New relationships are proposed to characterize the downstream variation of the non-dimensional ML width and centreline shift over the transition and quasi-equilibrium regimes. During the transition to equilibrium regime, the ML boundary on the fast-stream side remains close to vertical, while that on the slow-stream side becomes strongly tilted. The ML boundary on the slow-stream side becomes again close to vertical once the quasi-equilibrium regime is reached. During the transition to the equilibrium regime, the passage of the KH billows and the generation of streamwise cells of secondary flow generate regions of high instantaneous bed shear stress, such that the region where the erosive capacity of the flow peaks does not correspond to the fast stream. The paper also investigates the effects of flow shallowness and initial velocity ratio between the two streams on the turbulent kinetic energy inside the ML, the depth-averaged lateral momentum fluxes, the passage frequency and size of the KH billows and the wavelength and period of the undulatory motions of the ML during the early stages of the quasi-equilibrium regime.
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The nonlinear perturbation response of two families of vortices, the Norbury family of axisymmetric vortex rings and the Pierrehumbert family of two-dimensional vortex pairs, is considered. Members of both families are subjected t...
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The nonlinear perturbation response of two families of vortices, the Norbury family of axisymmetric vortex rings and the Pierrehumbert family of two-dimensional vortex pairs, is considered. Members of both families are subjected to prolate shape perturbations similar to those previously introduced to Hills spherical vortex, and their response is computed using contour dynamics algorithms. The response of the entire Norbury family to this class of perturbations is considered, in order to bridge the gap between past observations of the behaviour of thin-cored members of the family and that of Hills spherical vortex. The behaviour of the Norbury family is contrasted with the response of the analogous two-dimensional family of Pierrehumbert vortex pairs. It is found that the Norbury family exhibits a change in perturbation response as members of the family with progressively thicker cores are considered. Thin-cored vortices are found to undergo quasi-periodic deformations of the core shape, but detrain no circulation into their wake. In contrast, thicker-cored Norbury vortices are found to detrain excess rotational fluid into a trailing vortex tail. This behaviour is found to be in agreement with previous results for Hills spherical vortex, as well as with observations of pinch-off of experimentally generated vortex rings at long formation times. In contrast, the detrainment of circulation that is characteristic of pinch-off is not observed for Pierrehumbert vortex pairs of any core size. These observations are in agreement with recent studies that contrast the formation of vortices in two and three dimensions. We hypothesize that transitions in vortex formation, such as those occurring between wake shedding modes and in vortex pinch-off more generally, might be understood and possibly predicted based on the observed perturbation responses of forming vortex rings or dipoles.
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Vortex merging is a basic fluid phenomenon which has been much studied for two-dimensional flows. Here we extend such a study to a specific class of three-dimensional flows, namely to vortices possessing a helical symmetry. In add...
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Vortex merging is a basic fluid phenomenon which has been much studied for two-dimensional flows. Here we extend such a study to a specific class of three-dimensional flows, namely to vortices possessing a helical symmetry. In addition to the standard Reynolds number, this introduces another dimensionless control number, the pitch, which quantifies the periodicity length along the helix axis. Helical vortices with large pitches merge very much as in a two-dimensional setting. However, their rotation speed is reduced and the merging period is delayed. These effects, caused by the presence of a self-induced velocity in curved three-dimensional vortices, are understood by computing the streamfunction in the frame of reference rotating with the two vortices, and by inspecting the locations of its hyperbolic points. At intermediate pitch values, only viscous diffusion acts, resulting in a slow viscous type of merging. Finally for small pitches, the system is unstable resulting, at the nonlinear stage, in a different type of merging which breaks the initial central symmetry. (C) 2014 Elsevier Masson SAS. All rights reserved.
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The dynamics of interacting vortex filaments in an incompressible fluid, which are nearly parallel, have been approximated in the Klein-Majda-Damodaran model. The regime considers the deflection of each filament from a central axi...
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The dynamics of interacting vortex filaments in an incompressible fluid, which are nearly parallel, have been approximated in the Klein-Majda-Damodaran model. The regime considers the deflection of each filament from a central axis; that is to say, the vortex filaments are assumed to be roughly parallel and centred along parallel lines. While this model has attracted a fair amount of mathematical interest in the recent literature, particularly concerning the existence of certain specific vortex filament structures, our aim is to generalise several known interesting filament solutions, found in the self-induced motion of a single vortex filament, to the case of pairwise interactions between multiple vortex filaments under the Klein-Majda-Damodaran model by means of asymptotic and numerical methods. In particular, we obtain asymptotic solutions for counter-rotating and co-rotating vortex filament pairs that are separated by a distance, so that the vortex filaments always remain sufficiently far apart, as well as intertwined vortex filaments that are in close proximity, exhibiting overlapping orbits. For each scenario, we consider both co- and counter-rotating pairwise interactions, and the specific kinds of solutions obtained for each case consist of planar filaments, for which motion is purely rotational, as well as travelling wave and self-similar solutions, both of which change their form as they evolve in time. We choose travelling waves, planar filaments and self-similar solutions for the initial filament configurations, as these are common vortex filament structures in the literature, and we use the dynamics under the Klein-Majda-Damodaran model to see how these structures are modified in time under pairwise interaction dynamics. Numerical simulations for each case demonstrate the validity of the asymptotic solutions. Furthermore, we develop equations to study a co-rotating hierarchy of many satellite vortices orbiting around a central filament. We numerically s
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In the present study the mechanisms of evolution of propeller tip and hub vortices in the transitional region and the far field are investigated experimentally. The experiments involved detailed time-resolved visualizations and ve...
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In the present study the mechanisms of evolution of propeller tip and hub vortices in the transitional region and the far field are investigated experimentally. The experiments involved detailed time-resolved visualizations and velocimetry measurements and were aimed at examining the effect of the spiral-to-spiral distance on the mechanisms of wake evolution and instability transition. In this regard, three propellers having the same blade geometry but different number of blades were considered. The study outlined dependence of the wake instability on the spiral-to-spiral distance and, in particular, a streamwise displacement of the transition region at the increasing inter-spiral distance. Furthermore, a multi-step grouping mechanism among tip vortices was highlighted and discussed. It is shown that such a phenomenon is driven by the mutual inductance between adjacent spirals whose characteristics change by changing the number of blades.
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The influence of a horizontal wall on the evolution of the long-wave instability in equal strength counter-rotating vortex pairs is studied with direct numerical simulation. The two vortices descend under mutual induction and inte...
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The influence of a horizontal wall on the evolution of the long-wave instability in equal strength counter-rotating vortex pairs is studied with direct numerical simulation. The two vortices descend under mutual induction and interact with a ground plane, as would aircraft trailing vortices in ground effect. Both the linear and nonlinear development of the pair is studied for three initial heights above the wall, representative of three modes of interaction identified by experiment. A study of two vortex core sizes over a range of Reynolds numbers (1000 收起
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In the present study the wake flow past an isolated propeller operating in oblique flow conditions is investigated experimentally. In particular, the investigation concerns a systematic topological comparison of the wake behaviour...
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In the present study the wake flow past an isolated propeller operating in oblique flow conditions is investigated experimentally. In particular, the investigation concerns a systematic topological comparison of the wake behaviour in axisymmetric and in oblique inflow conditions, for three inclination angles, and is focused on an analysis of the underlying mechanisms of wake evolution and instability. To this end, the experiment has been designed to investigate the dynamics of propeller vortical structures over a wide spatial extent covering the wake region from the propeller disk up to 4.5 diameters in the streamwise direction. Detailed flow measurements have been undertaken by particle image velocimetry (PIV), using a multicamera configuration with three cameras arranged side by side. This allowed simultaneous acquisition of a large flow extent at a spatial resolution adequate to resolve the smallest vortical structures involved in the process of propeller wake instability. The analysis has been based on both phase-locked averaged and instantaneous flow fields. The study extends the knowledge on the subject of propeller wake dynamics, highlighting the major hydrodynamic effects that non-axisymmetric propeller operating conditions exert on the mechanisms of wake evolution, instability and breakdown, such as asymmetric destabilization of the tip vortices on the leeward and windward sides of the wake, and the interference between the tip and the junction vortices, as well as the cause-effect relation between the breakdown of the blade trailing wake and the instability of the tip and hub vortices.
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Tornadoes and other intense atmospheric vortices are known to occasionally transition to a flow structure with multiple vortices within their larger circulations. This phenomenon has long been ascribed to fluid dynamical instabili...
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Tornadoes and other intense atmospheric vortices are known to occasionally transition to a flow structure with multiple vortices within their larger circulations. This phenomenon has long been ascribed to fluid dynamical instability of the inner-core circulation, and many previous studies have diagnosed low-wavenumber unstable modes in tornado-like vortices that resemble the observed structures. However, relatively few of these studies have incorporated the strong vertical motions of the inner-core circulation into the stability analysis, and no stability analyses have been performed using a complete, frictionally driven secondary circulation with strong radial inflow near the surface. Stability analyses are presented using the complete circulations generated from idealized simulations of tornado-like vortices. Fast-growing unstable modes are found that are consistent with the asymmetric structures present in these simulations. Attempts to correlate the structures and locations of these modes with instability conditions for vortices with axial jets derived by Howard & Gupta and by Leibovich & Stewartson produce only mixed results. Analyses of perturbation energy growth show that interactions between eddy fluxes and the radial shear of the azimuthal wind contribute very little to the growth of the dominant modes. Rather, the radial shear of the vertical wind and the vertical shear of the vertical wind(corresponding to deformation in the axial direction) are the primary energy sources for perturbation growth. Relatively weak axisymmetric instabilities are also identified that have some similarity to symmetric oscillations that have been observed in tornadoes.
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