4,239 research outputs found
Numerical studies of interacting vortices
To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two dimensional vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis
The critical merger distance between two co-rotating quasi-geostrophic vortices
This paper examines the critical merger or strong interaction distance between two equal-potential-vorticity quasi-geostrophic vortices. The interaction between the two vortices depends on five parameters: their volume ratio, their height-to-width aspect ratios and their vertical and horizontal offsets. Due to the size of the parameter space, a direct investigation solving the full quasi-geostrophic equations is impossible. We instead determine the critical merger distance approximately using an asymptotic approach. We associate the merger distance with the margin of stability for a family of equilibrium states having prescribed aspect and volume ratios, and vertical offset. The equilibrium states are obtained using an asymptotic solution method which models vortices by ellipsoids. The margin itself is determined by a linear stability analysis. We focus on the interaction between oblate to moderately prolate vortices, the shapes most commonly found in turbulence. Here, a new unexpected instability is found and discussed for prolate vortices which is manifested by the tilting of vortices toward each other. It implies than tall vortices may merge starting from greater separation distances than previously thought.Publisher PDFPeer reviewe
Experimental study of the effect on span loading on aircraft wakes
Measurements were made in the NASA-Ames 40- by 80-foot wind tunnel of the rolling moment induced on a following model in the wake 13.6 spans behind a subsonic transport model for a variety of trailing edge flap settings of the generator. It was found that the rolling moment on the following model was reduced substantially, compared to the conventional landing configuration, by reshaping the span loading on the generating model to approximate a span loading, found in earlier studies, which resulted in reduced wake velocities. This was accomplished by retracting the outboard trailing edge flaps. It was concluded, based on flow visualization conducted in the wind tunnel as well as in a water tow facility, that this flap arrangement redistributes the vorticity shed by the wing along the span to form three vortex pairs that interact to disperse the wake
On The Phase Transition in D=3 Yang-Mills Chern-Simons Gauge Theory
Yang-Mills theory in three dimensions, with a Chern-Simons term of
level (an integer) added, has two dimensionful coupling constants,
and ; its possible phases depend on the size of relative to . For
, this theory approaches topological Chern-Simons theory with no
Yang-Mills term, and expectation values of multiple Wilson loops yield Jones
polynomials, as Witten has shown; it can be treated semiclassically. For ,
the theory is badly infrared singular in perturbation theory, a
non-perturbative mass and subsequent quantum solitons are generated, and Wilson
loops show an area law. We argue that there is a phase transition between these
two behaviors at a critical value of , called , with . Three lines of evidence are given: First, a gauge-invariant one-loop
calculation shows that the perturbative theory has tachyonic problems if .The theory becomes sensible only if there is an additional dynamic
source of gauge-boson mass, just as in the case. Second, we study in a
rough approximation the free energy and show that for there is a
non-trivial vacuum condensate driven by soliton entropy and driving a
gauge-boson dynamical mass , while both the condensate and vanish for . Third, we study possible quantum solitons stemming from an effective
action having both a Chern-Simons mass and a (gauge-invariant) dynamical
mass . We show that if M \gsim 0.5 m, there are finite-action quantum
sphalerons, while none survive in the classical limit , as shown earlier
by D'Hoker and Vinet. There are also quantum topological vortices smoothly
vanishing as .Comment: 36 pages, latex, two .eps and three .ps figures in a gzipped
uuencoded fil
A three-dimensional scalar field theory model of center vortices and its relation to k-string tensions
In d=3 SU(N) gauge theory, we study a scalar field theory model of center
vortices that furnishes an approach to the determination of so-called k-string
tensions. This model is constructed from string-like quantum solitons
introduced previously, and exploits the well-known relation between string
partition functions and scalar field theories in d=3. Center vortices
corresponding to magnetic flux J (in units of 2\pi /N) are composites of J
elementary J=1 constituent vortices that come in N-1 types, with repulsion
between like constituents and attraction between unlike constituents. The
scalar field theory involves N scalar fields \phi_i (one of which is
eliminated) that can merge, dissociate, and recombine while conserving flux mod
N. The properties of these fields are deduced directly from the corresponding
gauge-theory quantum solitons. Every vacuum Feynman graph of the theory
corresponds to a real-space configuration of center vortices. We study
qualitatively the problem of k-string tensions at large N, whose solution is
far from obvious in center-vortex language. We construct a simplified dynamical
picture of constituent-vortex merging, dissociation, and recombination, which
allows in principle for the determination of vortex areal densities and
k-string tensions. This picture involves point-like "molecules" (cross-sections
of center vortices) made of constituent "atoms" that combine and disassociate
dynamically in a d=2 test plane . The vortices evolve in a Euclidean "time"
which is the location of the test plane along an axis perpendicular to the
plane. A simple approximation to the molecular dynamics is compatible with
k-string tensions that are linear in k for k<< N, as naively expected.Comment: 21 pages; RevTeX4; 4 .eps figure
Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime
When one splits spacetime into space plus time, the spacetime curvature (Weyl
tensor) gets split into an "electric" part E_{jk} that describes tidal gravity
and a "magnetic" part B_{jk} that describes differential dragging of inertial
frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines,
their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity,
and tendexes), and also visualizations of a black-hole horizon's (scalar)
vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics
of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure
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