scholarly journals Spherical vortices in rotating fluids

2018 ◽  
Vol 846 ◽  
Author(s):  
M. M. Scase ◽  
H. L. Terry
Keyword(s):  
Ideal Fluid ◽  
Rotation Rate ◽  
Wave Motion ◽  
Infinite Family ◽  
Vortex Rings ◽  
Rotating Fluids ◽  
Critical Rotation ◽  
Spherical Vortex ◽  
Inertial Wave ◽  
Special Case

A popular model for a generic fat-cored vortex ring or eddy is Hill’s spherical vortex (Phil. Trans. R. Soc. A, vol. 185, 1894, pp. 213–245). This well-known solution of the Euler equations may be considered a special case of the doubly infinite family of swirling spherical vortices identified by Moffatt (J. Fluid Mech., vol. 35 (1), 1969, pp. 117–129). Here we find exact solutions for such spherical vortices propagating steadily along the axis of a rotating ideal fluid. The boundary of the spherical vortex swirls in such a way as to exactly cancel out the background rotation of the system. The flow external to the spherical vortex exhibits fully nonlinear inertial wave motion. We show that above a critical rotation rate, closed streamlines may form in this outer fluid region and hence carry fluid along with the spherical vortex. As the rotation rate is further increased, further concentric ‘sibling’ vortex rings are formed.

The Evolution of Rapidly Rotating B/Be Stars

1982 ◽  
Vol 98 ◽  
pp. 299-302 ◽  
Author(s):  
A. S. Endal
Keyword(s):  
Rotation Rate ◽  
Main Sequence ◽  
Critical Value ◽  
Moment Of Inertia ◽  
Maxwellian Distribution ◽  
Be Stars ◽  
Rotating Stars ◽  
Hydrogen Burning ◽  
Critical Rotation ◽  
The Moment

Rotation can significantly change the moment-of-inertia of a main sequence star. As a result, the ZAMS rotation rate need only be within ~30% of the critical value in order to reach critical rotation during the hydrogen burning stage. Calculations of the evolution of rotating stars show that the Be stars result from a normal (Maxwellian) distribution of B-star rotation velocities.

Head-on collision of two coaxial vortex rings in an ideal fluid

1990 ◽  
Vol 24 (4) ◽  
pp. 538-541 ◽  
Author(s):  
A. A. Gurzhii ◽  
M. Yu. Konstantinov
Keyword(s):  
Ideal Fluid ◽  
Vortex Rings

Vortex rings in an ideal fluid

2010 ◽  
pp. 274-285
Author(s):  
Antonio Ambrosetti ◽  
Andrea Malchiodi
Keyword(s):  
Ideal Fluid ◽  
Vortex Rings

Critical Rotation Rate for Vortex Nucleation in Ultracold Rotating Boson Atoms Trapped in 2D Deep Optical Lattice at Finite Temperature

2020 ◽  
Vol 200 (3-4) ◽  
pp. 102-117
Author(s):  
Ahmed S. Hassan ◽  
Azza M. Elbadry ◽  
Alyaa A. Mahmoud ◽  
A. M. Mohammedein ◽  
A. M. Abdallah
Keyword(s):  
Rotation Rate ◽  
Finite Temperature ◽  
Optical Lattice ◽  
Critical Rotation ◽  
Vortex Nucleation

Interaction of coaxial vortex rings in an ideal fluid

1988 ◽  
Vol 23 (2) ◽  
pp. 224-229 ◽  
Author(s):  
A. A. Gurzhii ◽  
M. Yu. Konstantinov ◽  
V. V. Meleshko
Keyword(s):  
Ideal Fluid ◽  
Vortex Rings

scholarly journals Applegate mechanism in post-common-envelope binaries: Investigating the role of rotation

2018 ◽  
Vol 615 ◽  
pp. A81 ◽  
Author(s):  
F. H. Navarrete ◽  
D. R. G. Schleicher ◽  
J. Zamponi Fuentealba ◽  
M. Völschow
Keyword(s):  
Orbital Period ◽  
Rotation Rate ◽  
Main Sequence ◽  
Magnetic Activity ◽  
Main Sequence Star ◽  
Common Envelope ◽  
Rotation Rates ◽  
Critical Rotation ◽  
Period Variations ◽  
Time Variations

Context. Eclipsing time variations are observed in many close binary systems. In particular, for several post-common-envelope binaries (PCEBs) that consist of a white dwarf and a main sequence star, the observed-minus-calculated (O–C) diagram suggests that real or apparent orbital period variations are driven by Jupiter-mass planets or as a result of magnetic activity, the so-called Applegate mechanism. The latter explains orbital period variations as a result of changes in the stellar quadrupole moment due to magnetic activity. Aims. In this work we explore the feasibility of driving eclipsing time variations via the Applegate mechanism for a sample of PCEB systems, including a range of different rotation rates. Methods. We used the MESA code to evolve 12 stars with different masses and rotation rates. We applied simple dynamo models to their radial profiles to investigate the scale at which the predicted activity cycle matches the observed modulation period, and quantifiy the uncertainty. We further calculated the required energies to drive the Applegate mechanism. Results. We show that the Applegate mechanism is energetically feasible in 5 PCEB systems. In RX J2130.6+4710, it may be feasible as well considering the uncertainties. We note that these are the systems with the highest rotation rate compared to the critical rotation rate of the main-sequence star. Conclusions. The results suggest that the ratio of physical to critical rotation rate in the main sequence star is an important indicator for the feasibility of Applegate’s mechanism, but exploring larger samples will be necessary to probe this hypothesis.

A family of steady vortex rings

1973 ◽  
Vol 57 (3) ◽  
pp. 417-431 ◽  
Author(s):  
J. Norbury
Keyword(s):  
Theoretical Work ◽  
Vortex Rings ◽  
Small Cross Section ◽  
The Core ◽  
Axisymmetric Vortex ◽  
Recent Theoretical Work ◽  
The Family ◽  
Core Boundary ◽  
Spherical Vortex ◽  
Axis Of Symmetry

Axisymmetric vortex rings which propagate steadily through an unbounded ideal fluid at rest at infinity are considered. The vorticity in the ring is proportional to the distance from the axis of symmetry. Recent theoretical work suggests the existence of a one-parameter family, [npar ]2 ≥ α ≥ 0 (the parameter α is taken as the non-dimensional mean core radius), of these vortex rings extending from Hill's spherical vortex, which has the parameter value α = [npar ]2, to vortex rings of small cross-section, where α → 0. This paper gives a numerical description of vortex rings in this family. As well as the core boundary, propagation velocity and flux, various other properties of the vortex ring are given, including the circulation, fluid impulse and kinetic energy. This numerical description is then compared with asymptotic descriptions which can be found near both ends of the family, that is, when α → [npar ]2 and α → 0.

scholarly journals QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

2008 ◽  
Vol 1 (1) ◽  
pp. 187-241
Author(s):  
P. D. Williams ◽  
T. W. N. Haine ◽  
P. L. Read ◽  
S. R. Lewis ◽  
Y. H. Yamazaki
Keyword(s):  
Laboratory Experiments ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Fluids ◽  
Stochastic Forcing ◽  
Internal Interface ◽  
Time Stepping ◽  
Beta Effect ◽  
Fluid Layers ◽  
Special Case

Abstract. QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

scholarly journals Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Rudong Chen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Minimum Norm ◽  
Practical Applications ◽  
Fixed Point Computation ◽  
The Common ◽  
Special Case

Fixed point (especially, the minimum norm fixed point) computation is an interesting topic due to its practical applications in natural science. The purpose of the paper is devoted to finding the common fixed points of an infinite family of nonexpansive mappings. We introduce an iterative algorithm and prove that suggested scheme converges strongly to the common fixed points of an infinite family of nonexpansive mappings under some mild conditions. As a special case, we can find the minimum norm common fixed point of an infinite family of nonexpansive mappings.

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