scholarly journals Vortex motion and geometric function theory: the role of connections

2019 ◽  
Vol 377 (2158) ◽  
pp. 20180341
Author(s):  
Björn Gustafsson
Keyword(s):  
Vortex Dynamics ◽  
Affine Connection ◽  
Vortex Motion ◽  
Hamiltonian Formulation ◽  
Point Vortex ◽  
Hamiltonian Function ◽  
Riemannian Metric ◽  
Minimal Amount ◽  
Dynamical Equations ◽  
The Difference

We formulate the equations for point vortex dynamics on a closed two-dimensional Riemannian manifold in the language of affine and other kinds of connections. This can be viewed as a relaxation of standard approaches, using the Riemannian metric directly, to an approach based more on local coordinates provided with a minimal amount of extra structure. The speed of a vortex is then expressed in terms of the difference between an affine connection derived from the coordinate Robin function and the Levi–Civita connection associated with the Riemannian metric. A Hamiltonian formulation of the same dynamics is also given. The relevant Hamiltonian function consists of two main terms. One of the terms is the well-known quadratic form based on a matrix whose entries are Green and Robin functions, while the other term describes the energy contribution from those circulating flows which are not implicit in the Green functions. One main issue of the paper is a detailed analysis of the somewhat intricate exchanges of energy between these two terms of the Hamiltonian. This analysis confirms the mentioned dynamical equations formulated in terms of connections. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

Latitudinal point vortex rings on the spheroid

2010 ◽  
Vol 466 (2118) ◽  
pp. 1749-1768 ◽  
Author(s):  
Sun-Chul Kim
Keyword(s):  
Vortex Ring ◽  
Stereographic Projection ◽  
Vortex Motion ◽  
Point Vortex ◽  
Vortex Rings ◽  
Dynamical Equations ◽  
Conformal Metric ◽  
The Stability ◽  
Pole Vortex

Point vortex motion on the surface of a spheroid is studied. Exact dynamical equations from the corresponding Hamiltonian are constructed by computing the conformal metric which induces a modified stereographic projection. As a concrete example, the motion of point vortices at the same latitude (called the point vortex ring ) is investigated as an extension of the sphere case. The role of eccentricity to the stability of the rotating motion is analysed. The influence of a pole vortex is also discussed.

scholarly journals Road lighting density and brightness linked with increased cycling rates after-dark

2020 ◽  
Author(s):  
Jim Uttley ◽  
Steve Fotios ◽  
Robin Lovelace
Keyword(s):  
Negative Impact ◽  
Time Of Day ◽  
Aerial Images ◽  
Minimal Amount ◽  
Night Time ◽  
Road Lighting ◽  
International Policies ◽  
Relative Brightness ◽  
Two Measures ◽  
The Difference

Cycling has a range of benefits as is recognised by national and international policies aiming to increase cycling rates. Darkness acts as a barrier to people cycling, with fewer people cycling after-dark when seasonal and time-of-day factors are accounted for. This paper explores whether road lighting can reduce the negative impact of darkness on cycling rates. Changes in cycling rates between daylight and after-dark were quantified for 48 locations in Birmingham, United Kingdom, by calculating an odds ratio. These odds ratios were compared against two measures of road lighting at each location: 1) Density of road lighting lanterns; 2) Relative brightness as estimated from night-time aerial images. Locations with no road lighting showed a significantly greater reduction in cycling after-dark compared with locations that had some lighting. A nonlinear relationship was found between relative brightness at a location at night and the reduction in cyclists after-dark. Small initial increases in brightness resulted in large reductions in the difference between cyclist numbers in daylight and after-dark, but this effect reached a plateau as brightness increased. These results suggest only a minimal amount of lighting may be sufficient to promote cycling after-dark.

Automated Geometric Correction System for Additive Manufacturing Considering Build Orientation

2021 ◽  
pp. 1-30
Author(s):  
Seyedeh Elaheh Ghiasian ◽  
Kemper Lewis
Keyword(s):  
Additive Manufacturing ◽  
Optimization Model ◽  
Experimental Validation ◽  
Minimal Amount ◽  
Feature Size ◽  
Build Orientation ◽  
Computational Performance ◽  
The Difference ◽  
Processing Effort ◽  
Correction System

Abstract One of the current challenges for the additive manufacturing (AM) industry lies in providing component designs compatible with the AM manufacturability and constraints without compromising the component structural functionalities. To address this challenge, we present an automated correction system that provides geometrically feasible designs for additive processes by applying locally effective modifications while avoiding substantial changes in the current designs. Considering a minimum printable feature size from the process parameters, this system identifies the problematic features in an infeasible part's design using a holistic geometric assessment algorithm. Based on the obtained manufacturability feedback, the system then corrects the detected problematic regions using a set of appropriate redesign solutions through an automated procedure. In addition, to reduce the difference between the current and modified part geometries, a novel optimization model for build orientation is presented. Using this model, one can identify appropriate orientations for obtaining a feasible design with a minimal amount of corrections while also reducing the post-processing effort by minimizing the area of contact with the support structure. The functionalities of the presented correction system and the optimization model are illustrated using a number of case studies with varying geometries. The computational performance of the system and an experimental validation are also presented to demonstrate the effectiveness of the implemented detection and modification approaches.

scholarly journals Parameterization of Mixed Layer and Deep-Ocean Mesoscales including Nonlinearity

2018 ◽  
Vol 48 (3) ◽  
pp. 555-572 ◽  
Author(s):  
V. M. Canuto ◽  
Y. Cheng ◽  
M. S. Dubovikov ◽  
A. M. Howard ◽  
A. Leboissetier
Keyword(s):  
Deep Ocean ◽  
Altimetry Data ◽  
Dynamical Equations ◽  
Mean Velocity ◽  
Ocean Stratification ◽  
Large Heat ◽  
Reference Experiment ◽  
The Mean ◽  
The Difference ◽  
Induced Velocity

AbstractIn 2011, Chelton et al. carried out a comprehensive census of mesoscales using altimetry data and reached the following conclusions: “essentially all of the observed mesoscale features are nonlinear” and “mesoscales do not move with the mean velocity but with their own drift velocity,” which is “the most germane of all the nonlinear metrics.” Accounting for these results in a mesoscale parameterization presents conceptual and practical challenges since linear analysis is no longer usable and one needs a model of nonlinearity. A mesoscale parameterization is presented that has the following features: 1) it is based on the solutions of the nonlinear mesoscale dynamical equations, 2) it describes arbitrary tracers, 3) it includes adiabatic (A) and diabatic (D) regimes, 4) the eddy-induced velocity is the sum of a Gent and McWilliams (GM) term plus a new term representing the difference between drift and mean velocities, 5) the new term lowers the transfer of mean potential energy to mesoscales, 6) the isopycnal slopes are not as flat as in the GM case, 7) deep-ocean stratification is enhanced compared to previous parameterizations where being more weakly stratified allowed a large heat uptake that is not observed, 8) the strength of the Deacon cell is reduced. The numerical results are from a stand-alone ocean code with Coordinated Ocean-Ice Reference Experiment I (CORE-I) normal-year forcing.

Effects of Cross-Section Geometry of Capillary on the Evaporation From the Meniscus

2005 ◽  
Author(s):  
Songwan Jin ◽  
Choonghyo Choi ◽  
Kenneth S. Breuer ◽  
Jung Yul Yoo
Keyword(s):  
Surface Tension ◽  
Cross Section ◽  
Evaporation Rate ◽  
Rectangular Channel ◽  
Vortex Motion ◽  
Meniscus Shape ◽  
Four Corners ◽  
The Difference ◽  
Circular Capillary ◽  
Cross Section Geometry

Effects of cross-section geometry of capillary on the evaporation from the meniscus have been investigated by adopting several circular and rectangular capillaries. The evaporating meniscus shape, evaporation rate and flow near the evaporating meniscus of various liquids such as water, ethanol and methanol are determined. The shapes of water and ethanol menisci in circular capillary are quite different from each other due to the difference in surface tension. But the difference in meniscus shapes is relatively small in rectangular channel. The averaged evaporation fluxes in rectangular channel are much larger than that in circular capillary. The rotating vortex motion is observed near the evaporating menisci of ethanol and methanol except for the case of methanol in 200 × 20-μm capillary. The reason for this is considered to be the existence of the corner menisci at the four corners.

Report on the IUTAM symposium: fundamental aspects of vortex motion

1988 ◽  
Vol 190 ◽  
pp. 571-595 ◽  
Author(s):  
H. Aref ◽  
T. Kambe
Keyword(s):  
Current Literature ◽  
Vortex Dynamics ◽  
Vortex Motion ◽  
New Developments ◽  
Potential Interest ◽  
Iutam Symposium

The IUTAM Symposium Fundamental Aspects of Vortex Motion was held in Tokyo, Japan, from 31 August to 4 September 1987. We present an account of the technical sessions of that meeting. The main goals of this report are (i) to provide a widely accessible record of the four-and-one-half day meeting; (ii) to identify important new developments in the field of vortex dynamics of potential interest to a larger audience than the invited attendees; and (iii) to attempt some overview comments with the wisdom of hindsight that may be useful as a guide to specific papers in the proceedings and other current literature.

scholarly journals ON THE ROLE OF MESOSCALE VORTICES IN THE OIL SPILL TRANSPORT IN THE SOUTH-EASTERN BALTIC SEA (SATELLITE INFORMATION)

2019 ◽  
Vol 47 (3) ◽  
pp. 8-19 ◽  
Author(s):  
A. I. Ginzburg ◽  
E. V. Krek ◽  
A. G. Kostianoy ◽  
D. M. Soloviev
Keyword(s):  
Vortex Dynamics ◽  
Vortex Motion ◽  
Landsat 8 ◽  
Radar Images ◽  
Optical Images ◽  
Total Transport ◽  
First Time ◽  
Vortex Movement ◽  
Eastern Baltic

In this paper, on the basis of an analysis of the successive satellite optical images (MODISAqua, TIRS Landsat-8, AVHRR NOAA-18) and radar images (SAR-C Sentinel-1A, SAR-C Radarsat-2) on June 8–11, 2015, the effect of the mesoscale vortex movement (anticyclone with diameter of 35 km and associated cyclone) on the transport of oil spots in the northern part of the Gdansk Bay was demonstrated for the first time. The velocities of this transport are estimated; the observed picture of the movement of the spots is compared with their transfer according to the Seatrack Web model. The largest (about 20 cm/s) drift velocity corresponded to the spot that appeared near the periphery of the anticyclonic vortex (the region of maximum velocities), the smallest one was at the spot near the center of the vortex. At a wind speed of not more than 5 m/s on June 10 and an assumed orbital velocity of the anticyclone of the order of 20 cm/s, the contribution of the vortex motion to the total transport of the spots under the influence of wind and vortex should be decisive. The observed drift of the spots did not correspond to the forecast of their movement by the Seatrack Web numerical model, which did not take into account the vortex dynamics of the waters.

Point vortex dynamics in a magnetized plasma

1994 ◽  
Author(s):  
Mitsuo Kono ◽  
Hideaki Shibahara ◽  
Kentaro Yabuki
Keyword(s):  
Vortex Dynamics ◽  
Point Vortex ◽  
Magnetized Plasma

On An Affine Connection Which Admits A Volume-Like Form

1990 ◽  
Vol 33 (4) ◽  
pp. 482-488 ◽  
Author(s):  
D. P. Chi ◽  
Y. D. Yoon
Keyword(s):  
Affine Connection ◽  
Riemannian Metric ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Connection ◽  
Cech Cohomology ◽  
Necessary And Sufficient

AbstractA necessary and sufficient condition to obtain a volumelike form from an affine connection is given in terms of the Čech cohomology, after the volume-like form is naturally defined without a Riemannian metric. A necessary condition for an affine connection to be a Riemannian connection for some metric is also given.

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