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Analytical formulae for the Kirchhoff–Routh path function in multiply connected domains

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 2005, Volume 461, Issue 2060, pp. 2477 - 2501

.... The method uses the Schottky–Klein prime function to find representations of the hydrodynamic Green's function in multiply connected circular domains...

Circles | Maps | Infinity | Conformal mapping | Hydrodynamics | Boundary conditions | Mathematical functions | Connected regions | Greens function | Cylinders | Kirchhoff-Routh | Hamiltonian | Point vortex | MOTION | VORTICES | MULTIDISCIPLINARY SCIENCES | point vortex | VORTEX | 2 DIMENSIONS

Circles | Maps | Infinity | Conformal mapping | Hydrodynamics | Boundary conditions | Mathematical functions | Connected regions | Greens function | Cylinders | Kirchhoff-Routh | Hamiltonian | Point vortex | MOTION | VORTICES | MULTIDISCIPLINARY SCIENCES | point vortex | VORTEX | 2 DIMENSIONS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2016, Volume 433, Issue 2, pp. 1531 - 1560

...–Routh-path function. In particular, we will prove that HΩ has a critical point, if it is possible to align the vortices along a line, such that the signs of the Γ...

Vortex dynamics | Kirchhoff–Routh path function | Kirchhoff-Routh path function | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SINH-POISSON | RELATIVE EQUILIBRIA | PLANAR DOMAINS

Vortex dynamics | Kirchhoff–Routh path function | Kirchhoff-Routh path function | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SINH-POISSON | RELATIVE EQUILIBRIA | PLANAR DOMAINS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 02/2016, Volume 260, Issue 3, pp. 2275 - 2295

...Ω has the formHΩ(z1,…,zN)=12π∑j,k=1j≠kNlog1|zj−zk|−F(z). The function F:ΩN→R depends on the regular part of the hydrodynamic Green's function and is unbounded from above: F(z)→∞ if zk→∂Ω for some k...

Singular first order Hamiltonian systems | N-vortex dynamics | Periodic solutions | Secondary | Primary | MATHEMATICS | VORTICES | MOTION | KIRCHHOFF ROUTH FUNCTION | EQUATIONS | CRITICAL-POINTS | ROBIN FUNCTION | 2 DIMENSIONS | Mathematics - Dynamical Systems

Singular first order Hamiltonian systems | N-vortex dynamics | Periodic solutions | Secondary | Primary | MATHEMATICS | VORTICES | MOTION | KIRCHHOFF ROUTH FUNCTION | EQUATIONS | CRITICAL-POINTS | ROBIN FUNCTION | 2 DIMENSIONS | Mathematics - Dynamical Systems

Journal Article

Japan Journal of Industrial and Applied Mathematics, ISSN 0916-7005, 2015, Volume 32, Issue 1, pp. 205 - 236

We present a fast and accurate numerical method for constructing incompressible, inviscid and irrotational flows in two-dimensional coastal domains, which are...

Generalized Neumann kernel | Multiply connected domains | Kirchhoff–Routh path function | Numerical conformal mappings | Potential flows | MATHEMATICS, APPLIED | Kirchhoff-Routh path function | RIEMANN-HILBERT PROBLEM | SLIT DOMAINS | SIMULATION | VORTEX | BOUNDARY INTEGRAL-EQUATION | MOTION | KIRCHHOFF ROUTH FUNCTION | REGIONS | 2 DIMENSIONS

Generalized Neumann kernel | Multiply connected domains | Kirchhoff–Routh path function | Numerical conformal mappings | Potential flows | MATHEMATICS, APPLIED | Kirchhoff-Routh path function | RIEMANN-HILBERT PROBLEM | SLIT DOMAINS | SIMULATION | VORTEX | BOUNDARY INTEGRAL-EQUATION | MOTION | KIRCHHOFF ROUTH FUNCTION | REGIONS | 2 DIMENSIONS

Journal Article

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 2016, Volume 472, Issue 2191, p. 20160271

.... In order to cultivate an insight into vortex interactions on this manifold, we derive the evolution equation for N-point vortices from Green's function associated with the Laplace-Beltrami operator...

Vortex interactions | Ring torus | Vortex dynamics | Hamiltonian dynamical system | Symplectic geometry | Hydrodynamic green function | VORTICES | MULTIDISCIPLINARY SCIENCES | vortex dynamics | symplectic geometry | vortex interactions | MOTION | hydrodynamic Green function | KIRCHHOFF ROUTH FUNCTION | ROTATING SPHERE | DOMAINS | ring torus | 2 DIMENSIONS | 1008 | 120

Vortex interactions | Ring torus | Vortex dynamics | Hamiltonian dynamical system | Symplectic geometry | Hydrodynamic green function | VORTICES | MULTIDISCIPLINARY SCIENCES | vortex dynamics | symplectic geometry | vortex interactions | MOTION | hydrodynamic Green function | KIRCHHOFF ROUTH FUNCTION | ROTATING SPHERE | DOMAINS | ring torus | 2 DIMENSIONS | 1008 | 120

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 04/2008, Volume 41, Issue 13, p. 135207

In the present paper, the problem of vortex images in the annular domain between two coaxial cylinders is solved by the q-elementary functions...

MULTIPLE CYLINDERS | MOTION | VORTICES | PHYSICS, MULTIDISCIPLINARY | QUANTUM GROUPS | KIRCHHOFF ROUTH FUNCTION | PHYSICS, MATHEMATICAL | FORMULAS | 2 DIMENSIONS | GEOMETRY

MULTIPLE CYLINDERS | MOTION | VORTICES | PHYSICS, MULTIDISCIPLINARY | QUANTUM GROUPS | KIRCHHOFF ROUTH FUNCTION | PHYSICS, MATHEMATICAL | FORMULAS | 2 DIMENSIONS | GEOMETRY

Journal Article

Journal of Mathematical Physics, ISSN 1089-7658, 2007, Volume 48, Issue 6, pp. 065401 - 065401-23

... function, projective geometry, and other topics. The hope and intent of the article is to garner further participation in the exploration of this intriguing dynamical...

VORTICES | MOTION | PHYSICS, MATHEMATICAL | 2 DIMENSIONS

VORTICES | MOTION | PHYSICS, MATHEMATICAL | 2 DIMENSIONS

Journal Article

Nonlinearity, ISSN 0951-7715, 04/2019, Volume 32, Issue 5, pp. 1882 - 1904

.... Moreover, we show that these vortex patches 'shrink' to a minimum point of the Kirchhoff-Routh function as the strength parameter of the background vorticity goes...

maximization | Euler equation | desingularization | vortex-wave system | vortex patch | Kirchhoff-Routh function | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

maximization | Euler equation | desingularization | vortex-wave system | vortex patch | Kirchhoff-Routh function | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 11/2015, Volume 259, Issue 9, pp. 4509 - 4560

We prove existence and uniqueness of a weak solution to the incompressible 2D Euler equations in the exterior of a bounded smooth obstacle when the initial...

Fluid mechanics | Euler equations | VANISHING VISCOSITY | INCOMPRESSIBLE FLUID | VORTICITY | FLOW | INVISCID LIMIT | UNIQUENESS | MATHEMATICS | DIMENSIONS | NAVIER-STOKES EQUATIONS | KIRCHHOFF ROUTH FUNCTION | INITIAL DATA

Fluid mechanics | Euler equations | VANISHING VISCOSITY | INCOMPRESSIBLE FLUID | VORTICITY | FLOW | INVISCID LIMIT | UNIQUENESS | MATHEMATICS | DIMENSIONS | NAVIER-STOKES EQUATIONS | KIRCHHOFF ROUTH FUNCTION | INITIAL DATA

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 11/2018, Volume 38, Issue 11, pp. 5443 - 5460

...)vertical bar - Sigma(N)(k,j=1) Gamma(j)Gamma(k)g(z(k),z(j)) with some regular and symmetric, but in general not explicitely known function g : Omega x Omega -> R...

EXISTENCE | MATHEMATICS, APPLIED | singular first order Hamiltonian systems | EQUATIONS | periodic solutions | vortex clusters | POINT VORTICES | MATHEMATICS | Vortex dynamics | KIRCHHOFF ROUTH FUNCTION | HAMILTONIAN-SYSTEMS | ORBITS | GINZBURG-LANDAU VORTICES | BOUNDED PLANAR DOMAINS | RELATIVE EQUILIBRIA | 2 DIMENSIONS

EXISTENCE | MATHEMATICS, APPLIED | singular first order Hamiltonian systems | EQUATIONS | periodic solutions | vortex clusters | POINT VORTICES | MATHEMATICS | Vortex dynamics | KIRCHHOFF ROUTH FUNCTION | HAMILTONIAN-SYSTEMS | ORBITS | GINZBURG-LANDAU VORTICES | BOUNDED PLANAR DOMAINS | RELATIVE EQUILIBRIA | 2 DIMENSIONS

Journal Article

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, ISSN 1937-1632, 11/2019, Volume 12, Issue 7, pp. 1867 - 1877

For a bounded domain Omega subset of R-n let H-Omega : Omega x Omega -> R be the regular part of the Dirichlet Green function for the Laplace operator...

EXISTENCE | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | Morse function | VORTICES | Kirchhoff-Routh path function | transversality theorem | CRITICAL-POINTS | NODAL SOLUTIONS | MOTION | 1ST-ORDER HAMILTONIAN-SYSTEMS | BOUNDED PLANAR DOMAINS | 2 DIMENSIONS

EXISTENCE | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | Morse function | VORTICES | Kirchhoff-Routh path function | transversality theorem | CRITICAL-POINTS | NODAL SOLUTIONS | MOTION | 1ST-ORDER HAMILTONIAN-SYSTEMS | BOUNDED PLANAR DOMAINS | 2 DIMENSIONS

Journal Article

Journal of fluid mechanics, ISSN 0022-1120, 04/2008, Volume 600, pp. 77 - 94

This paper considers the dynamics of a rigid body interacting with point vortices in a perfect fluid. The fluid velocity is obtained using the classical...

Papers | MECHANICS | MOTION | CYLINDER | FLUID | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | BODIES | N-POINT VORTICES | HAMILTONIAN-STRUCTURE | 2 DIMENSIONS | Fluid mechanics | Flow velocity | Fluid

Papers | MECHANICS | MOTION | CYLINDER | FLUID | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | BODIES | N-POINT VORTICES | HAMILTONIAN-STRUCTURE | 2 DIMENSIONS | Fluid mechanics | Flow velocity | Fluid

Journal Article

Physics of Fluids, ISSN 1070-6631, 05/2005, Volume 17, Issue 5, pp. 056602 - 056602-13

A new constructive method for computing the motion of a single point vortex around an arbitrary finite number of circular islands in the special case when the...

MECHANICS | VORTICES | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | 2 DIMENSIONS

MECHANICS | VORTICES | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | 2 DIMENSIONS

Journal Article

Journal of fluid mechanics, ISSN 0022-1120, 12/2007, Volume 593, pp. 235 - 254

This paper demonstrates that there is a contour dynamics formulation for the evolution of uniform vortex patches in any finitely connected planar domain...

Papers | SURGERY | POINT VORTEX | WALL | MECHANICS | MOTION | VORTICES | BOUNDARIES | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | SPHERE | GAPS | 2 DIMENSIONS | Mathematics | Algorithms | Fluid dynamics | Mechanical engineering

Papers | SURGERY | POINT VORTEX | WALL | MECHANICS | MOTION | VORTICES | BOUNDARIES | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | SPHERE | GAPS | 2 DIMENSIONS | Mathematics | Algorithms | Fluid dynamics | Mechanical engineering

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, ISSN 1364-5021, 08/2009, Volume 465, Issue 2108, pp. 2589 - 2611

.... The velocity field induced by the point vortices is described in terms of the Schottky–Klein prime function associated with the circular domain...

Circles | Saddle points | Mathematical functions | Trajectories | Topology | Semicircles | Equations of motion | Dynamical systems | Contour lines | Symmetry | MATHEMATICS | mathematical physics | fluid mechanics | Research articles | Multiply connected domain | Hamiltonian | Point vortex | point vortex | multiply connected domain | KIRCHHOFF ROUTH FUNCTION | MULTIDISCIPLINARY SCIENCES | 2 DIMENSIONS

Circles | Saddle points | Mathematical functions | Trajectories | Topology | Semicircles | Equations of motion | Dynamical systems | Contour lines | Symmetry | MATHEMATICS | mathematical physics | fluid mechanics | Research articles | Multiply connected domain | Hamiltonian | Point vortex | point vortex | multiply connected domain | KIRCHHOFF ROUTH FUNCTION | MULTIDISCIPLINARY SCIENCES | 2 DIMENSIONS

Journal Article

Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, 3/2010, Volume 24, Issue 1, pp. 51 - 57

We explore the relationship between the hydrodynamic Green’s function and the Dirichlet...

Engineering | Green’s function | Ideal flow | Vorticity | Engineering Fluid Dynamics | Hydrodynamics | Computational Science and Engineering | Classical Continuum Physics | Green's function | MECHANICS | VORTICES | MOTION | MULTIPLY CONNECTED DOMAINS | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | SMALL OBSTACLE | 2 DIMENSIONS | Fluid dynamics | Fluid mechanics | Flow velocity | Energy use | Green's functions | Computational fluid dynamics | Vortices | Fluid flow | Dirichlet problem | Two dimensional

Engineering | Green’s function | Ideal flow | Vorticity | Engineering Fluid Dynamics | Hydrodynamics | Computational Science and Engineering | Classical Continuum Physics | Green's function | MECHANICS | VORTICES | MOTION | MULTIPLY CONNECTED DOMAINS | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | SMALL OBSTACLE | 2 DIMENSIONS | Fluid dynamics | Fluid mechanics | Flow velocity | Energy use | Green's functions | Computational fluid dynamics | Vortices | Fluid flow | Dirichlet problem | Two dimensional

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 9/2015, Volume 17, Issue 3, pp. 597 - 624

...–Routh path function under some conditions on the vorticities...

variational methods | 37N10 | Mathematical Methods in Physics | Fluid dynamics | Analysis | Mathematics, general | Mathematics | 37C25 | Kirchhoff–Routh path function | 76M30 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Kirchhoff-Routh path function | EQUATIONS | BOUNDED PLANAR DOMAINS | SINH-POISSON

variational methods | 37N10 | Mathematical Methods in Physics | Fluid dynamics | Analysis | Mathematics, general | Mathematics | 37C25 | Kirchhoff–Routh path function | 76M30 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Kirchhoff-Routh path function | EQUATIONS | BOUNDED PLANAR DOMAINS | SINH-POISSON

Journal Article

Physical Review A, ISSN 2469-9926, 03/2016, Volume 93, Issue 3

We have studied numerically the Hamiltonian dynamics of two same-sign point vortices in an effectively two-dimensional, harmonically trapped Bose-Einstein...

STATISTICAL-MECHANICS | DIMENSIONS | ENERGY | STATES | MOTION | KIRCHHOFF ROUTH FUNCTION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | BOSE-EINSTEIN CONDENSATE | TURBULENCE | OPTICS | VORTEX LATTICES | Physics - Quantum Gases

STATISTICAL-MECHANICS | DIMENSIONS | ENERGY | STATES | MOTION | KIRCHHOFF ROUTH FUNCTION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | BOSE-EINSTEIN CONDENSATE | TURBULENCE | OPTICS | VORTEX LATTICES | Physics - Quantum Gases

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2008, Volume 227, Issue 12, pp. 6058 - 6070

.... By exploiting knowledge of the functional form of the relevant Green’s function in a pre-image circular domain that is conformally equivalent to a stereographic projection of the fluid domain on the spherical surface, we first generalize Kirchhoff...

Sphere | Contour dynamics | Multiply connected | Vorticity | SURGERY | POINT VORTEX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MOTION | VORTICES | vorticity | sphere | contour dynamics | KIRCHHOFF ROUTH FUNCTION | PHYSICS, MATHEMATICAL | multiply connected | 2 DIMENSIONS

Sphere | Contour dynamics | Multiply connected | Vorticity | SURGERY | POINT VORTEX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MOTION | VORTICES | vorticity | sphere | contour dynamics | KIRCHHOFF ROUTH FUNCTION | PHYSICS, MATHEMATICAL | multiply connected | 2 DIMENSIONS

Journal Article

Journal of fluid mechanics, ISSN 0022-1120, 06/2009, Volume 628, pp. 121 - 154

.... For viscous flow we derived the equation of stream function in the mapped (circle) domain, based on which approximate expressions for the critical Reynolds numbers...

Papers | SQUARE CYLINDER | MECHANICS | STABILITY ANALYSIS | CIRCULAR-CYLINDER | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | STEADY SEPARATED FLOW | HOPF-BIFURCATION | MODERATE REYNOLDS-NUMBERS | 3-DIMENSIONAL FLOW | NUMERICAL-SIMULATION | 2 DIMENSIONS

Papers | SQUARE CYLINDER | MECHANICS | STABILITY ANALYSIS | CIRCULAR-CYLINDER | PHYSICS, FLUIDS & PLASMAS | KIRCHHOFF ROUTH FUNCTION | STEADY SEPARATED FLOW | HOPF-BIFURCATION | MODERATE REYNOLDS-NUMBERS | 3-DIMENSIONAL FLOW | NUMERICAL-SIMULATION | 2 DIMENSIONS

Journal Article

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