A steady vortex ring in Poiseuille flow and rearrangements of a function

2006 ◽  
Vol 462 (2068) ◽  
pp. 1235-1253 ◽  
Author(s):  
Dirar Rebah
Keyword(s):  
Kinetic Energy ◽  
Variational Method ◽  
Fluid Mechanics ◽  
Vortex Ring ◽  
Ideal Fluid ◽  
Poiseuille Flow ◽  
Nonlinear Problems ◽  
Insight Into

This study proves the existence of a steady vortex ring of an ideal fluid in Poiseuille flow. The method that was used is a variational method proposed by Benjamin (Benjamin 1976 The alliance of practical and analytical insight into the nonlinear problems of fluid mechanics , vol. 503, pp. 8–29), in which a steady vortex ring can be obtained as a maximizer of a functional that is related to kinetic energy and the impulse over the set of rearrangements of a prescribed function.

scholarly journals On the derivation of the HOMFLYPT polynomial invariant for fluid knots

2015 ◽  
Vol 773 ◽  
pp. 34-48 ◽  
Author(s):  
Xin Liu ◽  
Renzo L. Ricca
Keyword(s):  
Field Strength ◽  
Fluid Mechanics ◽  
Ideal Fluid ◽  
Mechanical Behaviour ◽  
Fluid Flows ◽  
Numerical Implementation ◽  
Rigorous Proof ◽  
Polynomial Invariant ◽  
Real Fluid ◽  
Insight Into

By using and extending earlier results (Liu & Ricca,J. Phys. A, vol. 45, 2012, 205501), we derive the skein relations of the HOMFLYPT polynomial for ideal fluid knots from helicity, thus providing a rigorous proof that the HOMFLYPT polynomial is a new, powerful invariant of topological fluid mechanics. Since this invariant is a two-variable polynomial, the skein relations are derived from two independent equations expressed in terms of writhe and twist contributions. Writhe is given by addition/subtraction of imaginary local paths, and twist by Dehn’s surgery. HOMFLYPT then becomes a function of knot topology and field strength. For illustration we derive explicit expressions for some elementary cases and apply these results to homogeneous vortex tangles. By examining some particular examples we show how numerical implementation of the HOMFLYPT polynomial can provide new insight into fluid-mechanical behaviour of real fluid flows.

scholarly journals Port-Hamiltonian modeling of ideal fluid flow: Part I. Foundations and kinetic energy

2021 ◽  
Vol 164 ◽  
pp. 104201 ◽  
Author(s):  
Ramy Rashad ◽  
Federico Califano ◽  
Frederic P. Schuller ◽  
Stefano Stramigioli
Keyword(s):  
Fluid Flow ◽  
Kinetic Energy ◽  
Ideal Fluid ◽  
Ideal Fluid Flow ◽  
Flow Part

scholarly journals Energy–Vorticity Theory of Ideal Fluid Mechanics

2009 ◽  
Vol 66 (7) ◽  
pp. 2073-2084 ◽  
Author(s):  
Peter Névir ◽  
Matthias Sommer
Keyword(s):  
Fluid Mechanics ◽  
Shallow Water ◽  
Ideal Fluid ◽  
Characteristic Property ◽  
Incompressible Flows ◽  
Climate Simulations ◽  
Shallow Water Models ◽  
Complete Analogy ◽  
Potential Enstrophy

Abstract Nambu field theory, originated by Névir and Blender for incompressible flows, is generalized to establish a unified energy–vorticity theory of ideal fluid mechanics. Using this approach, the degeneracy of the corresponding noncanonical Poisson bracket—a characteristic property of Hamiltonian fluid mechanics—can be replaced by a nondegenerate bracket. An energy–vorticity representation of the quasigeostrophic theory and of multilayer shallow-water models is given, highlighting the fact that potential enstrophy is just as important as energy. The energy–vorticity representation of the hydrostatic adiabatic system on isentropic surfaces can be written in complete analogy to the shallow-water equations using vorticity, divergence, and pseudodensity as prognostic variables. Furthermore, it is shown that the Eulerian equation of motion, the continuity equation, and the first law of thermodynamics, which describe the nonlinear evolution of a 3D compressible, adiabatic, and nonhydrostatic fluid, can be written in Nambu representation. Here, trilinear energy–helicity, energy–mass, and energy–entropy brackets are introduced. In this model the global conservation of Ertel’s potential enstrophy can be interpreted as a super-Casimir functional in phase space. In conclusion, it is argued that on the basis of the energy–vorticity theory of ideal fluid mechanics, new numerical schemes can be constructed, which might be of importance for modeling coherent structures in long-term integrations and climate simulations.

Study on Kinetic Energy for Saving Materials with Analysis of Lumped Mass Matrix of Variable Cross-Section Beam Element

2013 ◽  
Vol 675 ◽  
pp. 158-161
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Yu Qin Yan ◽  
Xun Lin Diao
Keyword(s):  
Kinetic Energy ◽  
Cross Section ◽  
Mass Matrix ◽  
Nonlinear Problems ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Lumped Mass ◽  
Geometrical Nonlinear ◽  
Properties Of Materials

Based on positional finite element method (FEM), a new, simple and accurate lumped mass matrix to solve dynamic geometrical nonlinear problems of materials applied to variable cross-section beam element has been proposed. According to Hamilton theory and the concept of Kinetic energy, concentrate the beam element mass to the two nodes in certain proportion, the lumped mass matrix is deduced. The lumped mass matrix is diagonal matrix and its calculated quantity is less than using consistent mass matrix about properties of materials under the same calculation precision.

scholarly journals Energy-Vorticity Theory of Ideal Fluid Mechanics

2009 ◽  
pp. 100802084958071
Author(s):  
Peter Névir ◽  
Matthias Sommer
Keyword(s):  
Fluid Mechanics ◽  
Ideal Fluid

Ionic Wind Application to Vortex Ring Generator and its Transportation Efficiency

2019 ◽  
Author(s):  
Kengo Fukunaga ◽  
Masayoshi Satake ◽  
Noboru Maeda ◽  
Kazushi Shikata ◽  
Tomohisa Ezaka
Keyword(s):  
Kinetic Energy ◽  
Mechanical System ◽  
Electric Power ◽  
Vortex Ring ◽  
Energy Conversion Efficiency ◽  
Target Distance ◽  
Vortex Rings ◽  
Experimental Measurements ◽  
Ionic Wind ◽  
External Turbulence

Abstract In this study, ionic wind generated in corona discharge is focused for producing an air flow without having mechanical actuators. First, the kinetic energy conversion efficiency to ionic wind from electric power is experimentally estimated to be 0.32%. Then, it is confirmed that intermittent blows of ionic wind enable to produce vortex rings without using mechanical system. We adopt novel sub-chamber structure to avoid the concentration of the substance in a vortex ring low, so that the substance concentration transported to the target distance of 200 mm increases by 9%. As an application, the efficiency for moisture transportation is evaluated through experimental measurements. As a result, it is shown that the substance (moisture) can be transported at an efficiency of about 85% to target distance of 200 mm under conditions where the influence of external turbulence is small.

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