Dispersed Fluid and Ideal Fluid Mechanics

2016 ◽  
pp. 51-92
Keyword(s):  
Fluid Mechanics ◽  
Ideal Fluid

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.

scholarly journals Energy-Vorticity Theory of Ideal Fluid Mechanics

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

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 Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Huijing Zhan ◽  
Mingze Wu
Keyword(s):  
Fluid Dynamics ◽  
Fluid Mechanics ◽  
Numerical Method ◽  
Ideal Fluid ◽  
Calculation Method ◽  
Perturbation Technique ◽  
Current Method ◽  
Processing Method ◽  
Computing Power ◽  
Hydrodynamics Equations

In order to solve the numerical method of nonconservative ideal hydrodynamics equations, the viscous perturbation technique for solving nonconservative hydrodynamics equations is improved and tested by solving the Riemann problem. The calculation of nonconservative ideal fluid mechanics is based on the GRP format. This article aims at the calculation method of nonconservative ideal fluid mechanics in the GRP format. Riemann and the corresponding periodic vortex are processed. The multifluid network processing method in the article is compared with the current method. The result can prove that this format can be used to solve the nonconservative ideal fluid dynamics equation of multiple values in the GRP format group, its computing power is strong, and the result of the solution is accurate.

scholarly journals Infinitesimal quantum group from helicity in fluid mechanics

2020 ◽  
Vol 35 (30) ◽  
pp. 2050245
Author(s):  
S. G. Rajeev
Keyword(s):  
Fluid Mechanics ◽  
Quantum Group ◽  
Lie Algebra ◽  
Euler Equations ◽  
Ideal Fluid ◽  
Vector Fields ◽  
Classical Fluid ◽  
Manin Triple ◽  
Isotropic Subspaces

Arnold showed that the Euler equations of an ideal fluid describe geodesics in the Lie algebra of incompressible vector fields. We will show that helicity induces a splitting of the Lie algebra into two isotropic subspaces, forming a Manin triple. Viewed another way, this shows that there is an infinitesimal quantum group (a.k.a. Lie bi-algebra) underlying classical fluid mechanics.

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.

Fluid Mechanics

2018 ◽  
Author(s):  
Gregory Falkovich
Keyword(s):  
Fluid Mechanics
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