Axisymmetric Solutions of the Euler Equations for Polytropic Gases

1998 ◽  
Vol 142 (3) ◽  
pp. 253-279 ◽  
Author(s):  
Tong Zhang ◽  
Yuxi Zheng
Keyword(s):  
Euler Equations ◽  
Axisymmetric Solutions

On the existence of localized rotational disturbances which propagate without change of structure in an inviscid fluid

1986 ◽  
Vol 173 ◽  
pp. 289-302 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Euler Equations ◽  
Stream Function ◽  
Wide Class ◽  
Magnetic Relaxation ◽  
Topological Invariant ◽  
Vortex Rings ◽  
Inviscid Fluid ◽  
Arbitrary Signature ◽  
Axisymmetric Solutions ◽  
Uniform Stream

A wide class of solutions of the steady Euler equations, representing localized rotational disturbances imbedded in a uniform stream U0 is inferred by considering the process of magnetic relaxation to analogous magnetostatic equilibria. These solutions, which may be regarded as generalizations of vortex rings, are characterized by their streamline topology, distinct topologies giving rise to distinct solutions.Particular attention is paid to the class of axisymmetric solutions described by Stokes stream function ψ(s, z). It is argued that the appropriate topological ‘invariant’ characterizing the flow is the function Vψ representing the volume inside toroidal surfaces ψ = const, in the region of closed streamlines where ψ > 0. This function is described as the ‘signature’ of the flow, and it is shown that in a certain sense, flows with different signatures are topologically distinct. The approach yields a method by which flows of arbitrary signature V(ψ) may in principle be found, and the corresponding vorticity ωφ = sFψ calculated.

Axisymmetric solutions to the Euler equations

2007 ◽  
Vol 66 (9) ◽  
pp. 1938-1948
Author(s):  
Shen Gang ◽  
Zhu Xiangrong
Keyword(s):  
Euler Equations ◽  
Axisymmetric Solutions
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