Local interaction between vorticity and shear in a perfect incompressible fluid

1982 ◽  
Vol 43 (6) ◽  
pp. 837-842 ◽  
Author(s):  
P. Vieillefosse
Keyword(s):  
Incompressible Fluid ◽  
Local Interaction ◽  
Perfect Incompressible Fluid

Secondary circulation in fluid flow

1951 ◽  
Vol 206 (1086) ◽  
pp. 374-387 ◽  
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Velocity Distribution ◽  
Secondary Flow ◽  
General Expression ◽  
Total Pressure ◽  
Secondary Circulation ◽  
Perfect Incompressible Fluid ◽  
Uniform Velocity ◽  
Circular Pipes

Secondary circulation appears after fluid with a non-uniform velocity distribution passes round a bend. It alters the character of the flow and is a source of loss. A general expression is developed for its change along a streamline in a perfect, incompressible fluid. The flow in bent circular pipes is analyzed and the theory is compared with experiments on bent pipes and rectangular ducts. In bends the secondary flow is not spiral but oscillatory, the direction of the circulation changing periodically. The theory shows that secondary circulation remains unchanged if streamlines are geodesics on surfaces of constant total pressure.

On The Motion of Three Vortices

1949 ◽  
Vol 1 (3) ◽  
pp. 257-270 ◽  
Author(s):  
J. L. Synge
Keyword(s):  
Differential Equations ◽  
Incompressible Fluid ◽  
Linear Differential Equations ◽  
Vortex Filaments ◽  
First Order ◽  
Perfect Incompressible Fluid ◽  
Non Linear ◽  
The Mean ◽  
Linear Differential

In a perfect incompressible fluid extending to infinity, the determination of the motion of N parallel rectilinear vortex filaments involves the solution of N non-linear differential equations, each of the first order. The method of Kirchhoff provides certain constants of the motion. If we describe the positions of the vortices by their point-traces on a plane perpendicular to them, the following facts follow from the theory of Kirchhoff:(1.1) The mean centre of the system is fixed.

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