scholarly journals Two examples of nonconvex self-similar solution curves for a crystalline curvature flow

2004 ◽  
Vol 80 (8) ◽  
pp. 151-154 ◽  
Author(s):  
Tetsuya Ishiwata ◽  
Takeo K. Ushijima ◽  
Hiroki Yagisita ◽  
Shigetoshi Yazaki
Keyword(s):  
Curvature Flow ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Self Similar ◽  
Crystalline Curvature

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

Self-Similar Solution of an RC Transmission Line

1972 ◽  
Vol 40 (3) ◽  
pp. 484-486 ◽  
Author(s):  
K. E. Lonngren ◽  
W. F. Ames ◽  
H. C. S. Hsuan ◽  
I. Alexeff ◽  
William Wing
Keyword(s):  
Transmission Line ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Self Similar

The hydraulics of a stratified fluid flowing through a contraction

1993 ◽  
Vol 251 ◽  
pp. 355-375 ◽  
Author(s):  
Laurence Armi ◽  
Richard Williams
Keyword(s):  
Flow Rate ◽  
Fluid Flows ◽  
Stratified Fluid ◽  
Wave Mode ◽  
Similar Solution ◽  
Constant Density ◽  
Self Similar Solution ◽  
Hydraulic Theory ◽  
Self Similar

The steady hydraulics of a continuously stratified fluid flowing from a stagnant reservoir through a horizontal contraction was studied experimentally and theoretically. As the channel narrows, the flow accelerates through a succession of virtual controls, at each of which the flow passes from sub-critical to supercritical with respect to a particular wave mode. When the narrowest section acts as a control, the flow is asymmetric about the narrowest section, supercritical in the divergent section and self- similar throughout the channel. With increased flow rate a new enclosed self-similar solution was found with level isopycnals and velocity uniform with depth. This flow is only symmetric in the immediate neighbourhood of the narrowest section, and in the divergent section remains supercritical with respect to higher internal modes, has separation isopycnals and splits into one or more jets separated by regions of stagnant, constant-density fluid. Flows which are subcritical with respect to lowest modes can also be asymmetric about the narrowest section for higher internal modes. The experiments are interpreted using steady, inviscid hydraulic theory. Solutions require separation isopycnals and regions of stationary, constant-density fluid in the divergent section.

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