Exact solution for forced capillary-gravity waves in a circular basin under Hocking's edge condition

Wave Motion ◽  
1997 ◽  
Vol 26 (2) ◽  
pp. 117-126 ◽  
Author(s):  
M.C. Shen ◽  
N.S. Yeh
Keyword(s):  
Exact Solution ◽  
Gravity Waves ◽  
Edge Condition

THE EFFECT OF AN EXPLOSION IN A COMPRESSIBLE FLUID UNDER GRAVITY

1961 ◽  
Vol 39 (9) ◽  
pp. 1330-1346 ◽  
Author(s):  
R. A. Ross
Keyword(s):  
Exact Solution ◽  
Viscous Fluid ◽  
Gravity Waves ◽  
Speed Of Sound ◽  
Compressible Fluid ◽  
Asymptotic Methods ◽  
Axially Symmetric ◽  
Linearized Theory ◽  
The Waves ◽  
Special Case

In this paper an investigation is made of the effect of an axially symmetric explosion at any depth in a semi-infinite, compressible, non-viscous fluid, acted upon by gravity. The explosion is represented by a line source of the form δ(x)δ(z – h)δ(t), where h is the depth of the source. An exact solution is given using the linearized theory. This solution is studied in detail by asymptotic methods, for the special case of a surface explosion. It is found that compressibility results in the gravity waves being propagated with a speed less than c, the speed of sound in the fluid. If x is the distance from the explosion and t the time that has elapsed after the explosion, then for [Formula: see text] only "precursor" waves are noticed at the point of observation. For [Formula: see text] large amplitude waves are present, similar to the waves predicted by the incompressible theory.

Thermal buckling of a thin uniform circular disk: a comparison of predictions

2006 ◽  
Vol 110 (1112) ◽  
pp. 691-693
Author(s):  
K. A. Seffen
Keyword(s):  
Boundary Layer ◽  
Finite Element Analysis ◽  
Exact Solution ◽  
Approximate Solution ◽  
Circular Disk ◽  
Free Edge ◽  
Edge Condition ◽  
Constant Thickness ◽  
Element Analysis ◽  
Thermally Induced

AbstractThe conditions for thermally-induced buckling of an unloaded thin, circular disk are compared from two well-known but unconnected studies: an approximate solution by Freund for a constant thickness disk, which must neglect the free edge condition, and an exact solution by Mansfield but only for a disk whose thickness tapers to zero in a particular manner. It is shown that buckling occurs at slightly higher values compared to a finite element analysis of a constant thickness disk but that the case of variable thickness seems to offer a closer result, which suggests that it better models the boundary layer behaviour near the free edge.

The damping of capillary–gravity waves at a rigid boundary

1987 ◽  
Vol 179 ◽  
pp. 253-266 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Contact Angle Hysteresis ◽  
Edge Condition ◽  
Experimental Investigations ◽  
Rigid Boundary ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Damping Rate ◽  
Pure Gravity

The frequency and damping rate of surface capillary-gravity waves in a bounded region depend on the conditions imposed where the free surface makes contact with the boundary. Extreme cases are when the free surface meets the boundary orthogonally, as in the case of pure gravity waves, and when the contact line remains fixed throughout the motion. An edge condition that models to some extent the dynamics associated with moving contact lines, but not contact-angle hysteresis, is given by making the slope of the free surface at contact proportional to its velocity. This model, which includes the two extreme cases, is used to obtain the frequency and damping rate of a standing wave between two parallel vertical walls. The effect of viscosity in the boundary layers on the walls is included and it is shown that the dissipation associated with the surface forces can exceed that produced by viscosity. The results are compared with those obtained from a number of experimental investigations, in which damping rates too large to be attributed to viscous action have been measured.

scholarly journals CHANGES IN HEIGHT OP SHORT WAVES ON LONG WAVES

1978 ◽  
Vol 1 (16) ◽  
pp. 22
Author(s):  
Michio Sato ◽  
Kazuo Nakamura
Keyword(s):  
Experimental Study ◽  
Exact Solution ◽  
Gravity Waves ◽  
Approximate Expression ◽  
Long Waves ◽  
Experimental Results ◽  
Wave Flume ◽  
Short Waves

In this paper we describe an experimental study on changes in height of short gravity waves on long waves. Experiments were conducted by making mechanically generated long waves superpose on mechanically generated short waves in a wave flume of 30m long and lm wide. Exact solution by Longuet-Higgins and Stewart explained our experimental results, but approximate expression a'= a,(l+P) which is widely accepted seemed to be inadequate to explain our results.

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