scholarly journals Ship waves on a viscous fluid of finite depth

1997 ◽  
Vol 9 (4) ◽  
pp. 940-944 ◽  
Author(s):  
Andy T. Chan ◽  
Allen T. Chwang
Keyword(s):  
Viscous Fluid ◽  
Finite Depth ◽  
Ship Waves

scholarly journals Ship waves in the presence of uniform vorticity

2014 ◽  
Vol 742 ◽  
Author(s):  
Simen Å. Ellingsen
Keyword(s):  
Shear Flow ◽  
Finite Depth ◽  
Critical Value ◽  
Wave Problem ◽  
Transverse Waves ◽  
Ship Waves ◽  
Striking Result ◽  
Constant Vorticity ◽  
Shear Current ◽  
Half Angle

AbstractLord Kelvin’s result that waves behind a ship lie within a half-angle $\phi _{\mathit{K}}\approx 19^{\circ }28'$ is perhaps the most famous and striking result in the field of surface waves. We solve the linear ship wave problem in the presence of a shear current of constant vorticity $S$, and show that the Kelvin angles (one each side of wake) as well as other aspects of the wake depend closely on the ‘shear Froude number’ $\mathit{Fr}_{\mathit{s}}=VS/g$ (based on length $g/S^2$ and the ship’s speed $V$), and on the angle between current and the ship’s line of motion. In all directions except exactly along the shear flow there exists a critical value of $\mathit{Fr}_{\mathit{s}}$ beyond which no transverse waves are produced, and where the full wake angle reaches $180^\circ $. Such critical behaviour is previously known from waves at finite depth. For side-on shear, one Kelvin angle can exceed $90^\circ $. On the other hand, the angle of maximum wave amplitude scales as $\mathit{Fr}^{-1}$ ($\mathit{Fr}$ based on size of ship) when $\mathit{Fr}\gg 1$, a scaling virtually unaffected by the shear flow.

scholarly journals The theory of ship waves

1926 ◽  
Vol 111 (759) ◽  
pp. 491-529 ◽  
Keyword(s):  
Finite Depth ◽  
Wave Disturbance ◽  
Present Communication ◽  
Ship Waves ◽  
Infinite Depth ◽  
The Subject ◽  
Considerable Detail

The theory of ship waves, when the sea is considered to be of infinite depth, has been the subject of many researches. When the sea is of finite depth the integrals involved are more complicated, but in this case also the theory has been worked out in considerable detail. The main object of the present communication is to add to the number of cases which have been solved, or, to be more precise, which have been exactly formulated, a certain series in which the depth is variable. Of subsidiary interest, but coming under the title of the paper, are some considerations relating to the wave disturbance when the depth is finite. These are dealt with briefly in section 5.

scholarly journals The ideal velocity field of ship waves on a viscous fluid

2005 ◽  
Vol 54 (10) ◽  
pp. 4496
Author(s):  
Wu Yun-Gang ◽  
Tao Ming-De
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Ship Waves ◽  
The Ideal

Development of ship waves in a liquid of finite depth

1972 ◽  
Vol 3 (4) ◽  
pp. 46-49
Author(s):  
L. V. Cherkesov
Keyword(s):  
Finite Depth ◽  
Ship Waves

Velocity field in ship waves on the viscous fluid

2002 ◽  
Vol 23 (10) ◽  
pp. 1221-1228 ◽  
Author(s):  
Liu Min-jia ◽  
Tao Ming-de
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Ship Waves
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