## HydrodynamicsUniversity Press, 1916 - 708 pages |

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### Other editions - View all

### Common terms and phrases

amplitude angular velocity approximately assume axes axis boundary canal centre co-ordinates coefficients condition const constant corresponding cosh denote depth distance disturbing dx dy dz ellipsoid equation of continuity equilibrium expression extraneous forces finite fluid formula free surface function given harmonic Hence infinite integral investigation irrotational irrotational motion kinetic energy liquid Math nodal lines normal obtained origin oscillations parallel particle Phil plane positive pressure problem Proc quadratic function radius ratio Rayleigh result rotation satisfied shewn shews simple-harmonic sin² sinh solid solid harmonic solution sphere spherical spherical harmonics steady motion stream-lines suppose theorem theory tides vanish velocity-potential viscosity vortex vortices wave-length waves whence whilst zero zonal harmonic ΘΩ ат аф ди дп др ду дф дх

### Popular passages

Page 621 - ... begin with about an inch of amplitude, and a couple of inches long ; they enlarge as the velocity or duration of the wave increases; by and by conterminal waves unite; the ridges increase, and if the wind increase the waves become cusped, and are regular waves of the second order. They continue enlarging their dimensions; and the depth to which they produce the agitation increasing simultaneously with their magnitude, the surface becomes extensively covered with waves of nearly uniform magnitude.

Page 621 - Capillary waves disappear from the ridges of these waves, but are to be found sheltered in the hollows between them, and on the anterior slopes of these waves. The regularity of the distribution of these secondary waves over the surface is remarkable ; they begin with about an inch of amplitude, and a couple of inches long ; they enlarge as the velocity or duration of the wave increases ; by and by...

Page 620 - Let him begin his observations in a perfect calm, when the surface of the water is smooth and reflects like a mirror the images of surrounding objects. This appearance will not be affected by even a slight motion of the air, and a velocity of less than half a mile an hour (8£ in.

Page 15 - It is to be remarked that the quantities a, b, c need not be restricted to mean the initial co-ordinates of a particle ; they may be any three quantities which serve to identify a particle, and which vary continuously from one particle to another.

Page 369 - It has often been noticed that when an isolated group of waves, of sensibly the same length, is advancing over relatively deep water, the velocity of the group as a whole is less than that of the individual waves composing it. If attention be fixed on a particular wave, it is seen to advance through the group, gradually dying out as it approaches the front...

Page 462 - When a small obstacle, such as fishing-line, is moved forward slowly through still water, or (which, of course, comes to the same thing) is held stationary in moving water, the surface is covered with a beautiful wave-pattern, fixed relatively to the obstacle. On the up-stream side the wave-length is short, and, as Thomson has shown, the force governing the vibrations is principally cohesion. On the down-stream side the waves are longer and are governed principally by gravity. Both sets of waves...

Page 620 - ... noticed that the diminution of this reflecting power is owing to the presence of those minute corrugations of the superficial film which form waves of the third order. These corrugations produce on the surface of the water an effect very similar to the effect of those panes of glass which we see corrugated for the purpose of destroying their transparency, and these corrugations at once prevent the eye from distinguishing forms at a considerable depth, and diminish...

Page 31 - For, in the sum in question, the flow along each side common to two elements comes in twice, once for each element, but with opposite signs, and therefore disappears from the result. There remain then only the flows along those sides which are parts of the original boundary; whence the truth of the above statement. * Sir W. Thomson, "On Vortex Motion,

Page 620 - ... surface. A gentle zephyr flitting along the surface from point to point, may be observed to destroy the perfection of the mirror for a moment, and on departing, the surface remains polished as before ; if the air have a velocity of about a mile an hour, the surface of the water becomes less capable of distinct reflexion, and on observing it in such a condition, it is to be noticed that the diminution of this reflecting power is owing to the presence of those minute corrugations of the superficial...

Page 369 - If attention be fixed on a particular wave, it is seen to advance through the group, gradually dying out as it approaches the front, whilst its former place in the group is occupied in succession by other waves which have come forward from the rear*.