Marine Physics by R. Craig (Auth.)

By R. Craig (Auth.)

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This point cannot be over-emphasised. The effect of the tidal forces is to set up seiche-like oscillations of the great oceans, of quite small amplitude. At the fringe of these oceans, the water surges over the continental shelves as a series of progressive waves, whose amplitude builds up where conditions are favourable. Thus the shape, and presumably orientation, of the Bristol Channel is particularly favourable to the progressive build-up of the 58 MARINE PHYSICS amplitude of the tidal wave.

Determination of the phase velocity of waves in deep water, (a) Inclination of resultant force, (b) Slope of surface. 46 MARINE PHYSICS But Θ = -cot + 2πχ/λ so for t constant we have dfl = 2π άχ/λ Thus or dx = λ άθ/2π. tan φ = A cos 0d0/(dx - A sin 0d0) = A cos 0/(λ/2π - A sin 0). e. we must have A cos 0/(λ/2π - A sin 0) = A cos 0/(#/ω 2 - A sin 0) and these are evidently equal for all values of 0 if λ\2π = glco2. Μ)2. Substituting this value in equation (1) we obtain λ/2π = g λ 2 / 4 Α 2 that is c2 — g λ\2π or c = y/(gX/2n).

P P But pt = gp(z — h) and (3) pc = gp(z + h) so the equation becomes g(z - h) + i (c + t;)2 = 0(z + A) + i (c - v)2 which is the same as equation (1) and therefore confirms the previous conclusion. 53 5. WAVES VALIDITY The simplicity of the treatment depends on our selection of z and h small compared with λ. This means that the treatment is suitable for consideration of long shallow waves, such as coastal tides with wavelengths of the order of hundreds of miles. In such a case we can see that the fundamental difference from deep water waves is that the orbital motion of the water particles has been replaced by a to-and-fro almost purely horizontal motion.

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