Tides

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6. Both oscillating waves and the circulating tidal wave

Click here to initiate the simulation that shows simultaneously both forced standing waves generated by the two oscillating systems of the driving forces. The oscillating forces vary in time with the phase shift that equals a quarter of the period. Click here (or the button "Start") to see how the same phase shift exists between the standing waves:

At the moment when the displacement of water particles in one of the waves reaches its maximum, the displacement in the second wave is zero. The surface of the second wave at the moment is spherical and coincides with the water surface at equilibrium, which is shown by a red circle. The momentary shape of the water surface is determined by the superposition of these two waves.

Addition of the two standing waves produces a travelling wave of an ellipsoidal shape that circulates around the globe. Click here to observe this wave. (Click also here to see the applet.) The major axis of this ellipsoid rotates with the angular velocity equal half the frequency of superimposing standing waves (half the driving frequency), that is, with the angular velocity of the earth's axial rotation. The two bulges of this wave pass through any fixed point of the globe during a day, causing a high water level (a flow) twice a day. The circulating tidal wave lags behind the rotating system of the tide-generating forces. This phase lag depends on the damping factor and, more importantly, on the relationship between the driving frequency and the eigenfrequency of the corresponding mode of natural oscillations.

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The Oceanic Tides Section 6 (of 8)