Tides

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5. Standing waves driven by the oscillating forces

Each oscillating system of the driving tidal forces excites a steady-state oscillation of the ocean surface. The excited mode has the symmetry of the system of forces that gives rise to the oscillation. Click here to see the simulation that shows the forced oscillation of the ocean surface under the first system of tidal forces considered above.

This steady-state forced oscillation of the ocean surface is essentially a standing wave in which the surface twice a day acquires the shape of a stretched ellipsoid whose axis is directed along the axis of symmetry of the system of driving tidal forces. The amplitude and phase of the standing wave depends on the damping factor and on the relationship between the driving and natural frequencies. The simulation corresponds to slowly varying driving forces whose period is greater than the natural period. In this case the water moves in phase with the force. In the simulation, the amplitude of oscillation is strongly exaggerated.

Click here to observe the steady-state oscillation of the ocean water excited by the second oscillating system of forces. (Click also here to see the applet.) This oscillation is also a standing wave of an ellipsoidal shape whose axis coincides with the axis of symmetry of the second system of driving forces. On the screen, this axis makes an angle of 45 degrees with the vertical. The frequency and amplitude of the driving forces are in this case the same as for the first standing wave, as well as the eigenfrequency of the natural mode and the damping factor. Therefore for this standing wave the amplitude and the phase lag behind the driving force are the same as for the first standing wave.

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The Oceanic Tides Section 5 (of 8)