Exercise 5: Tides.

Let us begin by discussing the concept of waves. In oceanography, waves may be defined as periodic movements of an interface. Tides cause the periodic movement of the sea surface, so they are an example of surface waves.

A long wave is a wave with a wavelength much larger than the water depth. Consider the example shown in the graph: The undisturbed sea level is at the zero mark. The wave has an amplitude of 1 (expressed in arbitrary units), which gives it a total wave height (difference between high water and low water) of 2. The wavelength of a wave is defined as the distance from one high water to the next high water. The graph shows the wave over two wavelengths. The distance along the x-axis uses the same units as the elevation or y-axis, so the wavelength of this particular wave is about 5.5 times the water depth, which is just large enough to allow us to classify this wave as a long wave. The tides have wavelengths of several hundred to several thousand kilometers. Even at is deepest point, the ocean is less than 12 km deep, which is much less than 1000 km. We conclude that the tides are long waves.