Let me first describe two examples of water waves we encountered in our daily lives.

Example 1: water waves in a pond.

When I was little, I once had a small rubber ball as a toy, playing with other neighborhood kids. At one time, the ball was accidentally thrown into a pond. Trying to get the ball closer to the bank to recover it we threw stones into the pond nearby the ball to produce many surface water waves, hoping that those wave fronts would push the ball in the direction of propagation. We failed, for we noted that the ball was only doing up-and-down swings but did not move forward. [I now understand that the ball was actually doing a circular motion.] The ball was finally recovered by use of a long bamboo stick. [The bamboo stick was used for hanging wet clothes to dry them.]

Example 2: ocean waves at beaches.

When scientists go to beaches, they not only watch beautiful girls and handsome boys but also look, think, observe, and ponder about oceans, salt, waves, foam, etc.. Sometimes, they observe breaking beach waves and ponder the scientific explanations. It was first noted that storms or strong winds at sea generate wind-driven waves. The winds that produce the surface water waves can blow in any direction, which means that waves may be approaching the shore at almost any angle. However, what one observed at different beaches is the following fact: as a first approximation, the waves tend to move in only one direction – always toward you with the wave front in parallel to the shore. [I will explain this phenomenon next time.] The next spectacular thing at a beach to watch is the breaking of those waves for the shapes of breaking waves are never simple. Also beautifully to watch is the sparkling scene produced by the sunlight glinting on the small capillary waves riding on the larger waves. Occasionally, one also notices that the floating trashes (plastic bottles, sheets, etc) being pushed toward to the shore.

It should become clear intuitionally at this point why the waves in the pond could not push the ball whereas the waves at beaches can push floating trashes. The former was free-propagating conserved waves as they passed that ball whereas the latter was breaking dissipating waves as they approach beaches.

The breaking waves can produce the so-called mean flow that pushes things in water systematically forward. One sometimes can also feel the effect of such a mean flow at beaches in the following way. When there are moderate winds at beaches that are not perpendicular to the shore there could be a noticeable component of beach waves that their wave fronts are not exactly parallel to the shore. While swimming under such a condition, you may notice an unintended drifting away from the spot where you left your towels for you have been carried away by a mean flow induced by breaking beach waves that are not parallel to the shore.

(2003.07.21)