Superposition of Water Waves

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The sea surface motion is the superposition of numerous wave trains. Here one to four (linear) waves can be summed, travelling either in the +x direction (denoted with a +1) or the opposite direction (-1). You have the choice of examining one, two, three, or four waves together (by making the appropriate wave heights zero). The displayed quantities: x_max and time denote the width of the viewing panel in meters, and the elapsed time in seconds, repectively. Pressing Stop and then Calculate will reset the time. (Obviously the plot region is not to scale with the depth.) The waves that comprise the total wave field can be viewed in an unsummed form by choosing Components instead of Superpose with the Choice button; however, the animation is much slower and the buttons are less responsive.

A variety of phenomena can be examined with this applet:

The width of the plot window can be adjusted by the slide bar and hitting Stop and Calculate. Be careful that you don't plot too wide an area because the lack of plotting resolution can give spurious results.

The time step is taken as 1/30 of the period of the first wave.

Comments: Robert A. Dalrymple
Center for Applied Coastal Research
University of Delaware, Newark DE 19716