A wave is a mechanism by which energy is transferred through matter. The problem is to create a mathematical model of wave motion at the point in which a wave changes from a symmetric form to a chaotic one. Our model will consider what occurs at the boundary between two liquids of different densities. (Water and mineral oil are examples.) At this type of boundary, a wave behaves differently than air-to-liquid boundary. The wave keeps its shape, but the motion is slowed. The analytical model will be written in Java.

Problem Solution:

The team plans to construct a relatively large ripple tank with a bottom which can be inclined. The objective is to be able to observe and photograph waves changing from symmetric to chaotic forms as they move across the tank from the deeper to shallower end.

Two liquids of different densities will be used in the tank. The vibrator for generating waves will be placed so that waves may be generated at the surface between air and the liquid. Additionally, the wave generator will be submerged to generate waves at the interface between the two liquids. At this Similar to the inclined bottom, the objective is to observe waves changing from symmetric to chaotic forms as they move through the tank.

Progress to Date:

Presently, we have ordered the supplies to construct our ripple tank, which should be received shortly. We have begun to acquaint ourselves with the Java and Fortran programming languages. Once the supplies are received, we will begin experimenting with the construction and engineering component of the ripple tank.

Expected Results:

We expect to deliver a one-dimensional math model of the chaotic behavior that occurs at the boundary between air/liquid and liquids of different densities. Once this is achieved, we will plan to produce a two-dimensional math model of the same wave behavior. We then will determine how well the math model reflects the actual physical reality seen in the ripple tank. This comparison will be done by matching photographic images with computer generated images from the math model.

Team Members:

  Joseph Koby
  Sarah Armstrong
  Juan-Antonio Vigil
  Vanessa Trujillo

Sponsoring Teacher: Robert Dryja

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