Dispersion and Waves on Water

Abstract

This chapter asks how the time development of a wave may be described numerically. The algorithm may offer a better understanding of wave motion than the traditional treatment of the topic. We proceed by discriminating between phase and group velocities and introduce the concept of dispersion. Numerical modelling of dispersion is described in detail, computer programs are provided, and the calculations demonstrate distortion of pulses of waves when they pass through a dispersive medium. Finally, we discuss various phenomena related to gravity-driven surface waves on water, based on a formula for phase velocity of waves on water. As a curiosity, we present at the very end a fun experiment with an oscillating water drop on a hot surface.