Shallow- and deep-water ocean waves: deconstructing the dispersion relation

A set of hands-on lab activities allow students to visualize theoretical and observed ocean surface wave behavior through both an analytical model (MATLAB, Python, or R) and a physical model (wave tank). For the analytical model, students write code to visualize the linear superposition of waves and plot the dispersion relation and its shallow- and deep-water approximations to explore the dependence of wave speed on water depth and wavelength. For the physical model, students generate propagating and standing waves in a plexiglass wave tank and compare to the theoretical equations. Students are amazed at how well the theoretical equations predict the physical wave properties in the tank! Additional activities may include: 1) watching the groundbreaking 1967 film Waves Across the Pacific, featuring Oceanography legend Walter Munk, as a guided introduction to the concept of global wave energy propagation; 2) doing pencil-and-paper derivations of the dispersion relation and the deep- and shallow-water wave approximations; 3) going outside to observe waves in action. These activities have been implemented in undergraduate physics, physical oceanography, and general oceanography courses.