Visualizing the Dispersion of Internal Wave Beams in Density-Varying Fluid

Abstract. Physics curricula typically focus on electromagnetic, quantum, and standard mechanical waves propagating through media like air or taut strings. We investigated internal gravity waves, a peculiar type of mechanical wave that propagates through oceans and has significant geophysical implications. These dispersive waves obey a partial differential equation that accounts for the fluid density profile and buoyant force, resulting in a unique dispersion relation that couples their frequency directly to their angle of propagation. We explored this intricacy with a laboratory experiment to generate and observe internal waves in a more accessible environment than the ocean depths. In this experiment, we created and verified a linear saltwater stratification and applied an oscillatory topographic forcing. Because internal waves are invisible to the naked eye, we used background-oriented Schlieren optical techniques to track the density gradient and visualize wave propagation. Finally, we extracted a power spectrum of the density gradient to obtain the system’s wave vector modes, quantitatively demonstrating the unique dispersive properties of internal waves