Water waves

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Chapter 5 Water waves

In the mid-nineteenth century, George Gabriel Stokes made significant contributions to the study of water waves, establishing much of the theoretical foundation that underpins modern fluid mechanics. His analysis of periodic, finite-amplitude waves on the surface of an incompressible fluid led to what are now known as Stokes waves, which describe how real waves deviate from purely sinusoidal motion as their amplitude increases. Stokes’ work marked a shift from qualitative observation to quantitative description, providing a systematic framework for understanding the balance of gravity, inertia, and nonlinearity in wave motion.

Our main task in this chapter is to introduce the fundamental principles governing water waves and the mathematical models that describe their behavior across different regimes.

Note 5.0.1.

As part of our lecture, we will study the related video on the NCFMF database on Waves in Fluids. The particular section of relevance is at the start, concerning the particle trajectories in waves of deep water.