Final answer:
As waves reach shallow water and shoal, their energy shifts from kinetic to potential due to seabed friction, leading to higher wave heights. The fluid dynamics principle indicates an increase in kinetic energy due to work done on the fluid, contributing to the higher waves near shorelines.
Step-by-step explanation:
When waves reach shallow water near a shoreline, the water depth decreases causing the wave to shoal, which is when the wave height increases. This phenomenon occurs due to the re-partitioning of energy from kinetic to potential. The bottom of the wave is slowed down due to friction with the seabed, which causes the wave's energy to compress into a smaller volume of water, resulting in a taller wave, or increased amplitude. As per the principle that the energy of a wave increases with an increase in amplitude, when the wave shoals, its energy is concentrated into higher waves despite the decrease in water depth.
Furthermore, when considering the fluid dynamics of a wave entering a narrower channel, the speed and kinetic energy increase due to the net work done on the fluid and the work done by gravitational forces if there's a change in vertical position. This concept is also applicable when the waves change shape as they approach the shore, where the water behaves similarly to fluid moving through a narrowing channel.
If there are no dissipative forces acting on the waves, then the total energy remains constant, but the intensity of the energy is spread out over a larger area as the wave moves away from the source. When a wave shoals, the wave becomes taller but also shorter in wavelength, thereby conserving energy but redistributing it over a lesser area, which increases the wave's height further.