In tsunami propagation, what happens when waves move from deep to shallow water?

Question

BlackTom AI · Accepted Answer

The prompt asks about tsunami behavior as waves transition from deep water into shallower water. In this regime, several linked physical effects occur due to the decreasing water depth. First, wave speed depends on depth; as depth decreases, the wave speed drops. Second, the wavelength shortens because the gravity wave near the surface must adjust to the shallower depth. Third, with speed and wavelength changes, the wave amplitude tends to grow in order to conserve energy flux (and wave steepness increases). This combination—slower speed, shorter wavelength, and increasing height—is characteristic of shoaling.

Option analysis is constrained here because no alternative choices were provided to compare against. Nevertheless, focusing on the statement given in the provided answer, “Wave height increases,” this aligns with the shoaling phenomenon: as the tsunami waves enter shallower water, their height increases while their speed decreases and the wavelength shortens.

Additional context that supports this reasoning includes the fact that the period of the wave remains nearly constant during shoaling, energy flux (which is proportional to wave height squared times velocity) is conserved, and the changes in depth drive the conversion of energy into higher surface elevation. As a result, the wave can become highly steep and may break near shore, posing significant impact.

If there were other options, we would assess each for consistency with shoaling physics: an option claiming wave height decreases would contradict energy flux considerations; an option claiming speed increases would contradict the depth dependence of speed for gravity waves; an option claiming wavelength remains unchanged would conflict with the observed wavelength shortening in shallower water. In short, the dominant, well-supported outcome when deep-water tsunami waves move into shallow water is an increase in wave height accompanied by reduced speed and shortened wavelength.

In tsunami propagation, what happens when waves move from deep to shallow water?单项选择题

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