How Does Water Depth Affect Wave Speed and Particle Motion?

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SUMMARY

Water waves exhibit varying speeds based on water depth, specifically speeding up in depths greater than half the wavelength and slowing down in shallower depths. The particle motion in shallow water transitions to a flat elliptical orbit, which directly influences the reduction in wave speed. This phenomenon is attributed to the interaction between wave energy and the depth of the water, affecting the wave's propagation characteristics.

PREREQUISITES
  • Understanding of wave mechanics
  • Knowledge of fluid dynamics
  • Familiarity with particle motion in waves
  • Basic concepts of wavelength and depth relationships
NEXT STEPS
  • Research the mathematical relationship between wave speed and water depth
  • Explore the effects of particle motion on wave energy in shallow water
  • Study the transition of wave behavior from deep to shallow water
  • Investigate the implications of wave speed changes on coastal engineering
USEFUL FOR

Students of physics, oceanographers, and coastal engineers interested in the dynamics of water waves and their practical applications in marine environments.

Yuqing
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I have trouble understanding why water waves tend to speed up for waters deeper than 1/2 wavelength and slow down for waters shallower. I have read it has something to do with how the particle orbit changes to elliptical in shallow waters.

Why does the particle orbit become a flat ellipse in shallow water and is that the factor influencing the slower wave speed? If not not, what is?
 
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Does anyone have an answer for this?
 

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