Why do waves increase in amplitude when approaching a beach?

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Discussion Overview

The discussion centers on the phenomenon of wave amplitude increase as waves approach a beach, exploring the underlying mechanisms and theories, including nonlinear wave theory and energy conservation. Participants examine both linear and nonlinear effects, as well as the conditions under which these effects become significant.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why wave amplitude increases as waves approach a beach, noting that while upper particles travel faster than lower ones, this does not explain the amplitude increase.
  • Another participant introduces Green's law, stating that the amplitude increase can be explained by energy conservation considerations, applicable in both linear and nonlinear cases.
  • It is suggested that nonlinearity effects become significant when the nonlinearity parameter is large, typically occurring in shallow water as waves approach the beach.
  • A participant seeks clarification on whether the amplitude increase is independent of nonlinearity and dispersion effects, suggesting it may solely be a consequence of energy conservation.
  • Further discussion indicates that while nonlinear effects may perturb the amplitude increase, energy conservation arguments dominate in the linearized model when nonlinearity is small.
  • Another participant raises the question of whether a wave can break without steepening due to nonlinearity, suggesting that a linearized model fails to predict wave-breaking.
  • One participant argues that the amplitude does not actually increase; rather, the wave rises due to decreasing water depth, which is necessary to maintain amplitude.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between amplitude increase, nonlinearity, and energy conservation. There is no consensus on whether amplitude increase is solely due to energy conservation or if nonlinearity plays a significant role. The discussion remains unresolved regarding the conditions for wave breaking.

Contextual Notes

Participants note that the effects of nonlinearity and energy conservation are not strictly independent, and the discussion highlights the complexity of predicting wave behavior in varying depths.

hanson
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Hi all.
I am wondering why when a wave approach a beach, its amplitude will increase and then break?
From my study of nonlinear wave, I know that the velocity of upper paricles of the pulse will travel faster than the lower particles and hence steeping of wave occur. But this does not explain why the AMPLITUDE become large, actually why? Also, the before-said steeping of wave is significant only when approaching a beach? why?
 
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The amplitude increase is present in the linear case as well, and is called Green's law.
It follows from energy conservation considerations.

Non-linearity effects really only becomes significant when the non-linearity paremter (say amplitude/depth, (or more proplerly, the Ursell parameter)) is large.
This will typically occur when the depth is "small", i.e, in approaching the beach, rather than at deep waters.
 
arildno said:
The amplitude increase is present in the linear case as well, and is called Green's law.
It follows from energy conservation considerations.

Non-linearity effects really only becomes significant when the non-linearity paremter (say amplitude/depth, (or more proplerly, the Ursell parameter)) is large.
This will typically occur when the depth is "small", i.e, in approaching the beach, rather than at deep waters.

Thanks for the reply. So, you mean the amplitude increase has nothing to do the nonlinearity or dispersion effect etc. It is just a consequence of energy conservation?

In other words, the steepening of wave and the increase in wave amplitude act independently in a wave approaching a beach?

By the way, will a wave break if there is no steepening by nonlinearity but just amplitude increase due to decrease in wave depth?
 
hanson said:
Thanks for the reply. So, you mean the amplitude increase has nothing to do the nonlinearity or dispersion effect etc. It is just a consequence of energy conservation?
No, nonlinear effects will perturb the actual increase, but the dominant contribution for small non-linearities is predictable by energy conservation arguments for the linearized model.
In other words, the steepening of wave and the increase in wave amplitude act independently in a wave approaching a beach?
No, linear and non-linear effects are not strictly "independent", but the effects for the linearized model will dominate the actual picture when non-linearity is small.

By the way, will a wave break if there is no steepening by nonlinearity but just amplitude increase due to decrease in wave depth?
Indeed, a linearized model fails in that it cannot predict wave-breaking.
 
The amplitude does not actually increase, it's just that since the depth of the water decreases, in order to keep the amplitude the same, the wave has to rise.
 

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