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I have read that destructive interference between water waves always leads to the creation of smaller waves which eventually die out.

Why, in particular for water waves, it is hard to cancel each other?

Qmechanic
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veronika
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  • What do u mean by it difficult for water waves to cancel each other..? – Vishnu JK Dec 27 '16 at 09:06
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    It would be best if you cited the source where you read that. Then the context would be clearer. – Ruslan Dec 27 '16 at 09:11
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    Somewhere the energy contained in the waves have to go. In the idealized situation all the kinetic energy get converted into thermal energy, means in chaotic vibrations of the liquids molecules. Since the two incoming waves couldn't be identical (with opposite sign) in reality they couldn't cancel each other out (over going to pure thermal energy) and waves of smaller amplitude appear. – HolgerFiedler Dec 27 '16 at 10:58
  • @Ruslan I am sorry but it was an answer of user Anna V in this site and I don't even remember the question. Though I think it is a clear statetement and I know it from my job, ships try to canclel their own wave by means of a bulbous bow but they partially suceed. – veronika Dec 27 '16 at 11:16
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    Do you mean this answer? – Ruslan Dec 27 '16 at 12:52
  • Gravity waves (that is surface waves on a liquid where gravity is the primary restoring force) are disperssive even in deep water. This has implications to intentionally building regions of destructive interference with a finite number of sources. – dmckee --- ex-moderator kitten Dec 27 '16 at 19:47
  • Depending on what the question is actually asking, there are a variety of answers. There is an energy (and wave action) cascade for weakly nonlinear narow-banded deep water surface waves that lead to (small) waves being annihilated by viscosity (this of course doesn't happen in nature as waves break and dissipate energy over a range of scales). If you're interested in that question you can ask it separately and I can elaborate. Note, $standing$ waves do occur in nature (oppositely traveling waves with the same amplitude and phase) and are thought to be the source of microseisms in the ocean. – Nick P Dec 27 '16 at 21:40

4 Answers4

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Interference requires exactly same frequency in both the sources and also needs them to be coherent i.e. their phase relation must remain same throughout. It's very hard to create such things for macroscopic water bodies. Nevertheless in laboratory environment, you can see perfect interference in water waves.

Ari
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    The question seems to assert that creation of smaller waves happens even in ideal (laboratory) conditions. I'd assume it's related to nonlinearity of water waves. – Ruslan Dec 27 '16 at 09:12
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    I had also read that the Huygens principle is not satisfied on 2D surfaces (source: Strauss, PDEs with Applications), so that might also play a part, since there is no "sharp propagation of wavefronts"? – probably_someone Dec 27 '16 at 09:22
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    Add animated gifs please? – 10 Replies Dec 27 '16 at 21:51
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    https://www.youtube.com/watch?v=J_xd9hUZ2AY this is a good link. But this also illustrates the problem of generating coherent water waves. How hard it is compared to coherent light. Because of it's large wavelength and so on. – Ari Dec 29 '16 at 06:32
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Perfect destructive interference (cancellation) would require exactly equal frequency, phase, and amplitude. That is never going to happen in a real world setting, but as Ari stated, can be closely approximated in a laboratory.

And that is only for linear waves, i.e. waves with small steepness (wavenumber*amplitude < 1). Steep waves are nonlinear; the modes interact with energy exchange occurring on the third order terms; creating new higher order waves ("free" waves) that extract energy from the base modes. "Free" in the sense they are not bound (phase-locked) to the base modes; they propagate away. The second order terms are "bound".

So yes, interference creates smaller waves. And all surface water waves eventually dissipate.

Seminal references:

Phillips, O.M. 1960. On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions. Journal of Fluid Mechanics 9(2). pp 193-217.

Hasselmann, K. 1961. On the non-linear energy transfer in a wave spectrum. Ocean Wave Spectra. pp 191-197.

Longuet-Higgins, M.S. and Phillips, O.M. 1962. Phase velocity effects in tertiary wave interactions. Journal of Fluid Mechanics 12(3). pp 333-336.

Hasselmann, K. 1963. On the non-linear energy transfer in a gravity wave spectrum Part 1. Genery Theory. Journal of Fluid Mechanics 12(4). pp 481-500.

Hasselmann, K. 1963. On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irreversibly. Journal of Fluid Mechanics 15(2). pp 273-281.

Hasselmann, K. 1966. Feynman diagrams and interaction rules of wave-wave scattering processes. Review of Geophysics 4(1). pp 1-32.

Tyson Hilmer
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    Could you give easier to search references, not just "Author Year"? – Ruslan Dec 27 '16 at 13:58
  • These references appear to map to citations in http://www.wikiwaves.org, e.g. http://www.wikiwaves.org/Hasselmann_1963a. The attributions should be reproduced here in full. – Lightness Races in Orbit Dec 27 '16 at 14:36
  • You give a lot of references, but what do those actually contain? Currently it's just a list without any in-line citation or commentary - how do these references relate to the question or what's said in this answer? – ACuriousMind Dec 28 '16 at 02:51
  • My second paragraph is a very succinct explanation, that confirms the OP's first sentence with the fundamental reason why. The references are the seminal works that explain the theory; all heavily cited. Until someone else posts an in-depth explanation, your best option is reading the articles. I've yet to find a worthy summary. – Tyson Hilmer Dec 28 '16 at 10:12
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Somewhere the energy contained in the waves have to go. In the idealized situation all the kinetic energy get converted into thermal energy, means in chaotic vibrations of the liquids molecules.

Since the two incoming waves couldn't be identical (with opposite sign) in reality they couldn't cancel each other out (over going to pure thermal energy) and waves of smaller amplitude appear.

HolgerFiedler
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water waves are circular progressive waves which are poduced by vibrations and these waves travel only in a specific direction along their propagation and hence they do not

cancel each other

hitesh
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