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?
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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.
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.
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.
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.
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