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Article Dans Une Revue Physical Review E Année : 2019

Effect of finite amplitude of bottom corrugations on Fabry-Perot resonance of water waves

Résumé

Recently, the mechanism of Fabry-Perot (F-P) resonance in optics was extended to monochromatic water waves propagating in a domain with two patches of sinusoidal corrugations on an otherwise flat bottom. Assuming small-amplitude surface waves, an asymptotic linear analytical solution (ALAS) was derived by L. A. Couston et al. Phys. Rev. E 92, 043015 (2015). When resonance conditions are met, the ALAS predicts large amplification of the incident waves in the resonator area between the two patches of corrugations. Based on the ALAS, the amplitude of these standing waves is expected to increase exponentially with the relative amplitude of bottom corrugations (δ = d/h, where d is the corrugation amplitude and h the still water depth). In the present work, we examine the effects associated with the assumptions made in deriving the ALAS regarding the effect of a finite amplitude of bottom corrugation (i.e., finite value of δ), still in the linear wave framework. F-P resonance is studied by means of highly accurate numerical simulations, considering either the exact linear water wave problem (system A) or an approximate problem with a first-order expansion of the bottom boundary condition (system B). The numerical model is first validated on a Bragg resonance case, through comparisons with the ALAS, experimental measurements, and existing numerical simulations, showing its ability to represent well the so-called wave-number downshift of Bragg resonance (i.e., the slight decrease in the incident wave number where maximum resonance is reached in comparison with the value predicted by the ALAS). We then analyze how this downshift affects the F-P resonance, especially when the corrugations are of finite amplitude, i.e., δ varying from 0.05 to 0.4. The wave-number downshift appears to have a strong effect on the F-P resonance for δ > 0.1: very low wave amplification manifests for the wave number predicted by the ALAS. However, when the incident wave number is slightly decreased (by an amount increasing with δ) the F-P resonance case can be recovered, and the maximum amplification values are found to be close to the predictions from the ALAS (e.g., up to a factor of about 27 for δ = 0.4). The variations of the reflection coefficient and enhancement factor obtained from systems A and B as a function of the incident wave number are discussed and compared to ALAS predictions. In particular, it is found that the resonance peak is extremely narrow when δ = 0.2 and 0.4.
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Dates et versions

hal-02558399 , version 1 (29-04-2020)

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Jie Zhang, Michel Benoit. Effect of finite amplitude of bottom corrugations on Fabry-Perot resonance of water waves. Physical Review E , 2019, 99, pp.053109. ⟨10.1103/PhysRevE.99.053109⟩. ⟨hal-02558399⟩
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