Multiscale wave resonance in composite sinusoidal-elliptical topographies: Critical transitions and analytical control
This study presents the first analytical solution for wave propagation over composite seabeds integrating sinusoidal sandbars with truncated semi-elliptical topographies, overcoming limitations of conventional mild-slope equations in handling elliptical curvature effects, coupled Bragg scattering, a...
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-08-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000792 |
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| Summary: | This study presents the first analytical solution for wave propagation over composite seabeds integrating sinusoidal sandbars with truncated semi-elliptical topographies, overcoming limitations of conventional mild-slope equations in handling elliptical curvature effects, coupled Bragg scattering, and singularities at truncated boundaries. Utilizing Frobenius series expansion and multi-region field matching, we systematically quantify how geometric parameters—a/b ratio, δ/a, and h0/b—govern wave reflection coefficients (KR). Key discoveries reveal that the a/b ratio controls resonance peak frequencies (inducing 12% shifts per 0.1 change), the radius parameter r=(h0−h1)/h0 triggers complete reflection (KR→1) at a critical value of 0.5, and optimal δ/a expands reflection bandwidth by up to 22%. This work transcends classical studies on singular seabed types, establishes a theoretical foundation for designing wave-control metamaterials via multiscale resonances, and bridges classical potential flow theory with modern coastal engineering applications in wave energy harvesting, coastal protection, and offshore structure design. |
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| ISSN: | 2590-0374 |