Spatially quasi-periodic water waves of finite depth
| Autor: | Jon Wilkening, Xinyu Zhao |
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| Rok vydání: | 2023 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2301.01289 |
| Popis: | We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and traveling wave settings. We adopt a quasi-periodic conformal mapping formulation of the Euler equations, where one-dimensional quasi-periodic functions are represented by periodic functions on a higher-dimensional torus. We compute the time evolution of free surface waves in the presence of a background flow and a quasi-periodic bottom boundary and observe the formation of quasi-periodic patterns on the free surface. Two types of quasi-periodic traveling waves are computed: small-amplitude waves bifurcating from the zero-amplitude solution and larger-amplitude waves bifurcating from finite-amplitude periodic traveling waves. We derive weakly nonlinear approximations of the first type and investigate the associated small-divisor problem. We find that waves of the second type exhibit striking nonlinear behavior, e.g., the peaks and troughs are shifted non-periodically from the corresponding periodic waves due to the activation of quasi-periodic modes. Comment: 30 pages, 6 figures |
| Databáze: | OpenAIRE |
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