Abstract
The simplest geometry of the domain, for which internal wave attractors were for the first time investigated both experimentally and numerically, has the shape of a trapezium with one vertical wall and one inclined lateral wall, characterized by two parameters. Using the symmetries of such a geometry we give an exact solution for the coordinates of the wave attractors with one reflection from each of the lateral boundaries and an integer amount n of reflections from each of the horizontal boundaries. The area of existence for each (n,1) attractor has the form of a triangle in the (d,τ) parameter plane, and the shape of this triangle is explicitly given with the help of inequalities or vertices. The expression for the Lyapunov exponents and their connection to the focusing parameters is given analytically. The corresponding direct numerical simulations with low viscosity fully support the analytical results and demonstrate that in bounded domains (n,1) wave attractors can be effective transformers of the global forcing into traveling waves. The saturation time from the state of rest to the final wave regime depends almost linearly on the number of cells, n.
Original language | English |
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Article number | 319 |
Pages (from-to) | 1-11 |
Number of pages | 11 |
Journal | Symmetry-basel |
Volume | 14 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2022 |
Bibliographical note
Funding Information:Funding: This research was funded by the Ministry of Science and Higher Education of the Russian Federation, agreement N 075-15-2020-808. DNS are carried out using the shared research facilities of HPC computing resources at Lomonosov Moscow State University and UniHUB project [34].
Funding Information:
This research was funded by the Ministry of Science and Higher Education of the Russian Federation, agreement N 075-15-2020-808. DNS are carried out using the shared research facilities of HPC computing resources at Lomonosov Moscow State University and UniHUB project [34].
Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
Keywords
- Inertial waves
- Internal waves
- Wave attractors