On (n,1) Wave Attractors: Coordinates and Saturation Time

Symmetry

Xiulin Xu¹  Leo Maas²  Ilias Sibgatullin³  Alexandr Petrov⁴ 

[1] Department of Gas and Wave Dynamics, Lomonosov Moscow State University, 119991 Moscow, Russia;Institute for Marine & Atmospheric Research, Utrecht University, 3584 CS Utrecht, The Netherlands;Institute for System Programming of Russian Academy of Sciences, 109004 Moscow, Russia;Ishlinsky Institute for Applied Mechanics of Russian Academy of Sciences, 119526 Moscow, Russia;

关键词: internal waves;    inertial waves;    wave attractors;   

DOI  :  10.3390/sym14020319

来源: DOAJ

【 摘 要 】

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,$\tau$) 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.

【 授权许可】

Unknown