Wave attractors in viscous media exhibit laminar or turbulent behavior, dictated by the intensity of the external forcing. Laminar attractors are often assumed to behave as linear systems. However, existing studies typically focus on fully developed flows, neglecting the dynamic formation process of these attractors. This simplification overlooks crucial transient phenomena that govern their emergence and stability. In this paper, first, we investigate unconventional wave attractor configurations subjected to forcing with a complex spectrum, which lead to early nonlinearity demonstration. Next, we focus on the transient processes of attractor formation and destruction, providing insights into their dynamic evolution. Furthermore, we identify temporal and velocity scaling relationships across various viscosity parameters, revealing the self-similar behavior inherent in these wave-attractor systems.
Elistratov et al. (Tue,) studied this question.