Self-oscillations of a two-dimensional shear flow with forcing and dissipation

• Published in: Physics of fluids (1994) 2018-04, Vol.30 (4)
• Main Authors: López Zazueta, A., Zavala Sansón, L.
• Format: Article
• Language: English
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.5020130

Two-dimensional shear flows continuously forced in the presence of dissipative effects are studied by means of numerical simulations. In contrast with most previous studies, the forcing is confined in a finite region, so the behavior of the system is characterized by the long-term evolution of the global kinetic energy. We consider regimes with 1 < Reλ 36, in which the energy maintains a regular oscillation around a reference value. The flow configuration is an elliptical vortex tilted with respect to the forcing axis, which oscillates steadily also. Second, the flow is allowed to develop two Kelvin-Helmholtz billows and eventually more complicated structures. The regimes of the one-vortex case are observed again, except for Reλ > 135. At these values, the energy oscillates chaotically as the two vortices merge, form dipolar structures, and split again, with irregular periodicity. The self-oscillations are explained as a result of the alternate competition between forcing and dissipation, which is verified by calculating the budget terms in the energy equation. The relevance of the forcing-vs.-dissipation competition is discussed for more general flow systems.