Finite-amplitude self-oscillations in a rotating Hagen-Poiseuille flow
The nonlinear stability of a viscous incompressible flow in a circular pipe rotating about its own axis is investigated. The nonlinear evolution of the periodic self-oscillating regimes is studied, and their characteristic stabilization times, amplitudes, and other integral and fluctuational characteristics are found. The secondary instability of these finite-amplitude wave motions is examined. It is established that the secondary instability is initially weak and linear in character; the corresponding growth times are approximately an order greater than for the primary perturbations. There is the possibility of a sharp, explosive restructuring of the motion when the secondary perturbations reach a certain critical amplitude. A ''survival curve'' is constructed, which makes it possible to determine the preferred perturbation, distinguishable from the rest if the initial perturbation amplitudes are equal, and the critical amplitude values starting from which the other perturbations may prevail even over the preferred one. The range of these surviving perturbations is obtained. It is shown that as a result of the nonlinear interaction of several perturbations at low levels of supercriticality periodic motion in the form of a single traveling wave is generated.
nonlinear evolution of the periodic self-oscillating regimes
sharp, explosive restructuring of the motion
nonlinear interaction of several perturbations
scientific article; zbMATH DE number 3956668