A physical approach to dissipation-induced instabilities

Abstract

Self-oscillatory and self-rotatory process driven by non-conservative forces have usually been treated as applications of the concepts of Hopf bifurcation and limit cycle in the theory of differential equations, or as instability problems in feedback control. Here we explore a complimentary approach, based on physical considerations of work extraction and thermodynamic irreversibility. From this perspective, the fact that a system can be destabilized by dissipation does not appear as a mathematical paradox, but rather as a straightforward consequence of the dissipative medium's motion. We apply this analysis to various mechanical and hydrodynamical systems of interest and show how it clarifies questions on which the literature remains contentious, such as the conditions for the appearance of non-conservative positional forces, or the roles of viscosity and turbulence in the raising of ocean waves by the wind.