Instabilities in Fluid Dynamics

The investigation of instabilities in fluid dynamics is concerned with the following question: What happens to infinitesimal disturbances of a specific fluid flow, do the disturbances either grow or do they decay? In the case that the disturbances grow we call the fluid unstable. If the disturbances decay we call the fluid stable. For the occurrence of instability it is not necessary that all possible disturbances grow, just one growing disturbance means instability. Neither is it necessary that all disturbances are infinitesimal. However, the study of infinitesimal disturbances permits the use of the linear approximation of the Navier-Stokes equation and then leads in many cases to unambiguous analytical predictions about the conditions under which a fluid flow is unstable for a certain kind of disturbance. There are numerous types of instabilities in fluid dynamics, ranging from the very familiar instability of a water jet to the famous and cumbersome problem of turbulence. We will restrict the discussion here to two classical instabilities, Benard convection and Taylor vortex flow. These two instabilities relate most closely to Synergetics.