Fluid Instabilities and Transition to Turbulence

Abstract

Fluid instabilities show up in many places in everyday life, nature and engineering applications. An often seemingly stable system with a gradient will often give rise to the development of instability, which can cascade eventually into turbulence. Governed by the parameters of the flow and fluids, when exposed to perturbation in the system, some wavelengths will grow, while others will not. This selectivity of specific structure sizes can be determined by using linear stability theory and then accounting for viscosity. Once these unstable wavelengths have grown to a substantial degree, the system typically becomes nonlinear before turbulence eventually sets in. Initially, looking at buoyancy-driven instabilities, one can clearly see how certain wavelengths can be selected. This can be extended to shear-driven instabilities and to geophysical systems. For some flows, simplifications can be made to analyze the specific fluid structures, while for others, only broad conclusions can be drawn about the stability criteria. With parallel shear flows (like that over wings and through pipes), the applications are more obvious, but the equations more difficult. However, conclusions can be drawn as to how one can control, prevent and initiate instability to suit our engineering needs.