Hydrodynamic Instabilities

Abstract

Our discussion of the previous chapter focused on one-dimensional phenomena, in which a physical system was structured as a function of linear or radial distance, but by assumption was not structured in the other two dimensions. Common experience tells us that this will rarely be a good assumption. We see turbulent clouds and whirlwinds in the air and complex eddies in water. We know of three-dimensional turbulent motions within the Earth and within the Sun. For that matter, if we focus our attention, we can see amazing hydrodynamic phenomena every day in the bathroom sink. We know that one can save fuel in cars and in airplanes by careful design that reduces the energy delivered to turbulence in the air. In fact, our experiences and common knowledge would lead us to conclude that hydrodynamic fluids are more often than not unstable and turbulent in some sense.