The Rayleigh-Taylor Instability: From water falling out of a glass to fire falling out of the sky

We will discuss a well-known instability in fluid mechanics: the Rayleigh-Taylor (RT) instability. The classical RT instability is the instability that occurs at the bottom surface of a denser fluid that tops a lighter fluid, where both the fluids are initially at rest. We will start by performing a simple experiment to show that if a glass of water is inverted, the water falls out because of the RT instability. (You are advised not to sit in the front row!) Then, we will derive equations for the characteristic wavelength and the characteristic timescale of the RT instability. To that end, we will use a simple but uncommon energy-based analysis that gives a clear understanding of the mutually competing mechanisms that govern the RT instability. Then, we will explore a recently formulated turbulent analogue of the RT instability in which the fluids are initially turbulent. We will show that both the characteristic wavelength and the characteristic timescale of the instability are magnified by the initial turbulence. On the basis of this turbulent analogue of the RT instability, we will explain the curious shapes of two volcanic plumes---the scallop plume of Reventador's 2001 eruption and the starfish plume of Pinatubo's 1991 eruption. We will show that both plumes underwent the turbulent analogue of the RT instability: the Reventador plume when it was left to fall out of the sky by a loss of buoyancy, the Pinatubo plume when it was centrifuged out of its axis by a tyhoon. This research was done in collaboration with Profs. Susan Kieffer and Gustavo Gioia.

Reference:

Chakraborty, Pinaki; Gioia, Gustavo; Kieffer, Susan
Volcan Reventador's unusual umbrella
Geophys. Res. Lett.,Vol.33,No.5,L05313
10.1029 /2005GL024915, 2006
http://www.agu.org/journals/gl/gl0605/2005GL024915/