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 volcanic-mesocyclone. This research was done in
collaboration with Profs. Susan Kieffer and Gustavo Gioia.
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