5.5 Rayleigh-Taylor instability

Note that it is possible to turn the problem upside down, and imagine we have

water over air:

water

air

We can imagine this as the same scenario as before, but with gravity pull upwards.

So exactly the same equations hold, but we replace

−g

with

g

. In deep water,

we have

ω

gkt

−

√

gkt

We thus have an exponentially growing solution. So the system is unstable, and

water will fall down. This very interesting fact is known as Rayleigh-Taylor

instability.