5Water waves

IB Fluid Dynamics



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
2
= gk.
So we have
ω = ±i
p
gk.
Thus we get
h Ae
gkt
+ Be
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.