12.520 Lecture Notes 24 Rayleigh - Taylor Instability

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12.520 Lecture Notes 24 Rayleigh - Taylor Instability Growth of Boundary Undulations
• salt domes
• diapirs
• continental delamination
X3
ηu, �u
X1
ηl, �l
2�x1
λ = λ0cos
= λ0coskx
�
Figure 24.18
Figure by MIT OCW.
General problem: topography on an interface
ξ = ξ0 cos kx1
k=
2π
λ
(1) If ρu < ρl topography decays as ξ 0 e−t / τ .
(2) If ρu
> ρl topography grows.
Initially ξ = ξ 0 et / τ
. Eventually many wavelengths interact, problem is no longer simple. Characteristic time τ depends on ∆ρ, ηu , ηl , thickness of layers, …
Before glaciation
Subsidence caused by glaciation
Ice Sheet
Surface after melting of the ice sheet but prior to postglacial rebound
Full rebound
Figure 24.19. Subsidence due to glaciation and the subsequent postglacial
rebound.
Figure 24.19
Figure by MIT OCW.
•
Weight of ice causes viscous flow in the mantle.
•
After melting of ice, the surface rebounds – “postglacial rebound”.
•
Different regions have different behaviors (e.g., Boston is now sinking).
X3
� = �0coskx
Air
X1
�m
Figure 24.20
Figure by MIT OCW.
Problem: how to reconcile physical boundary conditions with mathematical description?
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