LA4JR -83-2130
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Los Alamos National Laboratory moperated by the LJmverwtyof Califormafor the United States Department o! Energy under contract W-7405 .ENG.36,
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TITLE:
AN OVERVIEW OF RAYLEiGH-TAYLOR INSTABILITY
Ab r}{ OR(S):
D. H. Sharp
SUBMITTED TO
Presented at the International conference on “Fronts, Interfaces
and Patterns,”
Los Alamos Nation,~l Laboratory, May 2-6, 1983.
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An Overview of Rayleigh-Taylor Instability
*t
D. H. Sharp
Theoretical Division
Los Alamos National Laboratory
Los Alamos, New Mexico 87545
*
Presented at the International Conference on “Fronts, Interfaces, and Pattern!,,”
Log Alamos National Laboratory, May 2-G, 19(33,
‘Work supported by the U.S. Department of Energy,
2
Abstract
The aim of this talk is to survey Rayleigh-Taylor in-
stability, describing the phenomenology that occurs at a
“Taylor unstable interface,
and reviewing attempts to under-
stand tlwse ph~nornena quantitatively,
,
1,
Introduction
The Rayleigh-Taylor instability is a fingering instability of an interface
between two fluids of different densities, which occurs when the light flllid is
pushing the heavy fluid.1’2 The aim of this talk is tc survey Ravleigh-Taylol’
instability, describing the phenomenology that occurs at a Taylor unstable
interface, and reviewing attempts to understand these phenomena quantitatively.
I will also emphasize some critical questions which require further ‘,tudy.
2, Simplest Explanation of the Occurrence of Rayleiqh-Taylor lnstabilu
This conference affords the
topics from speakcr~ with the
pl~asure of learning about,
most diverse backgrounds,
diversity, I hope the experts will forgive me if I begin
possible description of Rayleigh-Ttiylor instability,
a great variety of
In view of this
wi’~h the simplest.
Imagine the ceiling of a room plastered uniformly with water to a depth of
1 meter (Fig. 1). The laj.r of water’ will fall. However, it
!5 not through
lack of support from the air that the watur will fall,
lhe pressure of th~
atmosphere is equivalent to that of a column of water 10 meteri thick,, quite
sufficient to hold the wat~ih aqain~t the ceiling, But in one respect the atmus-
plwre fails as a supporting medium,
1- fails tu Cr,rllstraint.twair-water inter-
face to flatness,
No matt.pr how car~fu:ly the water layer was,prepc]rcd to Imjin
with, it will deviate from planarity by ~umc sm~ll amuur~t.. lhos~ portions of
‘,he fluid which Iiv higher than the av~r;lge
~x~J1’riencemore presburv than is
neerkd for their support.
llwy begin to ‘=iso,
uu~hing a!,ide water as tlwy do
so, A n~lghbor!nq portion of tho fluid, whel’e ~he surldce hangs a llttlv low~r
than av~rage, w{II ruquirv mow than av~rag~~ prP~surrJ for it!, support, It
4
begins to fal:.
The air cannot supply the variat”
OTISin pressure from place to
place necessarj to prevent the interface
irregularities from growing,
The
initial irregularities therefore increase in magnitude, exponentially with time
at the beginning. The water which is moving downward concentrates in spikes.
The air moves upward through the
to the floor,
The same layer of water
stable. Irregularities die out.
water in round topped columns. The water falls
ying on the floor would have been perfectly
Thus we can infer a simple criterio.1 for the
onset of Taylor instability at the interface between two fluids of different
densities:
If the heavy fluid pushes the iight fluid, the interface is stable.
If the liqht fluid pushes the teavy
fluid, the interface is unstable.
A crite-
rion of comparable simplicity governs the onset of Kelvin-Helmholtz instability:
The interface between two fluids is unstable if there is a j= in the tangential
——
component of the velocity across the interface.
These two criteria are among
— .—
the most basic principl~s in the subject of interface ~nstability.
J, Examples of Rayleigh-Taylor Instability
——
Ttty
A,
i)
ii]
or instability occurs in diverse situiition~.
As examl~’es, we mention:
Natural l)h~nomena;
....,—
,...-
.-....—-—
overturl of the outer portion of the collapsed cor~ of a massivf’
!3Li~l’;:J
lht’
forrnttion of hiqh Iulninohity twill-exlltiust,jots in rotating qa:,
1!.
l[!CIIIIO
....-
i)
!.dsPr