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The Rayleigh–Taylor instability, or RT instability (after
Lord Rayleigh John William Strutt, 3rd Baron Rayleigh ( ; 12 November 1842 – 30 June 1919), was an English physicist who received the Nobel Prize in Physics in 1904 "for his investigations of the densities of the most important gases and for his discovery ...
and
G. I. Taylor Sir Geoffrey Ingram Taylor Order of Merit, OM Royal Society of London, FRS FRSE (7 March 1886 – 27 June 1975) was a British physicist and mathematician, who made contributions to fluid dynamics and wave theory. Early life and education Tayl ...
), is an
instability In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior. ...
of an
interface Interface or interfacing may refer to: Academic journals * ''Interface'' (journal), by the Electrochemical Society * '' Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics'' * '' Inter ...
between two
fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...
s of different densities which occurs when the lighter fluid is pushing the heavier fluid. Drazin (2002) pp. 50–51. Examples include the behavior of water suspended above oil in the
gravity of Earth The gravity of Earth, denoted by , is the net force, net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a Eucl ...
,
mushroom cloud A mushroom cloud is a distinctive mushroom-shaped flammagenitus cloud of debris, smoke, and usually condensed water vapour resulting from a large explosion. The effect is most commonly associated with a nuclear explosion, but any sufficiently e ...
s like those from
volcanic eruption A volcanic eruption occurs when material is expelled from a volcanic vent or fissure. Several types of volcanic eruptions have been distinguished by volcanologists. These are often named after famous volcanoes where that type of behavior h ...
s and atmospheric
nuclear explosion A nuclear explosion is an explosion that occurs as a result of the rapid release of energy from a high-speed nuclear reaction. The driving reaction may be nuclear fission or nuclear fusion or a multi-stage cascading combination of the two, th ...
s,
supernova A supernova (: supernovae or supernovas) is a powerful and luminous explosion of a star. A supernova occurs during the last stellar evolution, evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion ...
explosions in which expanding core gas is accelerated into denser shell gas, merging binary quantum fluids in metastable configuration, instabilities in plasma fusion reactors and inertial confinement fusion.


Concept

Water suspended atop oil is an everyday example of Rayleigh–Taylor instability, and it may be modeled by two completely plane-parallel layers of
immiscible Miscibility () is the property of two chemical substance, substances to mix in all mixing ratio, proportions (that is, to fully dissolution (chemistry), dissolve in each other at any concentration), forming a homogeneity and heterogeneity, homoge ...
fluid, the denser fluid on top of the less dense one and both subject to the Earth's gravity. The
equilibrium Equilibrium may refer to: Film and television * ''Equilibrium'' (film), a 2002 science fiction film * '' The Story of Three Loves'', also known as ''Equilibrium'', a 1953 romantic anthology film * "Equilibrium" (''seaQuest 2032'') * ''Equilibr ...
here is unstable to any perturbations or disturbances of the interface: if a parcel of heavier fluid is displaced downward with an equal volume of lighter fluid displaced upwards, the potential energy of the configuration is lower than the initial state. Thus the disturbance will grow and lead to a further release of
potential energy In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity ...
, as the denser material moves down under the (effective) gravitational field, and the less dense material is further displaced upwards. This was the set-up as studied by Lord Rayleigh. The important insight by G. I. Taylor was his realisation that this situation is equivalent to the situation when the fluids are accelerated, with the less dense fluid accelerating into the denser fluid. This occurs deep underwater on the surface of an expanding bubble and in a nuclear explosion. As the RT instability develops, the initial perturbations progress from a linear growth phase into a non-linear growth phase, eventually developing "plumes" flowing upwards (in the gravitational buoyancy sense) and "spikes" falling downwards. In the linear phase, the fluid movement can be closely approximated by
linear equation In mathematics, a linear equation is an equation that may be put in the form a_1x_1+\ldots+a_nx_n+b=0, where x_1,\ldots,x_n are the variables (or unknowns), and b,a_1,\ldots,a_n are the coefficients, which are often real numbers. The coeffici ...
s, and the amplitude of perturbations is growing exponentially with time. In the non-linear phase, perturbation amplitude is too large for a linear approximation, and
non-linear In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...
equations are required to describe fluid motions. In general, the density disparity between the fluids determines the structure of the subsequent non-linear RT instability flows (assuming other variables such as surface tension and viscosity are negligible here). The difference in the fluid densities divided by their sum is defined as the Atwood number, A. For A close to 0, RT instability flows take the form of symmetric "fingers" of fluid; for A close to 1, the much lighter fluid "below" the heavier fluid takes the form of larger bubble-like plumes. This process is evident not only in many terrestrial examples, from
salt dome A salt dome is a type of structural dome formed when salt (or other evaporite minerals) intrudes into overlying rocks in a process known as diapirism. Salt domes can have unique surface and subsurface structures, and they can be discovered us ...
s to weather inversions, but also in
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
and
electrohydrodynamics Electrohydrodynamics (EHD), also known as electro-fluid-dynamics (EFD) or electrokinetics, is the study of the dynamics of electrically charged fluids. Electrohydrodynamics (EHD) is a joint domain of electrodynamics and fluid dynamics mainly foc ...
. For example, RT instability structure is evident in the
Crab Nebula The Crab Nebula (catalogue designations M1, NGC 1952, Taurus A) is a supernova remnant and pulsar wind nebula in the constellation of Taurus (constellation), Taurus. The common name comes from a drawing that somewhat resembled a crab with arm ...
, in which the expanding
pulsar wind nebula A pulsar wind nebula (PWN, plural PWNe), sometimes called a plerion (derived from the Greek "πλήρης", ''pleres'', meaning "full"), is a type of nebula sometimes found inside the shell of a supernova remnant (SNR), powered by winds generate ...
powered by the
Crab pulsar The Crab Pulsar (PSR B0531+21 or Baade's Star) is a relatively young neutron star. The star is the central star in the Crab Nebula, a remnant of the supernova SN 1054, which was widely observed on Earth in the year 1054.
is sweeping up ejected material from the
supernova A supernova (: supernovae or supernovas) is a powerful and luminous explosion of a star. A supernova occurs during the last stellar evolution, evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion ...
explosion 1000 years ago. The RT instability has also recently been discovered in the Sun's outer atmosphere, or
solar corona In astronomy, a corona (: coronas or coronae) is the outermost layer of a star's Stellar atmosphere, atmosphere. It is a hot but relatively luminosity, dim region of Plasma (physics), plasma populated by intermittent coronal structures such as so ...
, when a relatively dense
solar prominence In solar physics, a prominence, sometimes referred to as a filament, is a large Plasma (physics), plasma and magnetic field structure extending outward from the Sun's surface, often in a loop shape. Prominences are anchored to the Sun's surface ...
overlies a less dense plasma bubble. This latter case resembles magnetically modulated RT instabilities. Note that the RT instability is not to be confused with the
Plateau–Rayleigh instability In fluid dynamics, the Plateau–Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same total volume but less surface area per droplet. It is ...
(also known as Rayleigh instability) of a liquid jet. This instability, sometimes called the hosepipe (or firehose) instability, occurs due to surface tension, which acts to break a cylindrical jet into a stream of droplets having the same total volume but higher surface area. Many people have witnessed the RT instability by looking at a
lava lamp A lava lamp is a decorative lamp that was invented in 1963 by British entrepreneur Edward Craven Walker, the founder of the lighting company Mathmos. It consists of a bolus of a special coloured wax mixture inside a glass vessel, the remainde ...
, although some might claim this is more accurately described as an example of Rayleigh–Bénard convection due to the active heating of the fluid layer at the bottom of the lamp.


Stages of development and eventual evolution into turbulent mixing

The evolution of the RTI follows four main stages. In the first stage, the perturbation amplitudes are small when compared to their wavelengths, the equations of motion can be linearized, resulting in exponential instability growth. In the early portion of this stage, a sinusoidal initial perturbation retains its sinusoidal shape. However, after the end of this first stage, when non-linear effects begin to appear, one observes the beginnings of the formation of the ubiquitous mushroom-shaped spikes (fluid structures of heavy fluid growing into light fluid) and bubbles (fluid structures of light fluid growing into heavy fluid). The growth of the mushroom structures continues in the second stage and can be modeled using buoyancy drag models, resulting in a growth rate that is approximately constant in time. At this point, nonlinear terms in the equations of motion can no longer be ignored. The spikes and bubbles then begin to interact with one another in the third stage. Bubble merging takes place, where the nonlinear interaction of mode coupling acts to combine smaller spikes and bubbles to produce larger ones. Also, bubble competition takes places, where spikes and bubbles of smaller wavelength that have become saturated are enveloped by larger ones that have not yet saturated. This eventually develops into a region of turbulent mixing, which is the fourth and final stage in the evolution. It is generally assumed that the mixing region that finally develops is self-similar and turbulent, provided that the Reynolds number is sufficiently large.


Linear stability analysis

The
inviscid Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup h ...
two-dimensional Rayleigh–Taylor (RT) instability provides an excellent springboard into the mathematical study of stability because of the simple nature of the base state.Drazin (2002) pp. 48–52. Consider a base state in which there is an interface, located at z=0 that separates fluid media with different densities, \rho_1 for z<0 and \rho_2 for z>0. The gravitational acceleration is described by the vector \mathbf g = -g\, \mathbf_z. The velocity field and pressure field in this equilibrium state, denoted with an overbar, are given by :\overline=\mathbf, \quad \overline p = \begin-\rho_1 g z \quad \textz<0,\\ -\rho_2 g z \quad \textz>0,\end where the reference location for the pressure is taken to be at z=0. Let this interface be slightly perturbed, so that it assumes the position z=f(x,t). Correspondingly, the base state is also slightly perturbed. In the linear theory, we can write :\mathbf = \overline + \hat(z) e^, \quad p = \overline + \hat p(z) e^, \quad f =\hat e^ where k is the real wavenumber in the x-direction and \sigma is the growth rate of the perturbation. Then the linear stability analysis based on the inviscid governing equations shows that :\sigma^2 = \frac gk. Thus, if \rho_2<\rho_1, the base state is stable and while if \rho_2>\rho_1, it is unstable for all wavenumbers. If the interface has a
surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
\gamma, then the dispersion relation becomes :\sigma^2 = \fracgk - \frac, which indicates that the instability occurs only for a range of wavenumbers 0 where k_c^2 = (\rho_2-\rho_1)g/\gamma; that is to say, surface tension stabilises large wavenumbers or small length scales. Then the maximum growth rate occurs at the wavenumber k_m=k_c/\sqrt 3 and its value is :\sigma_m^2 = \frac\left frac\right. The perturbation introduced to the system is described by a velocity field of infinitesimally small amplitude, (u'(x,z,t),w'(x,z,t)).\, Because the fluid is assumed incompressible, this velocity field has the streamfunction representation \textbf'=(u'(x,z,t),w'(x,z,t))=(\psi_z,-\psi_x),\, where the subscripts indicate
partial derivatives In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Par ...
. Moreover, in an initially stationary incompressible fluid, there is no vorticity, and the fluid stays
irrotational In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not chan ...
, hence \nabla\times\textbf'=0\,. In the streamfunction representation, \nabla^2\psi=0.\, Next, because of the translational invariance of the system in the ''x''-direction, it is possible to make the
ansatz In physics and mathematics, an ansatz (; , meaning: "initial placement of a tool at a work piece", plural ansatzes or, from German, ansätze ; ) is an educated guess or an additional assumption made to help solve a problem, and which may later be ...
\psi\left(x,z,t\right)=e^\Psi\left(z\right),\, where \alpha\, is a spatial wavenumber. Thus, the problem reduces to solving the equation \left(D^2-\alpha^2\right)\Psi_j=0,\,\,\,\ D=\frac,\,\,\,\ j=L,G.\, The domain of the problem is the following: the fluid with label 'L' lives in the region -\infty, while the fluid with the label 'G' lives in the upper half-plane 0\leq z<\infty\,. To specify the solution fully, it is necessary to fix conditions at the boundaries and interface. This determines the wave speed ''c'', which in turn determines the stability properties of the system. The first of these conditions is provided by details at the boundary. The perturbation velocities w'_i\, should satisfy a no-flux condition, so that fluid does not leak out at the boundaries z=\pm\infty.\, Thus, w_L'=0\, on z=-\infty\,, and w_G'=0\, on z=\infty\,. In terms of the streamfunction, this is \Psi_L\left(-\infty\right)=0,\qquad \Psi_G\left(\infty\right)=0.\, The other three conditions are provided by details at the interface z=\eta\left(x,t\right)\,. ''Continuity of vertical velocity:'' At z=\eta, the vertical velocities match, w'_L=w'_G\,. Using the stream function representation, this gives \Psi_L\left(\eta\right)=\Psi_G\left(\eta\right).\, Expanding about z=0\, gives \Psi_L\left(0\right)=\Psi_G\left(0\right)+\text,\, where H.O.T. means 'higher-order terms'. This equation is the required interfacial condition. ''The free-surface condition:'' At the free surface z=\eta\left(x,t\right)\,, the kinematic condition holds: \frac+u'\frac=w'\left(\eta\right).\, Linearizing, this is simply \frac=w'\left(0\right),\, where the velocity w'\left(\eta\right)\, is linearized on to the surface z=0\,. Using the normal-mode and streamfunction representations, this condition is c \eta=\Psi\,, the second interfacial condition. ''Pressure relation across the interface:'' For the case with
surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
, the pressure difference over the interface at z=\eta is given by the Young–Laplace equation: p_G\left(z=\eta\right) - p_L\left(z=\eta\right) = \sigma\kappa,\, where ''σ'' is the surface tension and ''κ'' is the
curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
of the interface, which in a linear approximation is \kappa=\nabla^2\eta=\eta_.\, Thus, p_G\left(z=\eta\right)-p_L\left(z=\eta\right)=\sigma\eta_.\, However, this condition refers to the total pressure (base+perturbed), thus \left _G\left(\eta\right)+p'_G\left(0\right)\right\left _L\left(\eta\right)+p'_L\left(0\right)\right\sigma\eta_.\, (As usual, The perturbed quantities can be linearized onto the surface ''z=0''.) Using
hydrostatic balance In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and hydrostasy, is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. I ...
, in the form P_L=-\rho_L g z+p_0,\qquad P_G=-\rho_G gz +p_0,\, this becomes p'_G-p'_L=g\eta\left(\rho_G-\rho_L\right)+\sigma\eta_,\qquad\textz = 0.\, The perturbed pressures are evaluated in terms of streamfunctions, using the horizontal momentum equation of the linearised
Euler equations In mathematics and physics, many topics are eponym, named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, e ...
for the perturbations, \frac = - \frac\frac\, with i=L,G,\, to yield p_i'=\rho_i c D\Psi_i,\qquad i=L,G.\, Putting this last equation and the jump condition on p'_G-p'_L together, c\left(\rho_G D\Psi_G-\rho_L D\Psi_L\right)=g\eta\left(\rho_G-\rho_L\right)+\sigma\eta_.\, Substituting the second interfacial condition c\eta=\Psi\, and using the normal-mode representation, this relation becomes c^2\left(\rho_G D\Psi_G-\rho_L D\Psi_L\right)=g\Psi\left(\rho_G-\rho_L\right)-\sigma\alpha^2\Psi,\, where there is no need to label \Psi\, (only its derivatives) because \Psi_L=\Psi_G\, at z=0.\, ; Solution Now that the model of stratified flow has been set up, the solution is at hand. The streamfunction equation \left(D^2-\alpha^2\right)\Psi_i=0,\, with the boundary conditions \Psi\left(\pm\infty\right)\, has the solution \Psi_L=A_L e^,\qquad \Psi_G = A_G e^.\, The first interfacial condition states that \Psi_L=\Psi_G\, at z=0\,, which forces A_L=A_G=A.\, The third interfacial condition states that c^2\left(\rho_G D\Psi_G-\rho_L D\Psi_L\right)=g\Psi\left(\rho_G-\rho_L\right)-\sigma\alpha^2\Psi.\, Plugging the solution into this equation gives the relation Ac^2\alpha\left(-\rho_G-\rho_L\right)=Ag\left(\rho_G-\rho_L\right)-\sigma\alpha^2A.\, The ''A'' cancels from both sides and we are left with c^2=\frac\frac+\frac.\, To understand the implications of this result in full, it is helpful to consider the case of zero surface tension. Then, c^2=\frac\frac,\qquad \sigma=0,\, and clearly * If \rho_G<\rho_L\,, c^2>0\, and ''c'' is real. This happens when the lighter fluid sits on top; * If \rho_G>\rho_L\,, c^2<0\, and ''c'' is purely imaginary. This happens when the heavier fluid sits on top. Now, when the heavier fluid sits on top, c^2<0\,, and c=\pm i \sqrt,\qquad \mathcal=\frac,\, where \mathcal\, is the Atwood number. By taking the positive solution, we see that the solution has the form \Psi\left(x,z,t\right) = A e^ \exp \left \alpha\left(x-ct\right)\right= A \exp\left(\alpha\sqrtt\right)\exp\left(i\alpha x - \alpha, z, \right)\, and this is associated to the interface position ''η'' by: c\eta=\Psi.\, Now define B=A/c.\, When the two layers of the fluid are allowed to have a relative velocity, the instability is generalized to the Kelvin–Helmholtz–Rayleigh–Taylor instability, which includes both the
Kelvin–Helmholtz instability The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) is a fluid instability that occurs when there is shear velocity, velocity shear in a single continuum mechanics, continuous fluid or a velocity difference across t ...
and the Rayleigh–Taylor instability as special cases. It was recently discovered that the fluid equations governing the linear dynamics of the system admit a parity-time symmetry, and the Kelvin–Helmholtz–Rayleigh–Taylor instability occurs when and only when the parity-time symmetry breaks spontaneously.


Vorticity explanation

The RT instability can be seen as the result of
baroclinic In fluid dynamics, the baroclinity (often called baroclinicity) of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology, a baroclinic flow is one in which the dens ...
torque In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...
created by the misalignment of the pressure and density gradients at the perturbed interface, as described by the two-dimensional
inviscid Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup h ...
vorticity In continuum mechanics, vorticity is a pseudovector (or axial vector) field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point an ...
equation, \frac = \frac\nabla \rho \times \nabla p , where ω is vorticity, ρ density and ''p'' is the pressure. In this case the dominant pressure gradient is
hydrostatic Hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium and "the pressure in a fluid or exerted by a fluid on an immersed body". The word "hydrostatics" is sometimes used to refer specifically to water and o ...
, resulting from the acceleration. When in the unstable configuration, for a particular harmonic component of the initial perturbation, the torque on the interface creates vorticity that will tend to increase the misalignment of the
gradient In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase. The g ...
vectors. This in turn creates additional vorticity, leading to further misalignment. This concept is depicted in the figure, where it is observed that the two counter-rotating vortices have velocity fields that sum at the peak and trough of the perturbed interface. In the stable configuration, the vorticity, and thus the induced velocity field, will be in a direction that decreases the misalignment and therefore stabilizes the system. A much simpler explanation of the basic physics of the Rayleigh–Taylor instability was published in 2006.


Late-time behaviour

The analysis in the previous section breaks down when the amplitude of the perturbation is large. The growth then becomes non-linear as the spikes and bubbles of the instability tangle and roll up into vortices. Then, as in the figure, numerical simulation of the full problem is required to describe the system.


See also

*
Saffman–Taylor instability The Saffman–Taylor instability, also known as viscous fingering, is the formation of patterns in a morphologically unstable interface between two fluids in a porous medium or in a Hele-Shaw cell, described mathematically by Philip Saffman and ...
*
Darrieus–Landau instability The Darrieus–Landau instability, or density fingering, refers to an instability of chemical fronts propagating into a denser medium, named after Georges Jean Marie Darrieus and Lev Landau. It is a key Combustion instability#Classification of comb ...
* Richtmyer–Meshkov instability *
Kelvin–Helmholtz instability The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) is a fluid instability that occurs when there is shear velocity, velocity shear in a single continuum mechanics, continuous fluid or a velocity difference across t ...
*
Mushroom cloud A mushroom cloud is a distinctive mushroom-shaped flammagenitus cloud of debris, smoke, and usually condensed water vapour resulting from a large explosion. The effect is most commonly associated with a nuclear explosion, but any sufficiently e ...
*
Plateau–Rayleigh instability In fluid dynamics, the Plateau–Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same total volume but less surface area per droplet. It is ...
*
Salt fingering Salt fingering is a mixing process, example of double diffusive instability, that occurs when relatively warm, salty water overlies relatively colder, fresher water. It is driven by the fact that heated water diffuses more readily than salty water ...
*
Hydrodynamic stability In fluid dynamics, hydrodynamic stability is the field of study, field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so ...
*
Kármán vortex street In fluid dynamics, a Kármán vortex street (or a von Kármán vortex street) is a repeating pattern of swirling vortices, caused by a process known as '' vortex shedding,'' which is responsible for the unsteady separation of flow of a fluid aro ...
* Fluid thread breakup * Rayleigh–Bénard convection


Notes


References


Original research papers

* (Original paper is available at: https://www.irphe.fr/~clanet/otherpaperfile/articles/Rayleigh/rayleigh1883.pdf .) *


Other

* * xvii+238 pages. * 626 pages.


External links


Java demonstration of the RT instability in fluids



Experiments on Rayleigh–Taylor instability at the University of Arizona

plasma Rayleigh–Taylor instability experiment at California Institute of Technology
{{DEFAULTSORT:Rayleigh-Taylor instability Fluid dynamics Fluid dynamic instabilities Plasma instabilities