Like for benardmarangoni instability, manifestations of taylorcouette instability look like manisfestations of rayleighbenard instability. Direct numerical simulation of tilted rayleigh taylor instability tie wei, daniel livescu, ccs2 rayleigh taylor instability rti with tilted initial interface is investigated using direct numerical simulation dns. An example of rayleigh taylor instability we can see in our daily life is the example of a column of liquid which develops corrugations in its shape and ultimately breaks into discrete drops. The rt rayleightaylor instability is the hard reality that icf researchers must accommodate. The shear on the outer cylinder due to rotation of the inner cylinder was also measured for an intermediate range of reynolds number, i.
Rayleightaylor instability rti occurs whenever fluids of different density are. Rayleightaylor instability for the two phase navierstokes equations with surface tension in cylindrical domains. The dominant bubbles and spikes that grow in the initial unstable phase are found to be shredded by the trailing. Revisiting the latetime growth of singlemode rayleigh. Rayleightaylor instability plural rayleightaylor instabilities an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Emphasis changed to understanding turbulent mixing evolution of mixing from random multimode perturbations. Exampletaylorseriesmethod considersolving y y cosx, y01. Selfsimilarity and internal structure of turbulence induced by rayleigh taylor instability by s. Chowdhury abstract for computing sampling variances of the medical expenditure panel survey meps household component estimates, the taylor linearization method is generally used. Selfsimilarity and internal structure of turbulence induced. Experimental investigation of taylor instability using non. Taylor instability of an incompressible liquid, part i of document aecudddd september 4, 1951, pp. Starting with the classical potential flow theory for moving contact surfaces, the discussion extends to various fluid systems describing inhomogeneous, viscous, compressible, and isobaric flows. Turbulent mixing due to rayleightaylor instability american.
Rayleightaylor instability or, for that matter, any other instability of a twolayer couette. Saturated rayleightaylor instability of an oscillating couette lm. The rayleigh taylor instability rti causes small bumps or perturbations on the sphere or interface of the capsule to grow, exponentially fast. What links here related changes upload file special pages permanent link page information wikidata item. It is a dynamic process whereby the two fluids seek to reduce their combined potential energy. Other authors have separated a gravitationally unstable stratification with a barrier that is removed to initiate the flow. The rayleigh taylor rt instability is an important hydrodynamic effect that occurs at the plane interface between two fluids of different densities when a heavy fluid is accelerated into a lighter one. Selfsimilarity and internal structure of turbulence.
Taylor, is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Studies on rti show that this instability is troublesome because it obstructs the realization of icf 3 4. Overview of rayleightaylor instability unt digital library. In fluid dynamics, the taylor number ta is a dimensionless quantity that characterizes the importance of centrifugal forces or socalled inertial forces due to rotation of a fluid about an axis, relative to viscous forces in 1923 geoffrey ingram taylor introduced this quantity in his article on the stability of flow the typical context of the taylor number is in characterization of the. For other aspects of rayleightaylor instability, as well as some recent developments, see. Mathematicaand maple, taylor series can be considered a serious framework for numerical methods. Initially, the delete 1 jackknife method, a replication method, was used to estimate variances. Unlike the icf, where instabilities, especially the rayleightaylor instability, have been studied extensively, the instability study of the spherical pinch has just begun.
Moreover, it is not easy to see with our eyes such instability because it is an internal instability and our eyes dont detect movements of fluid inside. Rayleightaylor instability experiments with precise and. The rayleightaylor instability is a fundamental instability of an interface between two fluids of different densities, which occurs when the light fluid is pushing the heavy fluid. With this method, problems of source instability are eliminated, and the measuring instrument can be very sensitive and does not even need a scale. I would like to thank jim bullard, julio rotemberg, john taylor and john williams for helpful comments, argia sbordone for discussion and for providing the gures, and the nsf for research support through a grant to the nber. Also a file containing a brr replication structure in the form of a set of half. Jan 10, 20 rayleigh taylor instabilities occur when a fluid rests atop another fluid with lesser density, which caused the mixing seen in the video. Direct numerical simulation of tilted rayleightaylor instability tie wei, daniel livescu, ccs2 rayleightaylor instability rti with tilted initial interface is investigated using direct numerical simulation dns. Selfsimilarity and internal structure of turbulence induced by rayleightaylor instability. Rayleightaylor instability between two stable stratifications.
The spherical pinch sp concept is an outgrowth of the inertial confinement model icf. We consider the equations with or without surface tension, with the viscosity allowed to depend on the density, and in both periodic and nonperiodic settings. Rayleightaylor instability and mixing scholarpedia. Rayleightaylor instability fo titel elektronische hochschulschriften. Numerical simulations of the rayleightaylor instability. The temporal evolution of the rayleightaylor rt layer width is an important question in applications, and one metric to gauge the efficacy of various models and numerical simulations. Even at this reduced resolution, the run will take close to an hour to complete. Surface tension in incompressible rayleightaylor mixing. In fluid dynamics, the taylor number ta is a dimensionless quantity that characterizes the importance of centrifugal forces or socalled inertial forces due to rotation of a fluid about an axis, relative to viscous forces. A comparison of taylor linearization and balanced repeated replication methods for variance estimation in medical expenditure panel survey sadeq r.
On the other hand, the onset of instability even below the linear stability threshold when the disturbance has finite amplitude implies that this instability is a subcritical instability. Figures 3d, 3e, and 3f show the pd solutions, in which the decreasing influence function and the penalty force are used to control instabilities. Rayleightaylor instabilities occur when a fluid rests atop another fluid with lesser density, which caused the mixing seen in the video. The rayleightaylor instability, or rt instability after lord rayleigh and g. The rayleightaylor instability among the stars springerlink.
The general rayleightaylor rt instability occurs when a density gradient is subjected to an acceleration by an antiparallel pressure gradient in the presence of perturbations, i. This type of instability for afluid in a gravitational field was first investigated in his famous. The rayleightaylor instability is investigated for the first time in the sp in the present work. Taylor instability can occur whenever the density and pressure gradients are in opposite directions. Monetary policy conduct based on nonlinear taylor rule. The rayleightaylor instability in the spherical pinch. A comparison of taylor linearization and balanced repeated. On the rayleightaylor instability for two uniform viscous incompressible flows fei jianga.
Tshuma are respectively chief economist and vice president, african development bank. An overview of rayleightaylor instability sciencedirect. If the light fluid is above the heavy fluid, the interface between the two is stable because the heavy stuff may be considered to have already fallen and the light stuff has already risen. Saturated rayleightaylor instability of an oscillating. Taylor instability with surface tension, and good agreement in terminal bubble velocity is found when compared with analytic results. Pdf rayleightaylorinstability experiments with elastic. The critical taylor numbers for five different nonnewtonian solutions were determined experimentally by visual observation using the hydrogen bubble technique. The pd results in figure 3c and the fem result in figure 3d are in good agreement, indicating that the penalty method can suppress the instability of nosbpd effectively. The temporal evolution of the rayleigh taylor rt layer width is an important question in applications, and one metric to gauge the efficacy of various models and numerical simulations. Rayleightaylor instability with complex acceleration history. Examples include the behavior of water suspended above oil in the gravity of earth, mushroom clouds like those from volcanic eruptions and atmospheric nuclear. Rayleigh taylor instabilities with animations if a dense viscous layer rests on top of a less dense viscous layer, the lower layer will become unstable and form a rayleigh taylor instability. Shocks with different mach numbers are introduced ahead or behind the rayleightaylor interface, and their effect on the transition to instability is demonstrated.
Youngs2 1 department of applied mathematics and theoretical physics, university of cambridge, silver street, cambridge cb3 9ew, uk 2 awe, aldermaston, reading rg7 4pr, uk. When a heavy liquid pushes on a lighter one, rt mixes the boundary with growing turbulence. Failure to calibrate or check zero of instrument systematic the calibration of an instrument. The code will also have generated a series of vtk files. It can occur under gravity and, equivalently, under an acceleration of the fluid system. In a strophysics, this instability is related to the stellar structure and evolution 5 6. Two variance approximation procedures which account for the complex sample design and compute design effects are replication methods and taylor series linearization. The instability of a heavy fluid layer supported by a light one is generally known as rayleightaylor rt instability. As the fuel capsule compresses, there is an instability which occurs, causing the once spherical geometry to become askew. In the context of the rayleightaylor instability, there are two fluids being considered, one above the other, which are separated by a horizontal plane.
Oct 21, 2011 rayleigh taylor instability rti is the interpenetration of materials that occurs whenever a light fluid pushes on a heavy fluid rayleigh 1883, taylor 1950. An overview of linear and nonlinear rayleightaylor instability. An advantage of vtk files with 3d simulations is that visit, which has extensive visualization capabilities for 3d data, can read athena vtk files directly. Rti can occur when dense plasma is supported against the gravity. Frenkel department of mathematics, university of alabama, tuscaloosa, al 35487, usa received 24 march 1999 and in revised form 10 may 2001 the nonlinear stability of a two. Similar experiments have been performed by andronov et al. Lord rayleigh 1883 was the rst to consider this problem. Electrostatic rayleightaylor mode in electronpositron. Numerical simulation of the threedimensional rayleightaylor. The theory of the rayleightaylor instability of accelerated fluid layers is systematically developed from basic fluid equations. Magneticallyinduced rotating rayleightaylor instability.
The taylor instability is a secondary flow which occurs as a transition from rotary couette flow in the annular gap between two coaxial cylinders of differing diameter when the inner cylinder rotates faster than a critical value. For example, by making an isosurface plot of the density with one level at the end of the calculation select and open rt. Contrary to a finding by others, the present experiment indicates that the critical taylor number is decreased as the concentration is increased. An effective way to control numerical instability of a.
Direct numerical simulation of tilted rayleightaylor instability. The rayleigh taylor instability is investigated for the first time in the sp in the present work. If the horizontal surface of a liquid at rest under gravity is displaced into the form of regular small corrugations and then released, standing oscillatory waves are produced. Classical techniques for investigating the rayleightaylor instability include using compressed gasses, rocketry or linear electric motors to reverse the effective direction of gravity, and accelerate the lighter fluid toward the denser fluid. A mushroomshaped instability develops in time as illustrated on figure 6. Although three different gap sizes were used, only the data for the smallest size can be considered satisfactorily accurate. An impor tant example for this are kelvinhelmholtz and rayleightaylor instabilities, which we discuss in this chapter.
Effects of shock waves on rayleightaylor instabilities. Unlike the icf, where instabilities, especially the rayleigh taylor instability, have been studied extensively, the instability study of the spherical pinch has just begun. Previous studies of rayleigh taylor instabilities addressed the effect of the density structure, the wavelength of the density perturbation between the layers, and the rheology of the layers, on the timing and location of instability onset e. In this paper, we investigate the rayleightaylor instability of a two. On the rayleightaylor instability for two uniform viscous. Experiments and numerical simulations are performed on the rayleightaylor instability with a complex acceleration history g t consisting of consecutive periods of acceleration, deceleration, and acceleration. In 1923 geoffrey ingram taylor introduced this quantity in his article on the stability of flow. During the nonlinear stages, the growth of the rayleightaylor instability is greatly affected by threedimensional effects. Rayleightaylor instability encyclopedia of mathematics. Direct numerical simulation of tilted rayleightaylor. Pdf rayleightaylor instability under an inclined plane.
Fig 1 shows the beginnings of rt driven tendrils from the red heavier water into the lighter, clear water click the here to see the full discussion of this effect rt is a universal instability. Kull, theory of the rayleigh taylor instability more advanced stages of intermixing have been observed by read 10 and by dikarev and zatsepin 11 in the rt case. Direct numerical simulations of rayleightaylor instability. The taylor rule and optimal monetary policy michael woodford princeton university january 2001. An overview of linear and nonlinear rayleightaylor. These fluid dynamics video sequences show two rayleightaylor instability experiments. Pdf we revisit the canonical rayleightaylor instability and investigate the case of a thin film of fluid upon the underside of an inclined plane. Due to the novel nature of this flow and its importance in turbulence modeling, our. Rayleigh taylor instability plural rayleigh taylor instabilities an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. We study the equations obtained from linearizing the compressible navierstokes equations around a steadystate profile with a heavier fluid lying above a lighter fluid along a planar interface, i. We also simulate the immiscible rayleightaylor instability with random initial perturbations. A numerical solution of the two fluid incompressible euler equation is used to study the rayleightaylor instability.
Figure 3e shows the pd results with different hourglass force. We consider the equations with or without surface tension, with the viscosity allowed to depend on the. The rayleightaylor instability, or rt instability is an instability of an interface between two. Testing instability in a predictive regression model with nonstationary regressors volume 31 issue 5 zongwu cai, yunfei wang, yonggang wang. Evidence from south africa mthuli ncube and mthokozisi m. The rayleightaylor instability rti is a fundamental instability of an interface between two fluids of different densities, which occurs when a heavy fluid is superposed over a light fluid in a gravitational field or when a hydrodynamic instability occurs in any accelerating fluid system in which the density and pressure gradients have opposite signs.
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