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1 edition of Rayleigh-Taylor instability of a viscous film overlying a pasive fluid found in the catalog.

Rayleigh-Taylor instability of a viscous film overlying a pasive fluid

David Canright

Rayleigh-Taylor instability of a viscous film overlying a pasive fluid

by David Canright

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  • 16 Currently reading

Published by Naval Postgraduate School, Available from National Technical Information Service in Monterey, Calif, Springfield, Va .
Written in English

    Subjects:
  • VISCOUS FLOW,
  • BOUNDARY LAYER FLOW,
  • EARTH MODELS

  • About the Edition

    To help understand the stability of cold, viscous boundary layers in geophysical contexts such as lava lakes and mantle convection, the following model problem is analyzed: Beneath a shear-free horizontal boundary, a thin layer of very viscous fluid overlies a deep layer of less viscous, less dense fluid. The initial unstable equilibrium is perturbed, and the growth of the disturbance is followed, including the nonlinear effects of large amplitude, by a long-wave analysis. The result shows that, in the final catastrophic growth, the peak thickness of the upper layer approaches infinity inversely proportional to the remaining time. (This conclusion also applies to fluids with power-law rheology.) Thus nonlinear effects greatly enhance growth. Keywords: Earth models. (EDC)

    Edition Notes

    Other titlesNPS-53-89-012.
    StatementDavid Canright, Stephen Morris
    ContributionsMorris, Stephen, Naval Postgraduate School (U.S.). Dept. of Mathematics
    The Physical Object
    Pagination33, [13] p. :
    Number of Pages33
    ID Numbers
    Open LibraryOL25493000M

      The time t P for the large-scale Rayleigh–Taylor instability to reach the roof of the reservoir can be calculated, if its amplitude is small, by solving equation (13) for w(t P) = H − d with. Saturated Rayleigh{Taylor instability of an oscillating Couette lm flow are discussed in the book of Joseph & Renardy (). The instability is a long-wave one, the short waves being damped by surface instability of a viscous lm. The case of a steady linear basic velocity pro le between two plates (plane two-fluid Couette flow) has File Size: 1MB.

    present theory, this instability is of a viscous instability, rather than an inviscid instability. In terms of the present criterion, viscous flows with inflectional velocity profile is certainly unstable. We also notice that the Reynolds number at instability is very low (Re. The Rayleigh–Taylor instability, or RT instability, is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Examples include the behavior of water suspended above oil in the gravity of Earth, mushroom clouds like those from volcanic eruptions and atmospheric nuclear explosions, supernova explosions in which expanding core gas is .

    Direct Numerical Simulations of Rayleigh-Taylor instability, covering the range of Atwood number from to In particular, one of the simulations, at A = and grid size , is the largest fully resolved instability simulation performed to date. Some. The problem of stretching a viscoplastic (yield-stress) thread of a liquid hanging vertically is considered. The length of the thread at later times and the time at which it ruptures is by: 3.


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Rayleigh-Taylor instability of a viscous film overlying a pasive fluid by David Canright Download PDF EPUB FB2

Two cases are treated: the Rayleigh-Taylor instability with a dense viscous film over a half-space of lighter, much less viscous fluid; and a half-space of fluid whose viscosity depends strongly.

To help understand the stability of cold, viscous boundary layers in geophysical contexts such as lava lakes and mantle convection, the following model problem is analyzed: Beneath a shear-free horizontal boundary, a thin layer of very viscous fluid overlies a deep layer of less viscous, less dense : David Canright, Stephen Morris.

Beneath a shear-free horizontal boundary, a thin layer (thickness d 1) of very viscous fluid overlies a deep layer of less dense, much less viscous fluid; inertia and surface tension are negligible.

After the initial unstable equilibrium is perturbed, a long-wave analysis describes the growth of the disturbance, including the nonlinear effects of large by: Approved for public release; distribution is help understand the stability of cold, viscous boundary layers in geophysical contexts such as lava lakes and mantle convection, the following model problem is analyzed: Beneath a shear-free horizontal boundary, a thin layer of very viscous fluid overlies a deep layer of less viscous, less dense : David Canright and Stephen Morris.

The behavior of a viscous fluid film bounded by a wall and a heavier overlying immiscible phase is examined in the limit of small Bond number. Evolution equations governing the behavior of the interface between the two fluids are derived for spatially periodic disturbances and studied by: tension on Rayleigh-Taylor (RT) instability in a fi nite thickness layer of an incompressible viscous fluid bounded above by a denser fluid and below by a rigid impermeable surface have been studied using linear stability analysis.

A relation for the RT instability growth rate is found by calculating the eigenvalues of the stability equation. The effects of viscosity and surface tension on the nonlinear evolution of Rayleigh–Taylor instability of plane fluid layers are investigated.

Full two-dimensional incompressible Navier–Stokes equations and exact boundary equations are solved simultaneously for a precise prediction of this by:   The classical Rayleigh–Taylor instability occurs when two inviscid fluids, with a sharp interface separating them, lie in two horizontal layers with the heavier fluid above the lighter one.

A small sinusoidal disturbance on the interface grows rapidly in time in this unstable situation, as the heavier upper fluid begins to move downwards through the lighter lower by:   where C (∽ 1) is an empirical constant that depends on n, wavelength, and the nature of the density distribution (constant in the layer or linearly decreasing with depth), Δp is the density difference between the layer and the underlying half-space.B is a measure of resistance to deformation, h is the thickness of the layer, g is gravitational acceleration, t is time, and t b is the time at Cited by: Abstract: We study the equations obtained from linearizing the compressible Navier-Stokes equations around a steady-state profile with a heavier fluid lying above a lighter fluid along a planar interface, i.e.

a Rayleigh-Taylor instability. We consider the equations with or without surface tension, with the viscosity allowed to depend on the density, and in both periodic and non-periodic : Yan Guo, Ian Tice.

Plot of interfaces for Rayleigh-Taylor instability of layered flow of an ideal fluid. The Atwood number is unity. I,t: Case of a semi-infinite fluid. Right: A finite fluid layer. Figure is adapted from Verdon et al., ref. D.H. Sharp/An overview of Rayleigh-Taylor instability where they break down for reasons that are often not thoroughly Cited by: On the Rayleigh-Taylor Instability for Two Uniform Viscous Incompressible Flows Fei Jianga,⁄, Song Jianga, Weiwei Wangb aInstitute of Applied Physics and Computational Mathematics, Beijing,China.

bSchool of Mathematical Sciences, Xiamen University, XiamenChina Abstract We study the Rayleigh-Taylor instability for two incompressible immiscible °uids with or without. Abstract. The approximate but analytical solution of the viscous Rayleigh-Taylor instability (RTI) has been widely used recently in theoretical and numerical investigations due to its clarity.

In this paper, a modified analytical solution of the growth rate for the viscous RTI of incompressible fluids is obtained based on an approximate by: 4. For the viscous Rayleigh-Taylor problem with or without surface tension, Guo and Tice [8] proved the linear instability for compressible fluids, and with surface tension Prüss and Simonett [   Localized mechanical thickening of cold, dense lithosphere should enhance its gravitational instability.

Numerical experiments carried out with a layer in which viscosity decreases exponentially with depth, overlying either an inviscid or a viscous half-space, reveal exponential growth, as predicted by linear by: INTRODUCTION Viscous effects in Rayleigh-Taylor instability have not been considered in detail beyond the analytical aspects of the problem, and yet there are interesting situations in which the role of viscosity is quite decisive for the behavior of the Size: KB.

Ever wondered what's going on when you pour milk into your coffee. In this FYFD video, Nicole explains the Rayleigh-Taylor instability that can occur when fluids of different densities mix.

To understand this difference, we analyze analytical solutions and perform numerical 2‐D plane strain experiments for Rayleigh‐Taylor instability of a dense layer overlying a less dense substratum, representing the instability between the mantle lithosphere and the underlying asthenosphere, focusing on the effects of a shear stress free Cited by:   The jetting is excited by the spherical Rayleigh–Taylor instability where the radial acceleration is due to the oscillation of an internal bubble.

We study this jetting and the effect of fluid viscosity experimentally and by: 4. De is a Deborah number, which scales the relaxation time of a fluid process to a characteristic observation time (e.g., Reiner, ).

A general theory for viscoelastic Rayleigh–Taylor instability does not seem to exist, in part because quite different behavior can develop for a variety of limiting assumptions for constitutive by:.

Abstract. A simple, physical approximation is developed for the effect of viscosity for stable interfacial waves and for the unstable interfacial waves which correspond to Rayleigh‐Taylor instability.

The approximate picture is rigorously justified for the interface between a heavy fluid (e.g., water) and a. Quicktip Rayleigh Taylor Instability Using FLIP - Duration: Rayleigh–Bénard convection cells - Duration: Mod Lec Instability and Transition of Fluid Flows - Duration.Basic fluid equations are the main ingredient in the development of theories of Rayleigh–Taylor buoyancy-induced instability.

Turbulence arises in the late stage of the instability evolution as a result of the proliferation of active scales of motion. Fluctuations are maintained by the unceasing conversion of potential energy into kinetic energy.

Although the dynamics of turbulent Cited by: