Effect of initial conditions on two-dimensional Rayleigh–Taylor instability and transition to turbulence in planar blast-wave-driven systems

2004 ◽  
Vol 11 (11) ◽  
pp. 5278-5296 ◽  
Author(s):  
A. R. Miles ◽  
M. J. Edwards ◽  
J. A. Greenough
Keyword(s):  
Blast Wave ◽  
Initial Conditions ◽  
Taylor Instability ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Driven Systems ◽  
Rayleigh Taylor Instability

scholarly journals TWO-DIMENSIONAL BLAST-WAVE-DRIVEN RAYLEIGH-TAYLOR INSTABILITY: EXPERIMENT AND SIMULATION

2009 ◽  
Vol 696 (1) ◽  
pp. 749-759 ◽  
Author(s):  
C. C. Kuranz ◽  
R. P. Drake ◽  
E. C. Harding ◽  
M. J. Grosskopf ◽  
H. F. Robey ◽  
...  
Keyword(s):  
Blast Wave ◽  
Taylor Instability ◽  
Two Dimensional ◽  
Rayleigh Taylor Instability ◽  
Experiment And Simulation

Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems

2005 ◽  
Vol 12 (5) ◽  
pp. 056317 ◽  
Author(s):  
A. R. Miles ◽  
B. Blue ◽  
M. J. Edwards ◽  
J. A. Greenough ◽  
J. F. Hansen ◽  
...  
Keyword(s):  
Blast Wave ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Driven Systems

scholarly journals Singularities in water waves and Rayleigh–Taylor instability

1991 ◽  
Vol 435 (1893) ◽  
pp. 137-158 ◽  
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Initial Conditions ◽  
Finite Depth ◽  
Finite Amplitude ◽  
Taylor Instability ◽  
Two Dimensional ◽  
Water Wave Problem ◽  
Unphysical Region ◽  
Rayleigh Taylor Instability

This paper is concerned with singularities in inviscid two-dimensional finite-amplitude water waves and inviscid Rayleigh–Taylor instability. For the deep water gravity waves of permanent form, through a combination of analytical and numerical methods, we present results describing the precise form, number and location of singularities in the unphysical domain as the wave height is increased. We then show how the information on the singularity can be used to calculate water waves numerically in a relatively efficient fashion. We also show that for two-dimensional water waves in a finite depth channel, the nearest singularity in the unphysical region has the form as for deep water waves. However, associated with such a singularity, there is a series of image singularities at increasing distances from the physical plane with possibly different behaviour. Further, for the Rayleigh–Taylor problem of motion of fluid over vacuum, and for the unsteady water wave problem, we derive integro-differential equations valid in the unphysical region and show how these equations can give information on the nature of singularities for arbitrary initial conditions. We give indications to suggest that a one-half point singularity on its approach to the physical domain corresponds to a spike observed in Rayleigh-Taylor experiment.

Dripping instability of a two-dimensional liquid film under an inclined plate

2021 ◽  
Vol 932 ◽  
Author(s):  
Guangzhao Zhou ◽  
Andrea Prosperetti
Keyword(s):  
Liquid Film ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Bond Number ◽  
Quasi Equilibrium ◽  
Two Dimensional ◽  
Inclined Plate ◽  
Maximum Value ◽  
Critical Curvature ◽  
Rayleigh Taylor Instability

It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection between curvature and dripping weakens, although the critical curvature remains a useful reference point as it is intimately related to the short length scales promoted by the Rayleigh–Taylor instability. In the absence of flow, when the film is on the underside of a horizontal plate, the concept of a limit curvature is relevant only for small liquid volumes close to a critical value. Otherwise, the drops that form have a smaller curvature and a large volume. The paper also illustrates the peculiarly strong dependence of the dripping transition on the initial conditions of the simulations. This feature prevents the development of phase maps dependent only on the governing parameters (Reynolds number, Bond number, etc.) similar to those available for film flow on the upper side of an inclined plate.

scholarly journals The Inhibition of the Rayleigh-Taylor Instability by Rotation

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Kyle A. Baldwin ◽  
Matthew M. Scase ◽  
Richard J. A. Hill
Keyword(s):  
Coriolis Force ◽  
Rotation Rate ◽  
Initial Conditions ◽  
Taylor Instability ◽  
Numerical Work ◽  
Long Wavelength ◽  
Rate Dependent ◽  
Dense Fluid ◽  
Rayleigh Taylor Instability ◽  
Standard Techniques

Abstract It is well-established that the Coriolis force that acts on fluid in a rotating system can act to stabilise otherwise unstable flows. Chandrasekhar considered theoretically the effect of the Coriolis force on the Rayleigh-Taylor instability, which occurs at the interface between a dense fluid lying on top of a lighter fluid under gravity, concluding that rotation alone could not stabilise this system indefinitely. Recent numerical work suggests that rotation may, nevertheless, slow the growth of the instability. Experimental verification of these results using standard techniques is problematic, owing to the practical difficulty in establishing the initial conditions. Here, we present a new experimental technique for studying the Rayleigh-Taylor instability under rotation that side-steps the problems encountered with standard techniques by using a strong magnetic field to destabilize an otherwise stable system. We find that rotation about an axis normal to the interface acts to retard the growth rate of the instability and stabilise long wavelength modes; the scale of the observed structures decreases with increasing rotation rate, asymptoting to a minimum wavelength controlled by viscosity. We present a critical rotation rate, dependent on Atwood number and the aspect ratio of the system, for stabilising the most unstable mode.

Lattice Boltzmann simulation of the two-dimensional Rayleigh-Taylor instability

1998 ◽  
Vol 58 (5) ◽  
pp. 6861-6864 ◽  
Author(s):  
Xiaobo Nie ◽  
Yue-Hong Qian ◽  
Gary D. Doolen ◽  
Shiyi Chen
Keyword(s):  
Lattice Boltzmann ◽  
Taylor Instability ◽  
Two Dimensional ◽  
Lattice Boltzmann Simulation ◽  
Rayleigh Taylor Instability

Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability

1999 ◽  
Vol 399 ◽  
pp. 1-48 ◽  
Author(s):  
S. B. DALZIEL ◽  
P. F. LINDEN ◽  
D. L. YOUNGS
Keyword(s):  
Spatial Structure ◽  
Internal Structure ◽  
Initial Conditions ◽  
Salt Water ◽  
Concentration Field ◽  
Taylor Instability ◽  
Mixing Zone ◽  
Measured Velocity ◽  
Rigid Barrier ◽  
Rayleigh Taylor Instability

This paper describes an experimental investigation of mixing due to Rayleigh–Taylor instability between two miscible fluids. Attention is focused on the gravitationally driven instability between a layer of salt water and a layer of fresh water with particular emphasis on the internal structure within the mixing zone. Three-dimensional numerical simulations of the same flow are used to give extra insight into the behaviour found in the experiments.The two layers are initially separated by a rigid barrier which is removed at the start of the experiment. The removal process injects vorticity into the flow and creates a small but significant initial disturbance. A novel aspect of the numerical investigation is that the measured velocity field for the start of the experiments has been used to initialize the simulations, achieving substantially improved agreement with experiment when compared with simulations using idealized initial conditions. It is shown that the spatial structure of these initial conditions is more important than their amplitude for the subsequent growth of the mixing region between the two layers. Simple measures of the growth of the instability are shown to be inappropriate due to the spatial structure of the initial conditions which continues to influence the flow throughout its evolution. As a result the mixing zone does not follow the classical quadratic time dependence predicted from similarity considerations. Direct comparison of external measures of the growth show the necessity to capture the gross features of the initial conditions while detailed measures of the internal structure show a rapid loss of memory of the finer details of the initial conditions.Image processing techniques are employed to provide a detailed study of the internal structure and statistics of the concentration field. These measurements demonstrate that, at scales small compared with the confining geometry, the flow rapidly adopts self-similar turbulent behaviour with the influence of the barrier-induced perturbation confined to the larger length scales. Concentration power spectra and the fractal dimension of iso-concentration contours are found to be representative of fully developed turbulence and there is close agreement between the experiments and simulations. Other statistics of the mixing zone show a reasonable level of agreement, the discrepancies mainly being due to experimental noise and the finite resolution of the simulations.

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