Chaotic mode competition in parametrically forced surface waves

1985 ◽  
Vol 158 ◽  
pp. 381-398 ◽  
Author(s):  
S. Ciliberto ◽  
J. P. Gollub
Keyword(s):  
Fluid Layer ◽  
Chaotic Regime ◽  
Mode Competition ◽  
Sampling Techniques ◽  
Onset Of Chaos ◽  
Chaotic Mode ◽  
The Stability ◽  
Degenerate Modes ◽  
Local Sampling ◽  
Slow Timescale

Vertical forcing of a fluid layer leads to standing waves by means of a subharmonic instability. When the driving amplitude and frequency are chosen to be near the intersection of the stability boundaries of two nearly degenerate modes, we find that they can compete with each other to produce either periodic or chaotic motion on a slow timescale. We utilize digital image-processing methods to determine the time-dependent amplitudes of the competing modes, and local-sampling techniques to study the onset of chaos in some detail. Reconstruction of the attractors in phase space shows that in the chaotic regime the dimension of the attractor is fractional and at least one Lyapunov exponent is positive. The evidence suggests that a theory incorporating four coupled slow variables will be sufficient to account for the mode competition.

The Stability of Natural Convection in an Inclined Fluid Layer in the Presence of AC Electric Field

1996 ◽  
Vol 65 (8) ◽  
pp. 2479-2484 ◽  
Author(s):  
Mohamed A. K. El Adawi ◽  
El Sayed F. El Shehawey ◽  
Safaa A. Shalaby ◽  
Mohamed I. A. Othman
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Fluid Layer ◽  
Ac Electric Field ◽  
Inclined Fluid Layer ◽  
The Stability

Natural Convection in Horizontal Thin-Walled Honeycomb Panels

1973 ◽  
Vol 95 (4) ◽  
pp. 439-444 ◽  
Author(s):  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Layer ◽  
Convection Heat Transfer ◽  
Correlation Equation ◽  
Wave Number ◽  
Equivalent Wave ◽  
Side Walls ◽  
The Stability ◽  
Rayleigh Numbers

This paper presents an experimental study of the stability of and natural convection heat transfer through a horizontal fluid layer heated from below and constrained internally by a honeycomb. Examination of the types of boundary conditions exacted on the fluid at the cell side-walls has shown that there are three limiting cases: (1) perfectly conducting side-walls; (2) perfectly adiabatic side-walls; and (3) side-walls having zero thickness. Experiments described in this paper approach the latter category. The fluid used is air and the honeycomb used is square-celled. Measured critical Rayleigh numbers are found to be intermediate between those applying to cases (1) and (2), and consistent with an “equivalent wave number” of approximately 0.95 times that for case (1). The measured natural convective heat transfer after instability is found to be significantly less than that predicted by the Malkus-Veronis power integral technique. However, it is found to approach asymptotically the heat transfer which would take place through a similar fluid layer unconstrained by a honeycomb. A general correlation equation for the heat transfer is given.

Overstability of a Viscoelastic Fluid Layer Oscillating in a Vertical Periodic Motion and Heated From Below

1979 ◽  
Vol 46 (2) ◽  
pp. 454-456
Author(s):  
S. O. Onyegegbu
Keyword(s):  
Natural Frequency ◽  
Viscoelastic Fluid ◽  
Periodic Motion ◽  
Oscillation Frequency ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
The Stability ◽  
Oscillation Frequencies

This Note examines the effect of vertical periodic motion on the stability characteristics of a viscoelastic fluid layer in a classical Benard geometry. Numerical solutions show that a resonant type behavior which enhances stability occurs at oscillation frequencies near the convective natural frequency of the viscoelastic fluid, while the effect of the periodic motion vanishes as the oscillation frequency gets very large.

The onset of convective instability in a triply diffusive fluid layer

1989 ◽  
Vol 202 ◽  
pp. 443-465 ◽  
Author(s):  
Arne J. Pearlstein ◽  
Rodney M. Harris ◽  
Guillermo Terrones
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Fluid Layer ◽  
Neutral Curve ◽  
Interesting Consequence ◽  
Stability Criteria ◽  
Neutral Curves ◽  
The Stability ◽  
Rayleigh Numbers ◽  
Periodic Bifurcation

The onset of instability is investigated in a triply diffusive fluid layer in which the density depends on three stratifying agencies having different diffusivities. It is found that, in some cases, three critical values of the Rayleigh number are required to specify the linear stability criteria. As in the case of another problem requiring three Rayleigh numbers for the specification of linear stability criteria (the rotating doubly diffusive case studied by Pearlstein 1981), the cause is traceable to the existence of disconnected oscillatory neutral curves. The multivalued nature of the stability boundaries is considerably more interesting and complicated than in the previous case, however, owing to the existence of heart-shaped oscillatory neutral curves. An interesting consequence of the heart shape is the possibility of ‘quasi-periodic bifurcation’ to convection from the motionless state when the twin maxima of the heart-shaped oscillatory neutral curve lie below the minimum of the stationary neutral curve. In this case, there are two distinct disturbances, with (generally) incommensurable values of the frequency and wavenumber, that simultaneously become unstable at the same Rayleigh number. This work complements the earlier efforts of Griffiths (1979a), who found none of the interesting results obtained herein.

Instability of a gravity-modulated fluid layer with surface tension variation

2001 ◽  
Vol 434 ◽  
pp. 243-271 ◽  
Author(s):  
J. RAYMOND LEE SKARDA
Keyword(s):  
Surface Tension ◽  
Fluid Layer ◽  
Modulation Frequency ◽  
Galerkin Approximation ◽  
Neutral Stability ◽  
Modulation Amplitude ◽  
Neutral Stability Curve ◽  
Stability Curve ◽  
The Stability ◽  
Rayleigh Benard

Gravity modulation of an unbounded fluid layer with surface tension variations along its free surface is investigated. The stability of such systems is often characterized in terms of the wavenumber, α and the Marangoni number, Ma. In (α, Ma) parameter space, modulation has a destabilizing effect on the unmodulated neutral stability curve for large Prandtl number, Pr, and small modulation frequency, Ω, while a stabilizing effect is observed for small Pr and large Ω. As Ω → ∞ the modulated neutral stability curves approach the unmodulated neutral stability curve. At certain values of Pr and Ω, multiple minima are observed and the neutral stability curves become highly distorted. Closed regions of subharmonic instability are also observed. In (1/Ω, g1Ra)-space, where g1 is the relative modulation amplitude, and Ra is the Rayleigh number, alternating regions of synchronous and subharmonic instability separated by thin stable regions are observed. However, fundamental differences between the stability boundaries occur when comparing the modulated Marangoni–Bénard and Rayleigh–Bénard problems. Modulation amplitudes at which instability tongues occur are strongly influenced by Pr, while the fundamental instability region is weakly affected by Pr. For large modulation frequency and small amplitude, empirical relations are derived to determine modulation effects. A one-term Galerkin approximation was also used to reduce the modulated Marangoni–Bénard problem to a Mathieu equation, allowing qualitative stability behaviour to be deduced from existing tables or charts, such as Strutt diagrams. In addition, this reduces the parameter dependence of the problem from seven transport parameters to three Mathieu parameters, analogous to parameter reductions of previous modulated Rayleigh–Bénard studies. Simple stability criteria, valid for small parameter values (amplitude and damping coefficients), were obtained from the one-term equations using classical method of averaging results.

Thermal Stability of Two Fluid Layers Separated by a Solid Interlayer of Finite Thickness and Thermal Conductivity

1984 ◽  
Vol 106 (3) ◽  
pp. 605-612 ◽  
Author(s):  
I. Catton ◽  
J. H. Lienhard
Keyword(s):  
Thermal Conductivity ◽  
Fluid Layer ◽  
Heated Surface ◽  
Finite Thickness ◽  
Fluid Layers ◽  
The Stability ◽  
Stability Limits ◽  
Range Of Values ◽  
Two Fluid ◽  
Thermal Stability Of

Stability limits of two horizontal fluid layers separated by an interlayer of finite thermal conductivity are determined. The upper cooled surface and the lower heated surface are taken to be perfectly conducting. The stability limits are found to depend on the ratio of fluid layer thicknesses, the ratio of interlayer thickness to total fluid layer thickness, and the ratio of fluid thermal conductivity to interlayer thermal conductivity. Results are given for a range of values of each of the governing parameters.

Transformation of Liposomes: Mechanical Behavior and Stability

1993 ◽  
Vol 46 (11S) ◽  
pp. S289-S294
Author(s):  
D. Pamplona
Keyword(s):  
Critical Pressure ◽  
Fluid Layer ◽  
Biological Membrane ◽  
Finite Elasticity ◽  
Spherical Shape ◽  
Thin Shells ◽  
Side View ◽  
Front View ◽  
The Stability ◽  
Morphological Transformations

Liposomes are small artificial vesicles of lipid bilayer, wich enclose and are surrounded by water. Morphological transformations in liposomes, starting from a spherical shape, due to changes in the osmotic pressure, have been described in the literature. The first transformation is into a circular biconcave form, afterwards the biconcave side view is maintained, while the front view reveals transformations into elliptical or regular polygonal forms, usually triangular, square or pentagonal. Finite elasticity and the theory of thin shells were used to analyse the behavior of the liposomes under decreasing volume. The biological membrane was considered as a two dimensional fluid layer, exhibiting solid properties to some extent, e.g., elasticity. The stability of the liposmes was studied by using the method of elastic perturbation to obtain the critical pressure for the biconcave transformation and the long liposome tubes. The transformations to elliptical and regular polygonal forms were studied using the linear stability equations of elasticity.

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