Resonant surface waves and chaotic phenomena

1987 ◽  
Vol 183 ◽  
pp. 543-565 ◽  
Author(s):  
X. M. Gu ◽  
P. R. Sethna
Keyword(s):  
Surface Tension ◽  
Energy Dissipation ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Chaotic Behaviour ◽  
Chaotic Motions ◽  
Chaotic Phenomena ◽  
Rectangular Container ◽  
Effect Of Surface

Surface waves in a rectangular container subjected to vertical oscillations are studied. Effects of energy dissipation along the lines of Miles (1967) and the effect of surface tension are included. Sufficient conditions, for two modes to dominate the motion, are given. The analysis is along the lines of Miles (1984a) and Holmes (1986). A complete bifurcation analysis is performed, and the modal amplitudes and phases are shown to have chaotic behaviour. This result is obtained under assumptions different from those of Holmes (1986). The conclusions regarding chaotic motions are based on a theorem of šilnikov (1970).

On Three-Dimensional Nonlinear Subharmonic Resonant Surface Waves in a Fluid: Part I—Theory

1988 ◽  
Vol 55 (1) ◽  
pp. 213-219 ◽  
Author(s):  
X. M. Gu ◽  
P. R. Sethna ◽  
A. Narain
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Energy Dissipation ◽  
Surface Waves ◽  
Three Dimensional ◽  
Critical Depth ◽  
Transient Phenomena ◽  
Vertical Excitation ◽  
Rectangular Container ◽  
Dimensional Surface

Three-dimensional surface waves in a rectangular container subjected to vertical excitation are studied. The analysis includes the effects of surface tension, energy dissipation, and critical depth. Both steady state and transient phenomena are discussed.

Symmetry-breaking bifurcations in resonant surface waves

1989 ◽  
Vol 199 ◽  
pp. 495-518 ◽  
Author(s):  
Z. C. Feng ◽  
P. R. Sethna
Keyword(s):  
Normal Form ◽  
Symmetry Breaking ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Internal Resonance ◽  
Travelling Waves ◽  
Chaotic Behaviour ◽  
Derived Set ◽  
Parameter Values ◽  
Theoretical Results

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

DECOUPLING THE EFFECT OF SURFACE TENSION AND VISCOSITY ON SPRAY CHARACTERISTICS UNDER DIFFERENT AMBIENT PRESSURES: NEAR-NOZZLE BEHAVIOR AND MACROSCOPIC CHARACTERISTICS

2019 ◽  
Vol 29 (7) ◽  
pp. 629-654
Author(s):  
Zehao Feng ◽  
Shangqing Tong ◽  
Chenglong Tang ◽  
Cheng Zhan ◽  
Keiya Nishida ◽  
...  
Keyword(s):  
Surface Tension ◽  
Spray Characteristics ◽  
Effect Of Surface

Surfactant Impurities Can Explain the Jones-Ray Effect

2018 ◽  
Author(s):  
Timothy Duignan ◽  
Marcel Baer ◽  
Christopher Mundy
Keyword(s):  
Surface Tension ◽  
Electrostatic Potential ◽  
Driving Forces ◽  
Salt Water ◽  
Fundamental Property ◽  
Apparent Contradiction ◽  
Low Salt ◽  
Air Water Interface ◽  
Added Salt ◽  
Effect Of Surface

<div> <p> </p><div> <div> <div> <p>The surface tension of dilute salt water is a fundamental property that is crucial to understanding the complexity of many aqueous phase processes. Small ions are known to be repelled from the air-water surface leading to an increase in the surface tension in accordance with the Gibbs adsorption isotherm. The Jones-Ray effect refers to the observation that at extremely low salt concentration the surface tension decreases in apparent contradiction with thermodynamics. Determining the mechanism that is responsible for this Jones-Ray effect is important for theoretically predicting the distribution of ions near surfaces. Here we show that this surface tension decrease can be explained by surfactant impurities in water that create a substantial negative electrostatic potential at the air-water interface. This potential strongly attracts positive cations in water to the interface lowering the surface tension and thus explaining the signature of the Jones-Ray effect. At higher salt concentrations, this electrostatic potential is screened by the added salt reducing the magnitude of this effect. The effect of surface curvature on this behavior is also examined and the implications for unexplained bubble phenomena is discussed. This work suggests that the purity standards for water may be inadequate and that the interactions between ions with background impurities are important to incorporate into our understanding of the driving forces that give rise to the speciation of ions at interfaces. </p> </div> </div> </div> </div>

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

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