Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Pattern formation of parametrically driven surface waves induced by vibration

Esta tesis se centra en la generación de ondas superficiales subarmónicas en fluidos sometidos a vibración forzada en el régimen gravitatorio capilar con líquidos de baja viscosidad. Tres problemas diferentes han sido estudiados: un contenedor rectangular con vibración horizontal, la misma geometría pero con una combinación de vibración vertical y horizontal y un obstáculo completamente sumergido vibrado verticalmente en un contenedor grande. Se deriva una ecuación de amplitud desde primeros principios para describir las ondas subarmónicas con forzamiento parámetrico inducido por la vibración. La ecuación es bidimensional mientras que el problema original es tridimensional y admite un forzamiento espacial no uniforme. Usando esta ecuación los tres sistemas han sido analizados, centrándose en calcular la amplitud crítica, la orientación de los patrones y el carácter temporal de los patrones espaciotemporales, que pueden ser estrictamente subarmónicos o cuasiperiodicos con una frecuencia de modulación temporal. La dependencia con los parámetros adimensionales también se considera. La teoría será comparada con los experimentos disponibles en la literatura. Abstract This thesis focus on the generation of subharmonic surface waves on fluids subject to forced vibration in the gravity-capillary regime with liquids of small viscosity. Three different problems have been considered: a rectangular container under horizontal vibration; the same geometry but under a combination of horizontal and vertical vibration; and a fully submerged vertically vibrated obstacle in a large container. An amplitude equation is derived from first principles that fairly precisely describes the subharmonic surfaces waves parametrically driven by vibration. That equation is two dimensional while the underlying problem is three-dimensional and permits spatially nonuniform forcing. Using this equation, the three systems have been analyzed, focusing on the calculation of the threshold amplitude, the pattern orientation, and the temporal character of the spatio-temporal patterns, which can be either strictly subharmonic or quasi-periodic, showing an additional modulation frequency. Dependence on the non-dimensional parameters is also considered. The theory is compared with the experiments available in the literature.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Remarks on Parametric Surface Waves in a Nonlinear and Non-Ideally Excited Tank

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Remarks on Parametric Surface Waves in a Nonlinear and Non-Ideally Excited Tank

We studied free surface oscillations of a fluid in a cylinder tank excited by an electric motor with limited power supply. We investigated the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Numerical experiments are carried out to present the existence of several types of regular and chaotic attractors. For the first time powers (power of the motor, power consumed by the damping force under fluid free surface oscillations, and a total power) are calculated, investigated, and shown for different regimes, regular and chaotic ones for parametric resonance interactions. [DOI: 10.1115/1.4005844]

Standing surface waves in a dust-contaminated large-area planar plasma source

The effect of charged particulates or dusts on surface wave produced microwave discharges is studied. The frequencies of the standing electromagnetic eigenmodes of large-area flat plasmas are calculated. The dusts absorb a significant amount of the plasma electrons and can lead to a modification of the electromagnetic field structure in the discharge by shifting the originally excited operating mode out of resonance. For certain given proportions of dusts, mode conversion is found to be possible. The power loss in the discharge is also increased because of dust-specific dissipations, leading to a decrease of the operating mode quality factor.

Parametric excitation of high-frequency surface waves in a plasma-metal waveguide structure

The problem concerning the excitation of high-frequency surface waves (SW) propagating across an external magnetic field at a plasma-metal interface is considered. A homogeneous electric pump field is applied in the direction transverse with respect to the plasma-metal interface. Two high-frequency SW from different frequency ranges of existence and propagating in different directions are shown to be excited in this pump field. The instability threshold pump-field values and increments are obtained for different parameters of the considered waveguide structure. The results associated with saturation of the nonlinear instability due to self-interaction effects of the excited SW are given as well. The results are appropriate for both gaseous and semiconductor plasmas.

Surface waves in the presence of external high frequency fields

The system equations of a collisionless, unmagnetized plasma, contained in a box where a high frequency (HF) electric field is incident, are solved in the electrostatic approximation. The surface modes of the plasma in the semi-infinite and box geometry are investigated. In thi high frequency limit, the mode frequencies are not significantly changed by the HF field but their group velocities can be quite different. Two long wavelength low frequency modes, which are not excited in the absence of HF field, are found. These modes are true surface modes (decaying on one wavelength from the surface) unlike the only low frequency ion acoustic mode in the zero field case. In the short wavelength limit the low frequency mode occurs at omega i/ square root 2, omega i being the ion plasma frequency, as a result similar to the case of no HF field.

Surface waves in the presence of external high frequency fields

The system equations of a collisionless, unmagnetized plasma, contained in a box where a high frequency (h.f.1 electric field is incident, are solved in the electrostatic approximation. The surface modes of the plasma in the semi-infinite and box geometry are investigated. In the high frequency limit, the mode frequencies are not significantly changed by the h.f. field but their group velocities can be quite different. Two long wavelength low frequency modes, which are not excited in the absence of h.f. field, are found. These modes are true surface modes (decaying on one wavelength from the surface) unlike the only low frequency ion acoustic mode in the zero field case. In the short wavelength limit the low frequency mode occurs at &/2, oi being the ion plasma frequency, a result similar to the case of no h.f. field.

Surface-waves, stability, and scattering for a lined duct with flow

We consider a straight cylindrical duct with a steady subsonic axial flow and a reacting boundary (e.g. an acoustic lining). The wave modes are separated into ordinary acoustic duct modes, and surface modes confined to a small neighbourhood of the boundary. Many researchers have used a mass-spring-damper boundary model, for which one surface mode has previously been identified as a convective instability; however, we show the stability analysis used in such cases to be questionable. We investigate instead the stability of the surface modes using the Briggs-Bers criterion for a Flügge thin-shell boundary model. For modest frequencies and wavenumbers the thin-shell has an impedance which is effectively that of a mass-spring-damper, although for the large wavenumbers needed for the stability analysis the thin-shell and mass-spring-damper impedances diverge, owing to the thin shell's bending stiffness. The thin shell model may therefore be viewed as a regularization of the mass-spring-damper model which accounts for nonlocally-reacting effects. We find all modes to be stable for realistic thin-shell parameters, while absolute instabilities are demonstrated for extremely thin boundary thicknesses. The limit of vanishing bending stiffness is found to be a singular limit, yielding absolute instabilities of arbitrarily large temporal growth rate. We propose that the problems with previous stability analyses are due to the neglect of something akin to bending stiffness in the boundary model. Our conclusion is that the surface mode previously identified as a convective instability may well be stable in reality. Finally, inspired by Rienstra's recent analysis, we investigate the scattering of an acoustic mode as it encounters a sudden change from a hard-wall to a thin-shell boundary, using a Wiener-Hopf technique. The thin-shell is considered to be clamped to the hard-wall. The acoustic mode is found to scatter into transmitted and reflected acoustic modes, and surface modes strongly linked to the solid waves in the boundary, although no longitudinal or transverse waves within the boundary are excited. Examples are provided that demonstrate total transmission, total reflection, and a combination of the two. This thin-shell scattering problem is preferable to the mass-spring-damper scattering problem presented by Rienstra, since the thin-shell problem is fully determined and does not need to appeal to a Kutta-like condition or the inclusion of an instability in order to avoid a surface-streamline cusp at the boundary change.

Axially excited surface wave antennas /

"Contract No. AF33(616)-310 RDO No. R-112-110 SR-6f2"

Ion-acoustic surface waves on a dielectric-dusty plasma interface

The theory of ion-acoustic surface wave propagation on the interface between a dusty plasma and a dielectric is presented. Both the constant and variable dust-charge cases are considered. It is found that massive negatively charged dust grains can significantly affect the propagation and damping of the surface waves. Application of the results to surface-wave generated plasmas is discussed. © 1998 IEEE.

Nonlinear ion-acoustic surface waves on a dusty plasma

A nonlinear theory for ion-acoustic surface waves propagating at the interface between a dusty plasma and a dielectric is presented. The nonlinear effects are associated with density modulations caused by surface-wave induced anomalous ionization. The negative charge of the massive dust grains is assumed to be constant. It is shown that the effect of the ionization nonlinearity arising from the ion-acoustic surface waves can result in the formation of surface envelope solitons. The wave phase shifts and the widths of the solitons are estimated for typical gas discharge plasmas.