Sharif Digital Repository

The results of a flume investigation of surface wave motion over a fluidized bed are presented. It is shown that a resonant wave interaction between a surface wave and two interfacial waves at the interface of the fresh water and the fluidized bed is a strong mechanism for instability of the interface and the subsequent mixing of the layers. The interfacial waves are subharmonic to the surface wave and form a standing wave at the interface. The interaction is investigated theoretically using a fully viscous interaction analysis. It is shown that surface wave height and viscous effects are the determining factors in the instability mechanism. The results indicate that the net effect of... 

This paper is concerned with an analysis of image processing data to identify interfacial waves at the interface between two fluid layers in a laboratory flume. The interfacial waves are excited through a non-linear resonant interaction with a surface wave traveling in a wave flume filled with a two-layer fluid. A spatial harmonic analysis is proposed to extract information about the nonlinear evolution of the constituent waves from the interface oscillation data. The analysis is capable of handling different stages of the resonance in the wave flume and gives accurate and consistent results on time variations of the wave amplitudes. Contrary to a temporal harmonic analysis, the proposed... 

Motivated by environmental impacts of surface-wave induced mixing of fluid mud with clear water in nearshore areas, this paper presents quantitative measurements of excitation of interfacial waves over a bed mud layer by a surface wave in a wave flume. After an initial fluidization process, a quasi-standing interfacial wave comprised of four interfacial waves was observed at the interface as a result of a resonant wave interaction with the surface wave. The interfacial waves were subharmonic to the surface wave and traveled at the maximum possible angle from it. The growth rate and kinematic properties of the interfacial waves were measured, and good agreement with theoretical predictions of... 

A third-order asymptotic analysis is conducted to study the three-dimensional resonant interaction between a monochromatic progressive surface wave and two oblique interfacial waves in an open, lightly viscous, two-layer fluid of intermediate depth. By solving the evolution equations of the waves, the short- and long-term behaviors of the interfacial waves are studied. The analysis provides a correction to the second-order theory. The results indicate that the third-order analysis predicts a much lower limit on the growth of the interfacial waves than the second-order theory. Furthermore, in the long term, viscous effects cause the interfacial wave amplitudes to approach a constant value.... 

The results of a flume experiment and a theoretical study of surface wave motion over a fluidized bed are presented. It is shown that a resonant wave interaction between a surface wave and two interfacial waves at the interface of the fresh water and the fluidized bed is a strong mechanism for instability of the interface and the subsequent mixing of the layers. The interfacial waves are subharmonic to the surface wave and form a standing wave at the interface. The interaction is investigated theoretically using a viscous interaction analysis. It is shown that surface wave height and viscous effects are the determining factors in the instability mechanism. The results indicate that the net... 

Higher-order effects in three-wave resonant interaction of a surface wave, with a pair of interfacial waves in a two-layer fluid, are studied theoretically. Following an initial rapid growth, the interfacial waves approach a steady state of constant amplitude. An explicit solution is presented for transition to the ultimate state of the interaction. It is shown that for interaction in a wave flume, it is necessary to include a 2nd pair of the interfacial waves, resulting from a reflection of the original pair in the analysis. The effects of different parameters on the dynamics of the interaction are investigated. The results indicate that a faster initial growth does not necessarily lead to... 

Resonant interaction between one surface wave and two oblique interfacial waves is analyzed in a three dimensional system of a finite-depth, two-layer fluid. A third order perturbation analysis is carried out to obtain the evolution equations of the waves amplitudes. Taking the waves amplitudes as the perturbation small parameter, the evolution equations of the waves are solved simultaneously to obtain the short and long term behavior of the interfacial waves. In contrast to the second order analysis, the current analysis shows that after an initial exponential growth period, the interfacial waves stop growing and stabilize. Furthermore, the influences of surface wave frequency, density... 

We derive a new non-linear two dimensional model for melt flows and interface instability in aluminum reduction cells. This model is based on non-linear de St. Venant shallow water equations and contains the main features of an aluminum reduction cell. In this model we consider linear friction terms but in a new way that has not been considered in previous works. Our results are in good agreement with the results of simulation of viscous flow. This model is applicable both in determination of melt flows in molten aluminum and cryolite layers and also in finding the extreme limit for stability of interfacial waves in an aluminum reduction cell