Sharif Digital Repository

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 recent laboratory and field observations, this paper reports the first quantitative measurements of the stabilization phase of interfacial instability in a two-layer fluid in surface wave motion. The instability results from the formation of a resonant triad between the surface wave and noise-level sub-harmonic interfacial waves. To exclude the effects of interfacial mixing on the interaction, the experiments were carried out with immiscible fluids. Carrying out a resonant interaction analysis to the third order of nonlinearity using a Lagrangian formulation, we also show for the first time that the three-wave resonance is inherently accompanied by a harmonic four-wave resonant... 

In this paper, we consider resonant interaction between a surface wave and sub-harmonic interfacial waves forming a two-dimensional pattern at the interface between two fluid layers. The resulting interfacial pattern changes both in time and space. An image processing technique is proposed to extract information about the evolution of the component interfacial waves in a wave flume. The technique proved to give accurate and consistent results when applied to different stages of the interaction. The experimental measurements were used to verify the theoretical predictions. The method can be used for detection of some other wave motions  

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.... 

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...