013. Видання НаУКМА

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Browsing 013. Видання НаУКМА by Author "Avramenko, Olha"

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    Deviation of the interface between two liquid half-spaces with surface tension: multiscale approach
    (2024) Avramenko, Olha
    This paper investigates the deviation of the interface between two semi-infinite liquid media under the influence of surface tension and gravity using a multiscale analysis. The initial-boundary value problem is formulated based on key dimensionless parameters, such as the density ratio and the surface tension coefficient, to describe the generation and propagation of wave packets along the interface. A weakly nonlinear model is employed to examine initial deviations of the interface, enabling the derivation of integral solutions for both linear and nonlinear approximations. The linear approximation captures the fundamental structure of forward and backward waves, while nonlinear corrections account for higherorder effects derived through multiscale expansions. These corrections describe the evolution of the wave packet envelope, highlighting the interplay between dispersion, nonlinearity, and surface tension. Integral expressions are provided for both linear and nonlinear solutions, including those illustrating the role of even and odd initial deviations of the interface. Comparisons between linear and nonlinear approximations emphasize their interconnectedness. The linear model defines the primary wave dynamics, while the nonlinear terms contribute higher harmonics, refining the solutions and facilitating stability analysis. The results reveal significant contributions from higher-order harmonics in determining the dynamics of the interface. Furthermore, the study explores the conditions under which the nonlinear envelope remains stable, including constraints on initial amplitudes to prevent instability. This research opens new perspectives for further analysis of stability and wave dynamics at fluid interfaces using symbolic computations. Potential applications include the study of wave behavior under various geometric configurations and fluid properties. The findings contribute to advancing hydrodynamic wave modeling and establish a foundation for future research in this field.