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Examines the coupling between the adjacent odd and even modes of water waves using perturbation methods. Development of a criterion for predicting wave type transition; Representation of waves by superposition of standing waves; Identification of amplitude equations governing the slow time dynamics of the amplitude of the odd and even modes.

Discusses the use of the boundary element method combined with the fourth-order Runge-Kutta scheme as time integrator to simulate the dynamics of an acoustically levitated axisymmetric liquid drop. Study of the drop dynamics in an acoustic field in terms of the shape oscillation and translational motion of the drop.

Studies the translational instability of an oscillating bubble. Perturbation analysis; Derivation of amplitude equations; Insignificance of integral relations for motions of bubbles in an infinite perfect liquid; Intimate coupling between the translational motions and amplitudes.

A linear perturbation theory is developed to investigate the interface instabilities of a radially-expanding, liquid jet in cylindrical geometries. The theory is applied to rapidly spreading droplets upon collision with solid surfaces as the fundamental mechanism behind splashing. The analysis is based on the observation that the instability of the liquid sheet, i.e., the formation of the fingers at the spreading front, develops in the extremely early stages of droplet impact. The shape evolution of the interface in the very early stages of spreading is numerically simulated based on the axisymmetric solutions obtained by a theoretical model. The effects that factors such as the transient profile of an interface radius, the perturbation onset time, and the Weber number have on the analysis results are examined. This study shows that a large impact inertia, associated with a high Weber number, promotes interface instability, and prefers high wave number for maximum instability. The numbers of fingers at the spreading front of droplets predicted by the model agree well with those experimentally observed. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]