We develop an efficient high-order boundary-element method with the mixed-Eulerian–Lagrangian approach for the simulation of fully nonlinear three-dimensional wave–wave and wave–body interactions. For illustration, we apply this method to the study of two three-dimensional steep wave problems. (The application to wave–body interactions is addressed in an accompanying paper: Liu, Xue & Yue 2001.) In the first problem, we investigate the dynamics of three-dimensional overturning breaking waves. We obtain detailed kinematics and full quantification of three-dimensional effects upon wave plunging. Systematic simulations show that, compared to two-dimensional waves, three-dimensional waves generally break at higher surface elevations and greater maximum longitudinal accelerations, but with smaller tip velocities and less arched front faces. For the second problem, we study the generation mechanism of steep crescent waves. We show that the development of such waves is a result of three-dimensional (class II) Stokes wave instability. Starting with two-dimensional Stokes waves with small three-dimensional perturbations, we obtain direct simulations of the evolution of both L2 and L3 crescent waves. Our results compare quantitatively well with experimental measurements for all the distinct features and geometric properties of such waves.

The mixed-Eulerian–Lagrangian method using high-order boundary elements, described in Xue et al. (2001) for the simulation of fully nonlinear three-dimensional wave–wave and wave–body interactions, is here extended and applied to the study of two nonlinear three-dimensional wave–body problems: (a) the development of bow waves on an advancing ship; and (b) the steep wave diffraction and nonlinear high-harmonic loads on a surface-piercing vertical cylinder. For (a), we obtain convergent steady-state bow wave profiles for a flared wedge, and the Wigley and Series 60 hulls. We compare our predictions with experimental measurements and find good agreement. It is shown that upstream influence, typically not accounted for in quasi-two-dimensional theory, plays an important role in bow wave prediction even for fine bows. For (b), the primary interest is in the higher-harmonic ‘ringing’ excitations observed and quantified in experiments. From simulations, we obtain fully nonlinear steady-state force histories on the cylinder in incident Stokes waves. Fourier analysis of such histories provides accurate predictions of harmonic loads for which excellent comparisons to experiments are obtained even at third order. This confirms that ‘ringing’ excitations are directly a result of nonlinear wave diffraction.

Epitaxy between isotactic polystyrene (iPS) and isotactic poly(1-butene) (iPBu) has been studied. The epitaxial crystallization of iPS on the oriented form I iPBu film was realized through cold crystallization from its amorphous state at 130 °C for 10 h. The epitaxial crystallization of iPBu on the oriented iPS substrate induced initially by form I iPBu crystals, that is, the vice versa process, was achieved simply by heating the sample coldcrystallized at 130 °C up to 190 °C to melt the iPBu crystals completely and followed by melt crystallization of iPBu. The results show that the epitaxy of iPS on iPBu form I crystals is based on two-dimensional lattice matching, which results in a parallel chain alignment of both polymers. On the other hand, the oriented iPS thin film produced by the form I iPBu ordered film in turn generates still a chain parallel epitaxy of iPBu but in its form II, even though the matching of iPS with form II iPBu is much poorer than with form I iPBu. This demonstrates that polymer epitaxy is not solely caused by geometric matching as widely accepted up to date. In the present case, the form II crystallization of iPBu on the iPS substrate is clearly controlled by the crystallization kinetics, while the chain orientation is associated with less pronounced one-dimensional lattice matching. These results shed more light toward a better understanding of polymer epitaxy.

Thin films of isotactic polybutene-1 (iPBu) with large lathlike flaton form II crystals were prepared by isothermal crystallization from melt at 105 °C. The II−I phase transition of this kind of thin film was investigated by Fourier transform infrared spectroscopy, transmission electron microscopy, and atomic force microscopy (AFM). Spectroscopy results show that the phase transition starts immediately after cooling down to −10 °C. The phase transformation propagates quickly in the first 10 min but then slows down and reaches a plateau by further annealing at this temperature. Another quick transformation process has been realized by heating the related sample to room temperature. This has been associated with the nucleation and crystal growth processes of the phase transition and confirmed here by the morphological study. It has been confirmed by AFM that, at the early stage of II−I phase transition that happened at −10 °C, the formed form I crystals are too small to be visualized by AFM. With increasing aging time at room temperature, some form I iPBu crystals appear mostly at the edges of the flat-on crystalline sheet. These crystals grow further with time until the complete transformation of the individual whole sheet. This provides morphological evidence for the nucleation and crystal growth events during II−I phase transition of iPBu.

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