This study presents a unique data set that combines measurements of velocities and void fraction under an unsteady deep water plunging breaker in a laboratory. Flow properties in the aerated crest region of the breaking wave were measured using modified particle image velocimetry (PIV) and bubble image velocimetry (BIV). Results show that the maximum velocity in the plunging breaker reached 1.68C at the first impingement of the overturning water jet with C being the phase speed of the primary breaking wave, while the maximum velocity reached 2.14C at the beginning of the first splash-up. A similarity profile of void fraction was found in the successive impinging and splash-up rollers. In the highly foamy splashing roller, the increase of turbulent level and vorticity level were strongly correlated with the increase of void fraction when the range of void fraction was between 0 and 0.4 (from the trough level to approximately the center of the roller). The levels became constant when void fraction was greater than 0.5. The mass flux, momentum flux, kinetic energy, potential energy, and total energy were computed and compared with and without the void fraction being accounted for. The results show that all the mean and turbulence properties related to the air-water mixture are considerably overestimated unless void fraction is considered. When including the density variation due to the air bubbles, the wave energy dissipated exponentially a short distance after breaking; about 54% and 85% of the total energy dissipated within one and two wavelengths beyond the breaking wave impingement point, respectively.

This paper presents laboratory measurements of turbulent flow fields and void fraction in deep‐water plunging breaking waves using imaging and optical fiber techniques. Bubble‐size distributions are also determined based on combined measurements of velocity and bubble residence time. The most excited mode of the local intermittency measure of the turbulent flow and its corresponding length scale are obtained using a wavelet‐based method and found to correlate with the swirling strength and vorticity. Concentrated vortical structures with high intermittency are observed near the lower boundaries of the aerated rollers where the velocity shear is high; the length scale of the deduced eddies ranges from 0.05 to 0.15 times the wave height. The number of bubbles with a chord length less than 2 mm demonstrates good correlation with the swirling strength. The power‐law scaling and the Hinze scale of the bubbles determined from the bubble chord length distribution compare favorably with existing measurements. The turbulent dissipation rate, accounting for void fraction, is estimated using mixture theory. When void fraction is not considered, the turbulent dissipation rate is underestimated by more than 70% in the initial impinging and the first splash‐up roller. A significant discrepancy of approximately 67% between the total energy dissipation rate and the turbulence dissipation rate is found. Of this uncounted dissipation, 23% is caused by bubble‐induced dissipation.

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Laboratory measurements of turbulent flow and shear stresses in a surf zone under monochromatic breaking waves in a large‐scale wave flume are presented. Waves with various surf similarity parameters were generated to break at nearly identical water depths over a 1/100 mild slope. Free surface elevations were measured along the plane beach. Velocities in a water column located at the breaking region were measured by acoustic Doppler velocimeters. Results from wave shoaling coefficient, breaking index, and images are inconsistent with the breaker type categorizations from the surf similarity parameter. This suggests that a modification of the surf similarity parameter for very mild slopes may be necessary. For the plunging breakers, the ensemble‐averaged results indicate that intense turbulence kinetic energy was initially generated by large eddies at the surface then transported to the bottom frequently. The instantaneous results demonstrate that the intermittency of turbulence kinetic energy near the bed was caused by large eddies generated by wave overturning and relatively smaller obliquely descending eddies. Moreover, the magnitude of the wave shear stress (WSS) is one order of magnitude larger than that of the turbulent shear stress, indicating that the effects of the bottom slope, wave breaking, and bed friction are significant in the surf zone. The sign of the time‐averaged WSS switched between positive and negative, depending on the occurrences of phase lag and phase lead of the vertical coherent velocity. It suggests that a change may be required in Zou et al.'s (2006, https://doi.org/10.1029/2005JC003300) theory on the formulation of wave‐breaking induced WSS.

The Hall-Petch relation in aluminium is discussed based on the strain gradient plasticity framework. The thermodynamically consistent gradient-enhanced flow rules for bulk and grain boundaries are developed using the concepts of thermal activation energy and dislocation interaction mechanisms. It is assumed that the thermodynamic microstresses for bulk and grain boundaries have dissipative and energetic contributions, and in turn, both dissipative and energetic material length scale parameters are existent. Accordingly, two-dimensional finite element simulations are performed to analyse characteristics of the Hall–Petch strengthening and the Hall–Petch constants. The proposed flow rules for the grain boundary are validated using the existing experimental data from literatures. An excellent agreement between the numerical results and the experimental measurements is obtained in the Hall–Petch plot. In addition, it is observed that the Hall–Petch constants do not remain unchanged but vary depending on the strain level.