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Resonant response of water waves in a narrow gap, the so-called gap resonance, is a hydrodynamic phenomenon with practical applications. When coupled to body motions, the physics becomes rather complicated, involving body motions, fluid resonance and damping that determines the response amplitude. Gap resonances between two identical elongated bodies, with one held fixed and the other floating, are investigated experimentally for unidirectional waves with broadside incidence. Transient wave groups with different maximum surface elevations are generated, to examine the nonlinear physics. Sub- and super-harmonics, which can be substantially larger than the linear component, are observed in the responses. When going from the diffraction problem (both bodies fixed) to the coupled problem (allowing one body to move), the gap responses are significantly amplified, i.e. by a factor of 2. The first resonant mode that dominates the diffraction problem disappears in the coupled problem. A new resonant mode, which is shown to arise from body motions, is excited inside the gap through nonlinear processes. This mode features a double-humped ‘camel-back’ shape, leading to remarkably large responses. The floating body is observed to oscillate in sway with significant amplitudes at two distinct natural frequencies that are far apart. This is of great interest for the design of mooring lines connecting the two bodies, as it appears to cause resonances at the wave frequencies in addition to the low frequencies. A semi-analytical model is developed to investigate the multiple natural frequencies in sway, yielding further insight into gap resonances.
Water wave resonance between two side-by-side vessels is a multimode resonant hydrodynamic phenomenon with low damping. The potential flow damping and viscous damping inside the gap play a significant role, influencing the amplitudes of the gap resonances. The frequencies of the gap modes can be well predicted by linear potential flow theory, while much effort has been made to explore the nature of the viscous damping. A series of experiments is conducted to explore the temporal (Zhao et al., Journal of Fluid Mechanics, vol. 812, 2017, 905–939) and spatial structure (Zhao et al., Journal of Fluid Mechanics, vol. 883, 2020, A22) of the resonant responses along the gap. Ultimately, it is of practical interest to understand the response statistics along the gap in random seas, to facilitate decision making for safe offshore operations. Following our previous studies which focused on new physics, here we identify the design waves that produce the most probable maximum responses under unidirectional random linear wave excitation. This is achieved through an efficient prediction model within linear theory. Combining the experimental data and linear potential flow calculations, we provide the lower and upper bounds of gap responses, bracketing possible responses at field scale. The statistical model is expected to be of practical importance for offshore operations.
The spatial and temporal structure of the resonant fluid response in a narrow gap (the so-called gap resonance) between two identical fixed boxes is investigated experimentally. Transient wave groups are used to excite the gap resonance from different wave approach directions. This shows a strong beating pattern and a very long duration, reflecting that gap resonance is a multi-mode resonant and weakly damped phenomenon. For head sea excitation the linear transfer function of the $m=2$ gap mode is as significant as that of the $m=1$ mode. Gap resonance can be driven through different mechanisms, e.g. linear excitation and a nonlinear frequency-doubling process. Significant wave group structure is shown in the gap, and the group structure is more distinct in the case with frequency doubling, i.e. long wave, excitation. Then it is clearer visually that the groups originate at the end of the gap, propagate along the gap and are then partially reflected from the other end. The groups within the gap are very clear because the group velocity is close to constant for the first few gap resonance modes, and much smaller than that for free waves on the open sea. In contrast, the phase speed of waves in the gap is larger than that for free waves outside. Only in the limit of short waves do the group velocity and phase speed of the gap modes tend to those of deep-water free waves. The group and phase speeds from these experiments match well the theoretical forms given by Molin et al. (Appl. Ocean Res., vol. 24 (5), 2002, pp. 247–260), albeit for a slightly different box cross-sectional shape.
To compare various food-frequency questionnaires (FFQs) used in nutritional studies in China for various purposes.
In Study 1, a simplified FFQ with 17 questions on food was used in a large rural study. In Study 2, a questionnaire consisting of 84 questions on food consumption of 16 food categories was used in a study comparing dietary consumption data and various health indicators of elderly people in four geographical areas in China. In Study 3, a questionnaire with 149 items in 17 food categories is being validated by comparison with data obtained by repeated 24-hour recalls.
Study 1 was carried out in one southern site and a northern site in 1996 to 1997. Study 2 was conducted in four different geographical sites in 1998. The on-going study, Study 3, has been carried out in Jiangsu and Beijing since 1999.
Study 1 included 12 234 rural Chinese adults aged 40 years. There were 546 elderly people in Study 2. Study 3 is collecting data from 300 healthy adults.
The results of food consumption and nutrient intakes from Study 1 were comparable with those obtained from a previous household dietary survey, in which sensible correlations between diet and diseases were also found. In Study 2, the dietary data from the four geographical areas showed significant differences in food and nutrient intakes among the different areas. The validation of the new FFQ in Study 3 is still going on.
The FFQ is a useful method for the collection of individual food consumption information. The above FFQ forms could be used in studies with different purposes, especially in studying the relationship between diet, nutrition and chronic diseases.