Fig. 1

An infinite array of periodically floating structures for surface gravity waves (color online)"

Fig. 2

Sketch for waves across the MS with finite periodic pontoons (color online)"

Fig. 3

The fluid domain for a single period of the scatterer array (color online)"

Fig. 4

Convergence test of the cut-off Nsol on wave force: (a) Fe, 1*; (b) Fe, 2*; (c)Fe, 3*. The parameters for the case are L=10 m, A/L=0.01, h/L=2, w/L=0.05, and d/L=0.01. The wave frequencies range from 0.04 rad/s to 3.7 rad/s (color online)"

Fig. 5

Variations of Kr, Kt, and Kr2+Kt2 versus dimensionless wave 2L/λ. Case parameters are L=10 m, A/L=0.01, h/L=2, w/L=0.05, d/L=0.01, and N=3 (color online)"

Fig. 6

Variations of reflection coefficient Kr against 2L/λ. Case parameters are L=25 m, h/L=0.4, w/L=0.2, d/L=0.1, A/L=0.04, and N=3 (color online)"

Fig. 7

Variations of reflection and transmission coefficients versus dimensionless wave 2L/λ for the increased number of pontoons: (a) N=1; (b) N=2; (c) N=4; (d) N=6; (e) N=8; (f)N=10. The parameters for this case are L=10 m, A/L=0.01, h/L=2, w/L=0.05, and d/L=0.01 (color online)"

Fig. 8

Instantaneous wave elevation for an increased number of pontoons at wavelength 2L/λ=2 for different numbers of pontoons: (a) N=1; (b) N=2; (c) N=4; (d) N=10. The vertical grey lines represent the location of pontoons (color online)"

Fig. 9

Band structures for the MS with infinite periodic arrays of pontoons. The parameters for this case are L=10 m, A/L=0.01, h/L=2, w/L=0.05, and d/L=0.01. The wave frequencies range from 0.04 rad/s to 3.7 rad/s (color online)"

Fig. 10

Effects of the pontoons draft on (a) wave reflection, (b) wave transmission, and (c) bandgaps. Effects of the pontoons width on (d) wave reflection, (e) wave transmission, and (f) bandgaps. The parameters for this case are L=10 m, A/L=0.01, and h/L=2. Pontoon width w/L=0.05 for (a), (b), and (c), and pontoon draft d/L=0.01 for (d), (e), and (f). The wave frequencies range from 0.04 rad/s to 3.7 rad/s (color online)"

Fig. 11

(a) Water waves over bottom-mounted periodic bars. (b) Water waves across floating periodic pontoons (color online)"

Fig. 12

Reflection coefficients of the wave across floating periodic pontoons and bottom-mounted periodic bars (color online)"

Fig. 13

A diagram of the 2D numerical wave tank model (color online)"

Fig. 14

Mesh generation details of the wave tank (color online)"

Fig. 15

Comparisons of linear analytical results and CFD results: (a) reflection coefficients; (b) transmission coefficients. Model parameters for calculation are A=0.05 m, h=2 m, L/h=1.5, d/h=0.1, w/h=0.1, and N=3 (color online)"