Effects of Water Depth on the Performance of Geotextile-Armored and Vegetated Submerged Breakwaters

Water depth substantially affects wave transformation over hybrid submerged breakwaters, yet the incremental effects of geotextile armoring and crest vegetation remain insufficiently understood. Experiments were conducted in the 50.0 m long, 0.8 m wide, and 1.2 m high wave flume at the Hydraulic and Harbor Engineering Laboratory of Tongji University. A hard submerged breakwater (HSB), a geotextile-armored submerged breakwater (GSB), and a vegetation-integrated ecological submerged breakwater (ESB) with identical core geometry were compared. Six irregular-wave conditions with H₀ = 0.06–0.16 m and T_p = 1.4–2.2 s were tested at h = 0.50 m, corresponding to an incident Ursell number range of U_ri = 2.97–27.26. Three still-water depths, h = 0.44, 0.50, and 0.56 m, were examined under H₀ = 0.12 m and T_p = 1.8 s, corresponding to a relative crest-submergence range of δ_c = $d_{\mathrm{c}}/\overline{H_{\mathrm{s},1}}$ = 0.33–1.38, where d_c is the still-water depth above the breakwater crest and $\overline{H_{\mathrm{s},1}}$ is the measured incident significant wave height at W1. Wave transformation, relative mean water-level adjustment, bulk wave coefficients, coefficient-based energy partition, wave spectra, and harmonic bicoherence were examined. With increasing U_ri, the energy partition shifts from transmission toward residual energy loss, while reflection remains secondary. Adding crest vegetation to the GSB reduces the transmitted energy fraction, T = K_t², where K_t is the wave-transmission coefficient defined as the ratio of transmitted to incident significant wave height, by an average of 5.2 percentage points over the tested U_ri range, whereas the tested partially exposed GSC armor alone produces no systematic attenuation improvement relative to the HSB. Increasing δ_c increases transmission while reducing reflection, residual energy loss, and relative mean water-level contrast. The incremental vegetation effect is non-monotonic and is greatest at d_c/l_v = 0.67, where d_c is the still-water depth above the breakwater crest and l_v is the upright vegetation blade length. Mean squared harmonic bicoherence, defined as the average squared bicoherence over the selected harmonic-coupling frequency-pair region, is consistently higher at the immediate lee-side gauge than at the seaward gauge, indicating enhanced coherent quadratic phase coupling among harmonic frequency components during wave transformation across the breakwater; this lee-side coupling generally weakens with increasing δ_c. Overall, relative crest submergence governs not only bulk attenuation but also the associated mean water-level and nonlinear phase-coupling responses, while crest vegetation provides a more consistent attenuation benefit than the tested GSC armor alone.