In ocean engineering and coastal environmental studies, local scour around a submerged structure is a typical issue, which is affected by the inclination of the structure. To investigate the effect of inclination directions and angles on flow structure and the bed morphology, a three-dimensional numerical model of a submerged inclined cylinder was established. In this model, the hydrodynamics are solved from the RANS (Reynolds-averaged Navier–Stokes) equations closed with the RNG k-ε turbulence model, while the bed morphology evolution is captured by the sediment transport model. In the case of vertical-cylinder scour, the simulation results agree well with existing laboratory experiments. In the cases of inclined-cylinder scour, the results show that the inclination direction not only changes the intensity and the location of the downflow but also modulates the pattern of the horseshoe vortex in front of the cylinder, thus influencing the local scour depth and the morphology of the bed. Compared with the case of vertical cylinder, the scour around an upstream-inclined cylinder is deeper, mainly due to the enhancement of downflow in front of the cylinder. The scour around a downstream-inclined cylinder is shallower and broader due to the weakened downflow and accelerated incoming flow. The maximum scour depth decreases with the inclination angle in the downstream-inclination case. In the upstream-inclination case, the maximum scour depth does not vary monotonously with the inclination angle, which results from a competitive effect of the horseshoe vortex and downflow in the front of the cylinder.

The safety of coastal structures is a growing global concern due to the combined effects of strong tides and river flow. In this study, the local scour around cylinders under the influence of tides combined with river flows was investigated numerically. When only tidal current is considered, the distribution of vorticity and excess shear stress on the bed varies periodically with the inflow velocity. The scour depth gradually increased. When coupling the river flow and tidal current, the scour depth on the river side is 1.3 times deeper than that on the tide side; the relative scour depth (the ratio of scour depth to pile diameter, S/D) deepened linearly with the increase of river flow intensity. In the river–tide-coupled condition, the impact of river flow on scour is greater under fixed-bed conditions than under movable-bed conditions. Under fixed-bed conditions, the maximum scour depth in the river–tide-coupled case is 3.94 times larger than that in the tide case. The relative scour depth gradually decreased with the increase in the relative diameter of the cylinder. The scour hole becomes more asymmetric with the increased cylinder diameter. The scour process became slower and the scour rate was smaller when tidal periods increased. The findings supplement the mechanism of local scour under river–tide coupling and provide guiding significance for pile foundation protection in an estuary.

The structural breakup and recovery of coastal mud are closely related to wave propagation, mud transportation, and coastal morphology evolution. Due to the influence of climate, topography, and other factors, the wave frequency in marine environments is more variable than fixed. To investigate the mud structural breakup and recovery process under oscillatory shear loads with different frequencies, a series of oscillatory rheological experiments of the coastal mud collected from the tidal flats of Zhairuoshan Island, Zhejiang province, China, were carried out. The results revealed that the structural breakup of coastal mud had a two-step transition process. The fluidization occurs more rapidly at higher frequencies, but the influence of frequency on the two yield stresses is limited. In addition, frequency has a complex effect on the structural recovery of coastal mud. The normalized equilibrium storage modulus (G_∞′/G₀′) does not change monotonically with frequency. Moreover, the viscosity quickly approaches equilibrium when a shear load is applied. After that, when a low-frequency load is applied, G_∞′/G₀′ is no longer related to the pre-shear duration. However, when a high-frequency load is applied, G_∞′/G₀′ of the mud sample pre-sheared for 500 s is significantly larger than that of the sample pre-sheared to the minimum viscosity. This study is anticipated to provide reference and supplementary test data for understanding the interaction between waves of different frequencies and muddy seabed.

Modeling the rheological response of coastal mud under oscillatory shear loading is essential for understanding wave-mud interactions and the dynamics of muddy seabeds. Recent studies have shown that mud exhibits a characteristic two-step yielding process. However, existing two-step yielding models have difficulty of capturing the evolution of viscoelastic behavior during the yielding process under oscillatory shear loading. Based on rheological experiments, this study developed a rheological model for the two-step yielding behavior of coastal mud using fundamental elements of viscoelastoplastic mechanics. The corresponding rheological response of the model under oscillatory shear loading is then derived analytically. In the solid state, the model reduces to a Kelvin–Voigt model; in the solid–fluid transition state, it reduces to two Kelvin–Voigt elements connected in series; and in the fluid-like state, it reduces to a Jeffreys model. Empirical relationships among the model parameters, the two yield stresses, and solid volume fraction were established for the tested mud. The model was further evaluated using published data. Results show that the proposed model captures the main features of the rheological response of coastal mud under oscillatory shear loading. This study provides scientific support for the mechanistic characterization of the oscillatory rheological behavior of coastal mud and for subsequent investigations of wave-mud interaction.