Visualization Investigation of Energy Dissipation Induced by Eddy Currents for a Solitary-Like Wave Passing over Submerged Breakwater Sets

Abstract

Wave attenuation for the purpose of coastal protection has been an important topic in coastal engineering. Wave attenuation in relation to the vortices induced by a solitary-like wave propagating over submerged breakwaters (BWs) is discussed in this paper. A series of hydraulic model experiments was conducted to investigate the occurrence of eddies, the types and combinations of submerged BWs, and related phenomena of the range expansion of vortices. The microscopic changes in the flow field, the variation of eddies, and the distributions of streamlines were analyzed using the particle image velocimetry (PIV) technique. The measured transmission and reflection coefficients, along with the concept of energy conservation, were also examined to support the results. The results indicate that the attenuated wave energy is related to the induced vortices, and show that the total relative vortex energy for rectangular submerged BWs is larger than that for undulating submerged BWs in both the single and composite sets. The magnitude of the maximum vorticity of the undulating BW sets is larger and more concentrated than that of the rectangular BW sets; however, the total vortex energy is slightly smaller owing to the narrower vortex area range.

Directing Shallow-Water Waves Using Fixed Varying Bathymetry Designed by Recurrent Neural Networks

“…Equations ( 9) and (11) are discretized in the 2D space domain and in time domain using the finite difference method. The resulting discretized equations are converted into the recurrent update formulation as Equation ( 5) to establish a wave-equivalent RNN model using the PyTorch machine learning package.…”

“…We take the hyperbolic mild-slope equation for shallow water as an example to illustrate the derivation of the recurrent update equation. Adding the linear viscous damping and the source term in Equation (11), we obtain Equation (15):…”

“…Six different cases are studied using the proposed RNN approach in this section, revealing the directing effects of reflection and refraction of shallow-water waves. Both the simplified shallow-water wave equation (Equation ( 9)) and the hyperbolic mild-slope equation (Equation (11)) are used to develop the equivalent RNN models for training.…”

“…The presence of submerged breakwaters results in varying bathymetry, and it is fundamental to understand the wave-structure interactions. Li et al [11] performed wave flume experiments to study the flow field when a solitary-like wave passed a set of submerged breakwaters. Patil and Karmakar [12], Xue et al [13], and Jafarzadeh et al [14] conducted two-dimensional CFD analyses in the vertical plane to evaluate the wave energy transmission over different designs of submerged breakwaters.…”

The Hydrodynamic Characteristics Induced by Multiple Layouts of Typical Artificial M-Type Reefs with Sea Currents Typical of Liaodong Bay, Bohai Sea

“…To date, the most common methods to investigate the hydrodynamic characteristics of artificial reefs relate to numerical simulations or experimental tests conducted within wind tunnel or flumes, where particle image velocimetry (PIV) techniques can be applied [25][26][27][28][29][30][31]. Previous studies conducted by adopting these methods have highlighted a list of factors that can alter the hydrodynamic characteristics of artificial reefs, and this includes the original flow field and the existing terrain, the location of the new artificial reefs placed, the manufacturing materials, the shape and the structure, the opening ratio and the upstream area of the reefs, as well as the number of elements [32][33][34][35][36][37][38].…”