Accuracy of depth-integrated nonhydrostatic wave models

Depth-integrated nonhydrostatic models have been wildly used to simulate propagation of waves. Yet, there lacks a well-documented theoretical framework that can be used to assess the accuracy and scope of applications of these models and the related numerical approaches. In this work, we carry out Stokes-type Fourier and shoaling analyses to examine the linear and nonlinear properties of a popular one-layer depth-integrated nonhydrostatic model derived by Stelling and Zijlema (2003). The theoretical analysis shows that the model can satisfactorily interpret the dispersity for linear waves but presents evident divergence for nonlinear solutions even when kd → 0. A generalized depth-integrated nonhydrostatic formulation using arbitrary elevation as a variable is then derived and analyzed to examine the effects of neglecting advective and diffusive nonlinear terms in the previous studies and explore possible improvements in numerical solutions for wave propagation. Compared with the previous studies, the new generalized formulation exhibits similar dispersion relationship and improved shoaling effect. However, no significant improvement is presented for the nonlinear properties, indicating that retaining neglected nonlinear terms may not significantly improve the nonlinear performance of the nonhydrostatic model. Further analysis shows that the nonlinear properties of the depth-integrated nonhydrostatic formulation may be improved by defining variables at one-third of the still water level. However, such an improvement comes at the price of decreasing accuracy in describing dispersion and shoaling properties

A new multilayer nonhydrostatic formulation for surface water waves

This work presents a new multilayer nonhydrostatic formulation for surface water waves. The new governing equations define velocities and pressure at an arbitrary location of a vertical layer and only contain spatial derivatives of maximum second order. Stoke-type Fourier and shoaling analyses are carried out to scrutinize the mathematical properties of the new formulation, subsequently optimizing the representative interface and the location to define variables in each layer to improve model accuracy. Following the analysis, the one-layer model exhibits accurate linear and nonlinear characteristics up to kd = I, demonstrating similar solution accuracy to the existing second-order Boussinesq-type models. The two-layer model with optimized coefficients can maintain its linear and nonlinear accuracy up to kd = 4I, which boasts of better solution accuracy a larger application range than most existing fourth-order Boussinesq model and two-layer Boussinesq models. The three-layer model presents accurate linear and nonlinear characteristics up to kd = 10Ï, effectively removing any shallow water limitation. The current multilayer nonhydrostatic water wave model does not predefine the vertical flow structures, and more accurate vertical velocity distributions can be obtained by considering the velocity profiles in coefficient optimization

Higher-Order DCA Attacks on White-Box Implementations with Masking and Shuffling Countermeasures

On white-box implementations, it has been proven that differential computation analysis (DCA) can recover secret keys without time-costly reverse engineering. At CHES 2021, Seker et al. combined linear and non-linear masking protections (SEL masking) to prevent sensitive variables from being predicted by DCA. At Eurocrypt 2021, Biryukov and Udovenko introduced a public dummy shuffling construction (BU shuffling) to protect sensitive functions. In this paper, we extend higher-order DCA (HO-DCA) to higher-degree context for exploiting the vulnerabilities against the state-of-the-art countermeasures. The data-dependency HO-DCA (DDHO-DCA), which is proposed at CHES 2020, is improved to successfully recover the correct key of SEL masking. In specific, our improved DDHO-DCA can also enhance the attack result of #100 which is the third winning challenge in WhibOx 2019. Since the XOR phase plays the same role as linear masking, we prove that a specific BU shuffling is vulnerable to HO-DCA attacks. Furthermore, we demonstrate that the combination of SEL masking and the specific BU shuffling still cannot defeat our higher-degree HO-DCA and improved DDHO-DCA attacks

Analytic study on long wave transformation over a seamount with a pit

In this paper, an analytic solution is derived for linear long waves scattering over a submarine seamount landform with a pit. The seamount is axisymmetric with a pit on the top. The water depth is defined by a trinomial function in the radial direction. The governing linear shallow water equation for long waves is expressed in the polar coordination, which is solved through separation of variables. As the topography is axisymmetric, solutions can be written as Fourier-cosine series. Waves over the seamount are expressed using Frobenius series expansion, while the water surface elevation in the outer region is expressed as Fourier-Bessel series, and the final solution is obtained by matching them at the conjunction. The solution can be degenerated into the previous analytic solutions for waves propagation over an axisymmetric pit or a submerged hump by adjusting the topography parameters

Propagation of tidal waves up in Yangtze Estuary during the dry season

Tide is one of the most important hydrodynamic driving forces and has unique features in the Yangtze Estuary (YE) due to the complex geometry of third-order bifurcations and four outlets. This paper characterizes the tidal oscillations, tidal dampening, tidal asymmetry, and tidal wave propagation, which provides insights into the response of the estuary to tides during the dry season. The structural components of tidal oscillations are initially attained by tidal analysis. The increasingly richer spectrum inside the estuary shows an energy transfer corresponding to the generation and development of nonlinear overtides and compound tides. A 2-D numerical model is further set up to reproduce tidal dynamics in the estuary. The results show that the estuary is a strongly dissipative estuary with a strong nonlinear phenomenon. Three amplifications are presented in the evolution process of tidal ranges due to the channel convergence. Tidal asymmetry is spatiotemporally characterized by the M-4/M-2 amplitude ratio, the 2M(2)-M-4 phase difference, and the flood-ebb duration-asymmetry parameter, and the estuary tends to be flood-dominant. There exists mimic standing waves with the phase difference of the horizontal and vertical tide close to 90 degrees when tidal wave propagates into the estuary, especially during the neap tide. In addition, the differences in tidal distortion, tidal ranges, and tidal waves along the two routes in the South Branch (S-B) suggest the branched system behaves differently from a single system

Numerical Simulation of Solitary Wave Induced Flow Motion around a Permeable Submerged Breakwater

This paper presents a numerical model for the simulation of solitary wave transformation around a permeable submerged breakwater. The wave-structure interaction is obtained by solving the Volume-Averaged Reynolds-Averaged Navier-Stokes governing equations VARANS and volume of fluid VOF theory. This model is applied to understand the effects of porosity, equivalent mean diameter of porous media, structure height, and structure width on the propagation of a solitary wave in the vicinity of a permeable submerged structure. The results show that solitary wave propagation around a permeable breakwater is essentially different from that around impermeable one. It is also found that the structure porosity has more impact than equivalent mean diameter on the wave transformation and flow structure. After interacting with the higher structure, the wave has smaller wave height behind the structure with a lower travelling speed. When the wave propagates over the breakwater with longer width, the wave travelling speed is obviously reduced with more wave energy dissipated inside porous structure

Numerical simulation of solitary wave propagation over a steady current

YesA two-dimensional numerical model is developed to study the propagation of a solitary wave in the presence of a steady current flow. The numerical model is based on the Reynolds-averaged Navier-Stokes (RANS) equations with a k-ε turbulence closure scheme and an internal wave-maker method. To capture the air-water interface, the volume of fluid (VOF) method is used in the numerical simulation. The current flow is initialized by imposing a steady inlet velocity on one computational domain end and a constant pressure outlet on the other end. The desired wave is generated by an internal wave-maker. The propagation of a solitary wave travelling with a following/opposing current is simulated. The effects of the current velocity on the solitary wave motion are investigated. The results show that the solitary wave has a smaller wave height, larger wave width and higher travelling speed after interacting with a following current. Contrariwise, the solitary wave becomes higher with a smaller wave width and lower travelling speed with an opposing current. The regression equations for predicting the wave height, wave width and travelling speed of the resulting solitary wave are for practical engineering applications. The impacts of current flow on the induced velocity and the turbulent kinetic energy (TKE) of a solitary wave are also investigated.National Natural Science Foundation of China Grant #51209083, #51137002 and #41176073, the Natural Science Foundation of Jiangsu Province (China) Grant #BK2011026, the 111 Project under Grant No. B12032, the Fundamental Research Funds for the Central University, China (2013B31614), and the Carnegie Trust for Scottish Universitie

Engineering design and economic analysis of offshore seaweed farm

As global demand for sustainable biomass and need to mitigate global warming begin to rise, cultivation of seaweed has gained significant attention in recent years due to its potential for carbon recycling. However, limited availability of suitable coastal areas for large-scale seaweed cultivation has led to exploration of offshore environments as a viable alternative. The nature of many offshore environments often exposes seaweed farming systems to harsh environmental conditions, including strong waves, currents, and wind. These factors can lead to structural failures, kelp losses, and significant financial losses for seaweed farmers. The main objective of this study is to present a robust design and numerical analysis of an economically viable floating offshore kelp farm facility, and evaluate its stability and mooring system performance. A numerical method of preliminary designs of the offshore aquaculture systems were developed using the OrcaFlex software. The models were subjected to a series of dynamic environmental loading scenarios representing extreme events. These simulations aimed to forecast the overall dynamic response of an offshore kelp farm at a depth of 50m and to determine the best possible farm design with structural integrity for a selected offshore environment. Furthermore, to assess the economic feasibility of establishing offshore seaweed farms, a comprehensive capital expenses analysis was conducted. The results revealed that, in terms of the kelp farms with the same number of the kelp cultivating lines, the cost of building kelp farms will be strongly affected by the cost of mooring lines. The present study may help to understand the dynamic response and economic feasibility of offshore kelp farms