Search Results (392)

We investigate the Lagrange formulation for the one-dimensional Saint Venant–Exner system. The system describes shallow-water equations with a bed evolution, for which the bedload sediment flux depends on the velocity, $Q\left(t,x\right)=A_g{u}^m,m\ge 1$. In terms of the Lagrange variables, the nonlinear hyperbolic system is reduced to one master third-order nonlinear partial differential equation. We employ Lie’s theory and find the Lie symmetry algebra of this equation. It was found that for an arbitrary parameter m, the master equation possesses four Lie symmetries. However, for $m=3$, there exists an additional symmetry vector. We calculate a one-dimensional optimal system for the Lie algebra of the equation. We apply the latter for the derivation of invariant functions. The invariants are used to reduce the number of the independent variables and write the master equation into an ordinary differential equation. The latter provides similarity solutions. Finally, we show that the traveling-wave reductions lead to nonlinear maximally symmetric equations which can be linearized. The analytic solution in this case is expressed in closed-form algebraic form. Full article

Based on linear wave theory and potential flow theory, the wave scattering performance of a rectangular floating porous box with an impermeable bottom is investigated analytically. The mathematical formulation of the physical problem is well established and solved, and its analytical solutions are appropriately obtained using the matched eigenfunction expansion method. The convergency and accuracy of the analytical solutions are carefully verified and thoroughly validated. It is found that the present analytical solutions converge up to three decimal places and agree well with the numerical results published in the previous literature. Furthermore, important numerical results are calculated to thoroughly analyze the oblique wave scattering performance of the proposed rectangular floating porous box with an impermeable bottom and its efficiency in preventing incident waves when used as a floating breakwater. It is concluded that the dimensionless width ($L/h$), submergence depth ($d/h$), and frictional coefficient ($f$) have a significant influence on the scattering performance and the transmission coefficient of the proposed porous box. This work is beneficial for the design and future development of floating rectangular porous box breakwaters. Full article

As public attention to environmental issues grows, enterprises have begun implementing environment-centered business management. Achieving environmental sustainability requires the participation of all organizational members. This study was conducted in Chinese food manufacturing small and medium-sized enterprises located in Guangdong and Jiangsu provinces, China, and employed a three-wave, time-lagged survey design to collect and match data from team leaders and employees. Hierarchical linear modeling was used to test the cross-level hypotheses, and the indirect effect was assessed using Bayesian multilevel mediation analysis. Using cross-level data from both team leaders and team members, this study examines how green transformational leadership impacts employees’ pro-environmental behavior. In addition, this study examines the mediating role of employee value–action barriers and the moderating role of green brand image. The results indicate that (1) green transformational leadership positively influences employee pro-environmental behavior, (2) employee value–action barriers mediate the relationship between green transformational leadership and employee pro-environmental behavior, and (3) green brand image moderates both the correlation between green transformational leadership and employee pro-environmental behavior and the relationship between employee value–action barriers and employee pro-environmental behavior. These findings provide empirical support for the application of social learning theory and offer managerial insights into how managers can more effectively enhance their employees’ pro-environmental behavior. Future research may further test the robustness and applicability of these relationships in other industries and in different regional and national contexts. Full article

This study proposes a novel artificial neural network-based methodology for classifying the incident wave direction during ship navigation using the heave–roll–pitch motion response spectra as input. The proposed model demonstrated a balanced performance with an overall accuracy of approximately 0.888, effectively classifying the wave direction into three major categories: head-sea, beam-sea, and following-sea. The methodology utilizes Response Amplitude Operators derived from linear potential flow theory to generate motion response spectra, which are then used to classify the incident wave direction. The model effectively learns the frequency-distribution characteristics of the response spectrum, enabling wave direction classification without the need for complex inverse analysis procedures. This approach is significant in that it allows wave direction recognition solely based on measurable ship motion responses, without the need for additional external sensors or mathematical modeling. This data-driven approach has strong potential for integration into autonomous ship situational awareness modules and real-time wave monitoring technologies. However, the study simplified the directional domain into three representative groups, and the model was validated primarily using a numerically generated dataset, indicating the need for future improvements. Future research will expand the dataset to include a broader range of sea states, improve directional resolution, and explore continuous wave direction prediction. Additionally, further validation using field-measured data will be conducted to assess the real-time applicability of the proposed model. Full article

This study investigates the impact of eddy viscosity on equatorially trapped waves and the instability of the background shear in a simple barotropic–baroclinic model. It is the first study to include eddy viscosity in the study of tropical wave dynamics. This study also unifies the study of baroclinic and barotropic instabilities by using a coupled barotopic and baroclinic model of the tropical atmosphere. Linear wave theory is combined with a systematic Galerkin projection of the baroclinic dynamical fields onto parabolic cylinder functions. This study investigates varying shear strengths, eddy viscosities, and their combined effects. In the absence of shear, baroclinic and barotropic waves decouple. The baroclinic waves themselves separate into triads, forming the equatorially trapped wave modes known as Matsuno waves. However, when a strong eddy viscosity is included, the structure and propagation characteristics of these equatorial waves are significantly altered. Different wave types interact, leading to strong mixing in the meridional direction and coupling between meridional modes. This coupling destroys the Matsuno mode separation and offers pathways for these waves to couple and interact with one another. These results suggest that viscosity does not simply suppress growth; it may also reshape the propagation characteristics of unstable modes. In the presence of a background shear, some wave modes become unstable, and barotropic and baroclinic waves are coupled. Without eddy viscosity, instability begins with small scale and slowly propagating modes, at arbitrary small shear strengths. This instability manifests as an ultra-violet catastrophe. As the shear strength increases, the catastrophic instability at small scales expands to high-frequency waves. Meanwhile, instability peaks emerge at synoptic and planetary scales along several Rossby mode branches. When a small eddy viscosity is reintroduced, the catastrophic small-scale instabilities disappear, while the large-scale Rossby wave instabilities persist. These westward-moving modes exhibit a mixed barotropic–baroclinic structure with signature vortices straddling the equator. Some vortices are centered close to the equator, while others are far away. Some waves resemble synoptic-scale monsoon depressions and tropical easterly waves, while others operate on the planetary scale and present elongated shapes reminiscent of atmospheric-river flow patterns. Full article

Perceived time poverty is a major stress factor in university life, reflecting a lack of attentional resources. While nature-based interventions (NBIs) are recognized for restoring psychological resources, the psychological processes behind these interventions are not fully understood. This three-wave longitudinal study (N = 36) used linear mixed-effects models to examine the impact of a three-day camping trip on students’ psychological outcomes before, immediately after, and one month later. Findings show that the trip immediately and significantly boosted state nature connectedness and prosocial behavior intentions, while reducing perceived time poverty and psychological distress. Unexpectedly, it also led to a temporary decrease in both hedonic and eudaimonic well-being. By one month, most benefits had returned to baseline levels. Significantly, perceived time poverty fully mediated the link between nature connectedness and most outcomes. These results suggest camping helps restore attention, but short-term NBIs can only exert a temporary effect. The study enhances scarcity and attention restoration theories by testing specific psychological pathways and targets, offering valuable insights for creating nature-based programs that reduce stress and improve experiences, especially for university wellness initiatives. Full article

A theoretical model of the interaction between a following current and a semi-infinite floating ice sheet under compressive stress near a vertical impermeable wall is developed, within the scope of linear water wave theory, to study the hydroelastic behavior. The conceptual framework defining the buoyant ice structure incorporates the tenets of elastic beam theory. The associated fluid dynamics are governed by strict adherence to the potential flow paradigm. To resolve the undetermined parameters appearing in the Fourier series decomposition of the potential functions, investigators systematically apply higher-order criteria detailing the coupling relationships between modes. The current results are compared with a specific case of results available in the literature, and the convergence analysis of the analytical solution is made for computational accuracy. Further, the free edge conditions are applied at the edge of the floating ice sheet, and the effects of current speed, compressive stress, the thickness of the ice sheet, flexural rigidity, water depth on the strain, displacements, reflection wave amplitude, and the horizontal force on the rigid vertical wall are analyzed in detail. It is found that the higher values of the following current heighten the strain, displacements, reflection amplitude, and force on the wall. The study’s outcomes are considered to benefit not just cold region design applications but also the engineering of resilient floating structures for oceanic and offshore environments, and to the design of marine structures. Full article

Theories of modern physics are based on dynamical equations that describe the evolution of particles and waves in space and time. In classical physics, particles and waves are described by different equations, but this distinction disappears in quantum physics, which is predominantly based on wave-like equations. The main purpose of this paper is to present a comprehensive review of all known classical and quantum linear wave equations for scalar wavefunctions, and to discuss their origin and applications to a broad range of physical problems. Full article

A variety of Offshore Floating Photovoltaics (OFPVs) applications rely on the capacity of their floating support structures displacing in the shape of surface waves to reduce extreme wave-induced loads exerted on their floating-mooring system. This wave-adaptive displacement behaviour is typically realized through two principal design approaches, either by employing slender and continuously deformable structures composed of highly elastic materials or by decomposing the structure into multiple floating rigid pontoons interconnected via flexible connectors. The hydrodynamic behaviour of these structures is commonly analyzed in the literature using potential flow theory, to characterize wave loading, whereas in order to deploy such OFPV prototypes in realistic marine environments, a high-fidelity numerical fluid–structure interaction model is required. Thus, a versatile three-dimensional numerical scheme is herein presented that is capable of handling non-linear fluid-flexible structure interactions for Very Flexible Floating Structures (VFFSs): Multibody Dynamics (MBD) for modularized floating structures and floating-mooring line interactions. In the present study, this is achieved by employing the Smoothed Particles Hydrodynamics (SPH) fluid model of DualSPHysics, coupled both with the MBD module of Project Chrono and the MoorDyn+ lumped-mass mooring model. The SPH-MBD coupling enables modelling of large and geometrically non-linear displacements of VFFS within an Applied Element Method (AEM) plate formulation, as well as rigid body dynamics of modularized configurations. Meanwhile, the SPH-MoorDyn+ captures the fully coupled three-dimensional response of floating-mooring and floating-floating dynamics, as it is employed to model both moorings and flexible interconnectors between bodies. The coupled SPH-based numerical scheme is herein validated against physical experiments, capturing the hydroelastic response of VFFS, rigid body hydrodynamics, mooring line dynamics, and flexible connector behaviour under wave loading. The demonstrated numerical methodology represents the first validated Computational Fluid Dynamics (CFD) application of moored VFFS in three-dimensional domains, while its robustness is further confirmed using modular floating systems, enabling OFPV engineers to comparatively assess these two types of wave-adaptive designs in a unified numerical framework. Full article

In naval and ocean engineering, accurate simulation of incident waves is essential for predicting the motion response of offshore structures. Traditional wave generation methods, such as piston- and flap-type wave makers, often face challenges in accurately replicating the orbital motion of water particles beneath the free surface, which can limit their applicability in high-fidelity simulations. In this study, a numerical investigation is conducted to compare the performance of piston-type, flap-type, and double-flap-type wave makers using STAR-CCM+2310(18.06.006-R8). The influence of water depth on wave height accuracy is evaluated across different measurement locations within a numerical wave tank. Theoretical analysis of wave generation mechanisms is incorporated to clarify the applicability limits of linear theory and to better interpret the numerical results. Results indicate that, under the tested two-dimensional CFD conditions, the double-flap-type wave maker tended to provide closer agreement with theoretical predictions, particularly at greater depths, compared with conventional methods. These findings suggest potential advantages of the double-flap configuration and provide insights for refining wave generation techniques in numerical and experimental wave tanks, thereby supporting more reliable hydrodynamic analyses of floating structures. Full article

In the development of quantum mechanics in the 1920s, both matrix mechanics (developed by Born, Heisenberg and Jordon) and wave mechanics (developed by Schrödinger) prevailed. These early attempts corresponded to the quantum mechanics of particles. Matrix mechanics was found to lead directly to the Schrödinger equation, and the Schrödinger equation could be used to derive the alternative problem for matrix mechanics. Later emphasis lay on the development of the dynamics of fields, where the classical field equations were quantized (see, for example, Weinberg). Today, quantum field theory is one of the most successful physical theories ever developed. The symmetry between particle and wave mechanics is exploited herein. One of the important properties of quantum mechanics is that it is linear, leading to some confusion about how to treat the problem of nonlinear classical field equations. In the present paper we address the case of classical nonlinear soliton equations which are exactly integrable in terms of the periodic/quasiperiodic inverse scattering transform. This means that all physical spectral solutions of the soliton equations can be computed exactly for these specific boundary conditions. Unfortunately, such solutions are highly nonlinear, leading to difficulties in solving the associated quantum mechanical problems. Here we find a strategy for developing the quantum mechanical solutions for soliton dynamics. To address this difficulty, we apply a recently derived result for soliton equations, i.e., that all solutions can be written as quasiperiodic Fourier series. This means that soliton equations, in spite of their nonlinear solutions, are perfectly linearizable with quasiperiodic boundary conditions, the topic of finite gap theory, i.e., the inverse scattering transform with periodic/quasiperiodic boundary conditions. We then invoke the result that soliton equations are Hamiltonian, and we are able to show that the generalized coordinates and momenta also have quasiperiodic Fourier series, a generalized linear superposition law, which is valid in the case of nonlinear, integrable classical dynamics and is here extended to quantum mechanics. Hamiltonian dynamics with the quasiperiodicity of inverse scattering theory thus leads to matrix mechanics. This completes the main theme of our paper, i.e., that classical, nonlinear soliton field equations, linearizable with quasiperiodic Fourier series, can always be quantized in terms of matrix mechanics. Thus, the solitons and their nonlinear interactions are given an explicit description in quantum mechanics. Future work will be formulated in terms of the associated Schrödinger equation. Full article

The stability of a circular vortex is studied in the thermal quasi-geostrophic (TQG) model. Several radial distributions of vorticity and buoyancy (temperature) are considered for the mean flow. First, the linear stability of these vortices is addressed. The linear problem is solved exactly for a simple flow, and two stability criteria are then derived for general mean flows. Then, the growth rate and most unstable wavenumbers of normal-mode perturbations are computed numerically for Gaussian and cubic exponential vortices, both for elliptical and higher mode perturbations. In TQG, contrary to usual QG, short waves can be linearly unstable on shallow vorticity profiles. Linearly, both stratification and bottom topography (under specific conditions) have a stabilizing role. In a second step, we use a numerical model of the nonlinear TQG equations. With a Gaussian vortex, we show the growth of small-scale perturbations during the vortex instability, as predicted by the linear analysis. In particular, for an unstable vortex with an elliptical perturbation, the final tripolar vortices can have a turbulent peripheral structure, when the ratio of mean buoyancy to mean velocity is large enough. The frontogenetic tendency indicates how small-scale features detach from the vortex core towards its periphery, and thus feed the turbulent peripheral vorticity. We confirm that stratification and topography have a stabilizing influence as shown by the linear theory. Then, by varying the vortex and perturbation characteristics, we classify the various possible nonlinear regimes. The numerical simulations show that the influence of the growing small-scale perturbations is to weaken the peripheral vortices formed by the instability, and by this, to stabilize the whole vortex. A finite radius of deformation and/or bottom topography also stabilize the vortex as predicted by linear theory. An extension of this work to stratified flows is finally recommended. Full article

In this paper, the propagation of surface gravity waves over multiple bottom-standing porous semicircular humps is examined in the absence and presence of double floating $\mathit{C}$-type detached asymmetric breakwaters. Both wave scattering and trapping phenomena are investigated within the framework of small-amplitude linear water wave theory, with the governing problem numerically solved using the multi-domain Boundary Element Method (BEM) in finite-depth water. A detailed parametric analysis is conducted to evaluate the effects of key physical parameters, including hump radius, porosity, spacing between adjacent humps, and the separation between the two $\mathit{C}$-type detached breakwaters. The study presents results for reflection and transmission coefficients, free-surface elevations, and the horizontal and vertical forces acting on the first perforated semicircular hump, as well as on the shore-fixed wall. The findings highlight the significant role of porous humps in altering Bragg scattering characteristics. For larger wavenumbers, wave reflection increases notably in the presence of a vertical shore-fixed wall, while it tends to vanish in its absence. Reflection is also observed to decrease with an increase in semicircle radius. Furthermore, as the wavenumber approaches zero, the vertical force on multiple permeable semicircles converges to zero, whereas for impermeable semicircles, it approaches unity. In addition, the horizontal force acting on the shore-fixed wall diminishes rapidly with increasing porosity of the semicircular humps. Full article

Few experimental studies have analyzed the wave energy conversion performance and underlying mechanisms of wave-driven profilers in controlled environments. Therefore, building on linear wave theory, Newton–Euler equations, and the working mechanisms of wave-driven profilers, this study has designed a crank mechanism-driven experimental tank facility. A comprehensive dynamic model of a wave-driven profiler has been established, and the impacts of wave height, wave period, and net buoyancy on the wave energy conversion performance of the wave-driven profiler and their underlying mechanisms have been analyzed. The results show that increased wave height enhances the buoy’s heave velocity, improving the dynamic performance of the wave-driven profiler by 441%. However, increased hydrodynamic resistance and mechanical collisions decreased the wave energy conversion efficiency by 57%. Longer wave periods reduce the wave excitation frequency, decreasing the buoy’s heave velocity; this results in a 35% reduction in the dynamic performance of the wave-driven profiler and a 53% decrease in wave energy conversion efficiency. During the descent phase, increased net buoyancy offsets more propulsive force, causing a 26% decrease in the wave-driven profiler’s dynamic performance yet increasing its energy conversion efficiency by 136%. This study provides a theoretical basis for optimizing the performance of similar wave-driven profilers. Full article

In this paper, we develop the explicit finite difference method (FDM) to solve an ill-posed Cauchy problem for the 3D acoustic wave equation in a time domain with the data on a part of the boundary given (continuation problem) in a cube. FDM is one of the numerical methods used to compute the solutions of hyperbolic partial differential equations (PDEs) by discretizing the given domain into a finite number of regions and a consequent reduction in given PDEs into a system of linear algebraic equations (SLAE). We present a theory, and through Matlab Version: 9.14.0.2286388 (R2023a), we find an efficient solution of a dense system of equations by implementing the numerical solution of this approach using several iterative techniques. We extend the formulation of the Jacobi, Gauss–Seidel, and successive over-relaxation (SOR) iterative methods in solving the linear system for computational efficiency and for the properties of the convergence of the proposed method. Numerical experiments are conducted, and we compare the analytical solution and numerical solution for different time phenomena. Full article