Free Surface Elevation Research Articles

A Study of Free Surface Agitation in a Shipyard Using Numerical Modeling

In recent years, the Port of Topolobampo, Sinaloa, Mexico, has experienced unusual free sea surface elevations, particularly during the months of November and December, affecting the shipyard areas, service docks, and berthing locations. This study focuses on analyzing the oscillatory behavior of free surface elevations in shipyard regions. A hydrodynamic model was employed to simulate the circulation and sea surface agitation, aiming to quantify the elevation magnitudes based on oceanographic and meteorological data from November of the preceding year. A 30-day numerical simulation was conducted, revealing the velocity fields associated with coastal currents and tides during November, as well as the interaction between incident waves and wave transformations due to protective structures. The results demonstrated accurate behavior in 95% of the simulation period, while anomalous elevations exceeding those specified in the design and operational guidelines of the Port of Topolobampo were observed during the final five days of the simulation. An ANOVA test was performed between the surface elevation and vertically integrated velocity to assess whether the deviations in the last five days were statistically significant compared to the rest of the simulation period. With a P-value of less than 0.05, the null hypothesis of no difference was rejected, confirming a significant variation. These findings suggest that the extreme values recorded should be considered for the potential redesign of shipyard infrastructure.

Examining a Conservative Phase-Field Lattice Boltzmann Model for Two-Phase Flows

In this study, a conservative phase-field lattice Boltzmann model is examined for simulating immiscible two-phase flows with large density and viscosity ratios. This model is built upon the Allen–Cahn equation, incorporating a filtered collision operator and high-order corrections in the equilibrium distribution functions. The numerical model is also integrated with the volumetric boundary scheme and the immersed boundary method to achieve various stationary and moving boundary conditions on arbitrary geometries for different application scenarios. A comprehensive evaluation of this phase-field solver is conducted through a range of academic and industrial cases. First, droplet splashing cases at different Reynolds numbers are studied. The phase-field LB model effectively captures the surface wave motion and splashing of the droplet, although some smearing of small structures is observed due to the diffused interface property of the numerical model. Second, a tuned liquid damper is simulated, accurately capturing sloshing forces on solid walls. In the simulation of a dam-breaking case, predicted gauge pressure and free-surface elevation time histories compare well with experimental data. Lastly, a gearbox case under dip lubrication is simulated, with both the gearbox churning loss and oil distribution being well predicted across a range of rotating speeds. The validation studies demonstrate the effectiveness of the present phase-field lattice Boltzmann model in simulating immiscible two-phase flows with large and realistic density and viscosity ratios. The strengths, limitations, and weaknesses of the conservative phase-field LB model are discussed, and suggestions for the development and application of this numerical model are provided.

Real-time phase-resolved ocean wave prediction in directional wave fields: Second-order Lagrangian wave models

The Improved Choppy Wave Model (ICWM) was established to achieve a second-order Lagrangian expansion of surface waves. The second-order Lagrangian nonlinear interaction terms were found to be negligible and were therefore discarded. However, these interactions in directional wave fields remained unexplored. ICWM was successfully used, especially for floating offshore wind turbines, but it was noted that its accuracy in predicting directional sea states needed improvement. Hence, we formulated the Complementary ICWM (CICWM) with the nonlinear terms for free surface elevation in directional waves. Detailed formulations for data assimilation and wave propagation were provided, enabling real-time wave forecasting for directional seas using a simplified assimilation method. Comparing the model performances against tank-scale experiments showed that CICWM enhances the surface elevation description in directional seas. Ultimately, it was confirmed that the second-order Lagrangian model can reduce the prediction error of the linear wave model by 90% in directional seas for the experimental setups and sea states investigated in this study.

Large Eddy Simulation of Cross‐Shore Hydrodynamics Under Random Waves in the Inner Surf and Swash Zones

AbstractA 3D large eddy simulation coupled with a free surface tracking scheme was used to simulate cross‐shore hydrodynamics as observed in a large wave flume experiment. The primary objective was to enhance the understanding of wave‐backwash interactions and the implications for observed morphodynamics. Two simulation cases were carried out to elucidate key processes of wave‐backwash interactions across two distinct stages: berm erosion and sandbar formation, during the early portion of a modeled storm. The major difference between the two cases was the bathymetry: one featuring a berm without a sandbar (Case I), and the other, featuring a sandbar without a berm (Case II) at similar water depth. Good agreement (overall Willmott's index of agreement greater than 0.8) between simulations and measured data in free surface elevation, wave spectrum, and flow velocities validated the model skill. The findings indicated that the bottom shear stress, represented by the Shields parameter, was significant in both cases, potentially contributing substantial sediment transport. Notably, the occurrence of intense wave‐backwash interactions were more frequent in the absence of a sandbar. These intense wave‐backwash interactions resulted in a pronounced horizontal pressure gradient, quantified by high Sleath parameters, exceeding the criteria for momentary bed failure. Additionally, a more vigorous turbulence‐bed interaction, characterized by near‐bed turbulent kinetic energy, was observed in the case lacking a sandbar, potentially augmenting sediment suspension. These insights are pivotal in understanding the mechanisms underlying berm erosion and how sandbar formation serves to protect further beach erosion.

Experimental Study on the Spring-like Effect on the Hydrodynamic Performance of an Oscillating Water Column Wave Energy Converter

The oscillating water column (OWC) wave energy converter has demonstrated significant potential for converting ocean wave energy. The spring-like effect of air compressibility can significantly affect the hydrodynamic behavior of the device, but it has rarely been investigated through experimental studies. In this study, an experimental test on a model-scaled OWC device was carried out in a wave flume using a series of regular and irregular waves. The spring-like effect was taken into account by the combination of the air chamber with an additional air reservoir of appropriate volume, where the total volume was scaled according to the square of the Froude scale. The hydrodynamic performance was compared with the results obtained without considering the spring-like effect. A phase difference between the air pressure and airflow rate was observed when employing the additional air reservoir. The amplitudes of free surface elevation and airflow rate increased, while the air pressure was reduced when the spring-like effect was considered. The results demonstrate that failure to consider the spring-like effect can lead to overestimation of the hydrodynamic efficiencies, and the errors were mainly affected by the incident wave frequency.

Kinematics of nonlinear waves over variable bathymetry. Part I: Numerical modelling, verification and validation

Fluid particle kinematics due to wave motion (i.e. orbital velocities and accelerations) at and beneath the free surface is involved in many coastal and ocean engineering applications, e.g. estimation of wave-induced forces on structures, sediment transport, etc. This work presents the formulations of these kinematics fields within a fully nonlinear potential flow (FNPF) approach. In this model, the velocity potential is approximated with a high-order polynomial expansion over the water column using an orthogonal basis of Chebyshev polynomials of the first kind. Using the same basis, original analytical expressions of the components of velocity and acceleration are derived in this work. The estimation of particle accelerations in the course of the simulation involves the time derivatives of the decomposition coefficients, which are computed with a high-order backward finite-difference scheme in time. The capability of the numerical model in computing the particle kinematics is first validated for regular nonlinear waves propagating over a flat bottom. The model is shown to be able to predict both the velocity and acceleration of highly nonlinear and nearly breaking waves with negligible error compared to the corresponding stream function wave solution. Then, for regular waves propagating over an uneven bottom (bar-type bottom profile), the simulated results are confronted with existing experimental data, and very good agreement is achieved up to the sixth-order harmonics for free surface elevation, velocity and acceleration.

Observation and modelling of infragravity waves at a large meso-tidal inlet and lagoon

The role of infragravity waves (IG waves) in beach and dune erosion or in flood hazard has been extensively studied on open beaches. In contrast, the detailed characterization of IG waves and their contribution to the Total Water Level (TWL) along the shore of inlets received little attention so far. In such environment, there is a real lack of in situ observations of waves and hydrodynamics conditions at appropriate spatial and temporal coverage to study the role of infragravity (IG) waves (long waves of frequency typically ranging between 0.004 Hz and 0.04–0.05 Hz) on coastal hazards. This contribution is based on field observations collected at the Arcachon Lagoon, a shallow semi-enclosed lagoon connected to the ocean by a large tidal inlet, located in southwest France. Analyses combine observations made at several locations during storm events within the inlet and the lagoon with numerical simulation with the XBeach surfbeat model to explore the spatial variability of IG waves and simulate observed, historical, and idealized storm conditions. The results show that IG waves are substantial during typical winter storms at the inlet and range from Hm0 = 0.8 to over 1 m across the ebb delta and about 0.4–0.6 m in the inner part of the inlet. At the lagoon entrance, IG waves remain substantial (about 0.1–0.2 m) and decrease to a few centimeters at the lagoon shore. The spatial variability and magnitude of IG waves along the inlet coast, simulated for the historical storms, are quite comparable to those observed during classical winter, and do not increase linearly with offshore wave energy. However, both observations and simulations reveal local amplifications of IG waves in the inner part of the inlet, especially along the sheltered coast were IG waves dominate the variance of free surface elevation, reaching about 0.6–0.7 m during common storms and more than 1 m for an extreme storm scenario. A numerical experiment indicates that IG wave reflection from one coast to the other contributes up to 35–40% of the measured IG wave height at a hot spot located along the sheltered coast. Finally, the contribution of IG waves to TWL at the shore on both sides of the inlet has been estimated to be about 0.4–0.6 m for a common storm and 0.6–0.9 m for an extreme scenario, locally peaking at 0.74 and 1.1 m respectively and overpassing the contribution of wave-induced setup. This work provides new insights into the contribution of IG waves to TWL and its implications for overtopping flooding hazard and overwash processes at large inlets, highlighting the need to consider IG waves in Early Warning Systems or hazard mapping for flood prevention plans in these environments.

Performance of dual‐chamber oscillating water column device under irregular incident waves using Reynolds averaged Navier–Stokes model

AbstractThe purpose of this study is to analyze the hydrodynamic performance and efficiency of a dual‐chamber oscillating water column (OWC) device. For the Joint North Sea Wave Project (JONSWAP) incident waves spectrum, a two dimensional numerical wave tank is employed with nonlinear Reynolds averaged Navier–Stokes equations model along with the standard turbulence model. The free surface elevation is measured using the volume of fluid method. The numerical simulation demonstrates the streamline and velocity vector profiles throughout an entire pressure fluctuation cycle inside the chambers of the given OWC device. Further, investigation is carried out to analyze the impact of pressure drop and air flow rate through the orifice of the dual‐chamber OWC device on the power generation. Moreover, the power spectral density analysis of the free surface elevation is provided to know the variation of the parameters in the frequency domain. These results demonstrate that the effectiveness of the dual‐chamber OWC device is more near the significant wave height m.

Interaction between incident and reflected mechanical waves in the presence of an opposing wind

The interaction between wind and waves largely determines exchanges of mass, momentum, energy, and substances which take place at the air–sea interface. Usually, the parameterization of such interaction considers only the case of progressive waves. However, reflection is practically ubiquitous in the field, especially in coastal areas, and in the lab. Recent experimental studies have extensively treated this subject, showing that even a small amount of wave reflection can significantly modify the free surface elevation and the velocity field on the water side. Nonetheless, a theoretical framework for an exhaustive description of the wave reflection role is still lacking. In this work, an analytical model is developed to emphasize the role of reflection in terms of incident-reflected waves interaction in the 2D momentum equations. A non-null interaction between the incident and the reflected waves is predicted for partially-reflected monochromatic waves, and it is represented by a reflection-induced stress tensor. A phase shift is found among the total wave height, the velocity and the shear stress, with implications on the partition of the wave velocity and stresses. Then, the incident, reflected, and total components of the velocity and of the stresses along the regular wave phase are compared with a set of laboratory experiments, where monochromatic waves in condition of partial reflection are ruffled by an opposing wind. The overlap between experiments and theory is remarkably good, thus validating the entire procedure and assumptions. From the experiments, the fluctuating shear stress and kinetic energy are also extracted for different reflection conditions of the mechanical wave, showing a peak of both quantities near the wave trough (close to the surface). Overall, the experimental analysis gives insights into the velocity, momentum and energy fluxes along the wave phase, based on velocity measurements at one fetch length.

Three-Dimensional Numerical Simulation of a Two-Phase Supercritical Open Channel Junction Flow

This study investigates the computational fluid dynamics (CFD) modeling of supercritical open channel junction flow using two different turbulence models: k-ω shear stress transport (SST) and k-ω SST scale-adaptive simulation (SAS), in conjunction with Volume of Fluid (VOF) and mixture multiphase models. The efficacy of these models in predicting the intricate free surface fluctuation and free surface elevation in a supercritical junction is evaluated through a comprehensive analysis of time-averaged free surface data obtained from CFD simulations and Light Detection and Ranging (LIDAR) measurements. The dimensionless Reynolds (Re) and Froude (Fr) numbers of the investigated scenario were Fr = 9 and Re = 5.1 × 104 for the main channel, and Fr = 6 and Re = 3.3 × 104 for the side channel. The results of the analysis demonstrated a satisfactory level of agreement with the experimental data. However, certain limitations associated with both CFD and LIDAR were identified. Specifically, the CFD performance was limited by the model’s incapacity to consider small-scale turbulent effects and to model air bubbles smaller than the cell size while the LIDAR measurements were limited by instrument range, inability to provide insight into what is happening below the water surface, and blind spots. Nonetheless, the k-ω SST turbulent model with the VOF multiphase model most closely matched the LIDAR results.

Transient resonance of sloshing liquid with time-varying mass

This study examines the sloshing of liquid with time-varying mass in a tank. A set of innovative experiments is carried out involving a shaking table supporting a water tank equipped with a drain pipe. Physical evidence of transient resonance is observed for the first time. Transient resonance occurs under specific excitation conditions when the instantaneous average water level (AWL) approaches a critical depth. During transient resonance, the oscillatory amplitude of the free-surface elevation increases sharply and then decreases in an envelope pattern. A bifurcation of the frequency band is first found in the Morlet-wavelet time–frequency spectrum, coinciding with the appearance of the maximum oscillatory amplitude. How the excitation conditions, drainage rate, and initial water depth affect transient resonance is recognized. Two mathematical models—one based on linear modal theory and the other based on nonlinear asymptotic theory and the Bateman–Luke variational principle—are derived to replicate the physical observations, by which application scopes of both models have been greatly broadened. The linear solution fails to predict the key feature of transient resonance, namely, the asymmetric envelopes of the oscillatory component about the AWL. By contrast, the nonlinear asymptotic solution captures this asymmetric feature accurately, and predicts both the steady and maximum oscillatory amplitudes well. The nonlinear solution is decomposed into terms of order 1/3, 2/3, and 1 using an asymptotic series for component analyses. A special nonlinear jump behavior is observed. The effects of draining and filling on transient resonance are compared.

A Set of Accurate Dispersive Nonlinear Wave Equations

In this study, a set of accurate dispersive nonlinear wave equations is established, using the wave velocity and free surface elevation as variables. These equations improve upon previous equations in which the velocity potential is used as a variable by considering the rotational wave motion and by adding a second-order bottom slope term that applies to general situations, allowing the equations to consider the influence of rapidly changing, horizontal, two-dimensional bottom topographies. The problem of the inaccuracy of the integral calculations used in previous equations in nearshore areas is solved by approximating the integral calculations into differential calculations, and a set of coupled wave equations is established by keeping the free surface elevation and the horizontal velocity constant, thus allowing the calculation of nearshore wave-generated currents. The benefits of the current model are confirmed through comparisons with corresponding laboratory experimental findings and are illustrated through a comparison with the numerical outcomes of other pertinent models.

Analysis of Hydrodynamic Loads by a Vertical Hollow Cylindrical Structure in A Two-Layer Fluid of Finite Depth

This paper aims to study the effect of surge radiation by a vertically hollow cylinder floating in a two-layer fluid of finite depth. Since most of the important characteristics of the oscillating water column are preserved by the hollow cylindrical structure, so the proposed device can be considered as an oscillating water column (OWC) which is one of the important wave energy device. In this two-layer fluid system, the upper layer is bounded above by a free surface and the lower layer is bounded below by a solid impermeable bottom, and the submerged hollow cylindrical structure allows it to oscillate in a surge mode of motion in the upper layer. On the assumption that wave amplitudes are small in comparison to wavelengths, hence the linear water wave theory is applied to formulate boundary value problems by dividing whole domain into 2 sub-domains. The formulated boundary value problems for surge radiated potentials in each sub-domain; we execute to obtain solutions in each sub-domain by using variable separation and matched eigenfunction expansion methods. With the help of obtained surge radiated potentials, we derive the radiation forces by the device in terms of added mass and damping coefficients. A set of influences of different parameters of the device on the added mass and damping coefficients are demonstrated in both surface and internal wave modes of motion. Hydrodynamic coefficients oscillate highly near a particular frequency, which leads to the resonance phenomena. In addition to that, the 3D plots of the free surface elevation in surface and internal wave modes are presented. A density ratio γ = 0.97 has a higher oscillation than a density ratio γ = 0.93, 0.95. High oscillations occur around a particular frequency ω = 3.83 due to the resonance phenomenon in which the waves incoming match with the natural motion of the object. HIGHLIGHTS A floating hollow vertical cylindrical structure is considered in a two-layer fluid system having finite depth The separation of variables and matched eigenfunction expansion methods are utilized to obtain the solutions to the boundary-value problems The diffracted velocity potentials under the surge mode of motion are evaluated in the identified regions The added mass, damping coefficients, free surface and interface elevations in surface and internal wave modes are evaluated with different set of parameters of the device A number of results are presented regarding the effect of parameters of the device on the added mass, damping coefficients, free surface and interface elevations It is observed that the density ratio of the two-layer fluid has significant effect on the added mass, damping coefficient and the elevations GRAPHICAL ABSTRACT

Experimental and Numerical Prediction of Slamming Impact Loads Considering Fluid–Structure Interactions

Slamming impacts on water are common occurrences, and the whipping induced by slamming can significantly increase the structural load. This paper carries out an experimental study of the water entry of rigid wedges with various deadrise angles. The drop height and deadrise angle are parametrically varied to investigate the effect of the entry velocity and wedge shape on the impact dynamics. A two-way coupled approach combing CFD method software STAR-CCM+12.02.011-R8 and the FEM method software Abaqus 6.14 is presented to analyze the effect of structural flexibility on the slamming phenomenon for a wedge and a ship model. The numerical method is validated through the comparison between the numerical simulation and experimental data. The slamming pressure, free surface elevation, and dynamic structural response, including stress and strain, in particular, are presented and discussed. The results show that the smaller the inclined angle at the bottom of the wedge-shaped body, the faster the entry speed into the water, resulting in greater impact pressure and greater structural deformation. Meanwhile, studies have shown that the bottom of the bow is an area of concern for wave impact problems, providing a basis for the assessment of ship safety design.

TYPHOON KARDING (NORU) STORM SURGE ANALYSIS USING THE COAWST MODELING SYSTEM

Abstract. The Philippines, frequently affected by typhoons, faces the hazard of storm surges. This study examined the Coupled-Ocean-Atmosphere-Wave-Sediment Transport Modeling System (COAWST) to simulate Typhoon Karding's September 2022 storm surge. COAWST integrates the Regional Ocean Modeling System (ROMS), Simulating WAves Nearshore (SWAN), and Weather Research and Forecasting (WRF) coupled using the Model Coupling Toolkit (MCT). Four setups were analyzed: i. ROMS only, ii. ROMS-SWAN, iii. ROMS-WRF, and iv. ROMS-SWAN-WRF, focusing on four variables: a. Surface air pressure, b. Wind speed, c. Free-surface elevation, and d. Significant wave height. Results show that the ROMS-WRF and ROMS-SWAN-WRF setups accurately simulated Typhoon Karding's track with minimal positional error and wind speed. However, the models overestimated the typhoon's minimum air pressure with p-biases of 7.74% (i and ii), 4.1% (iii), and 3.9% (iv), and RMSE values of 68.529 hPa (i and ii), 36.744 hPa (iii), and 36.789 hPa (iv). Additionally, water levels were underestimated, with RMSE ranging from 0.31 to 0.35 meters and p-biases from −72.56% to −154.89% at Baler, Aurora validation point. At the Real, Quezon validation point, RMSE and p-bias ranged from 0.30 to 0.34 meters and −84.80% to −166.44%, respectively. Nonetheless, the models were able to simulate the storm surge and significant wave height at Baler and Real points similar to recorded data, with setup iv performing best in storm surge simulation. In summary, COAWST may be employed for typhoon simulations, with coupling being able to increase accuracy.

Heavy tails and probability density functions to any nonlinear order for the surface elevation in irregular seas

The probability density function (PDF) for the free surface elevation in an irregular sea has an integral formulation when based on the cumulant generating function. To leading order, the result is Gaussian, whereas nonlinear extensions have long been limited to Gram–Charlier series approximations. As shown recently by Fuhrman et al. (J. Fluid Mech., vol. 970, 2023, A38), however, the second-order integral can be represented exactly in closed form. The present work extends this further, enabling determination of this PDF to even higher orders. Towards this end, a new ordinary differential equation (ODE) governing the PDF is first derived. Asymptotic solutions in the limit of large surface elevation are then found, utilizing the method of dominant balance. These provide new analytical forms for the positive tail of the PDF beyond second order. These likewise clarify how high-order cumulants (involving statistical moments such as the kurtosis) govern the tail, which is shown to get heavier with each successive order. The asymptotic solutions are finally utilized to generate boundary conditions, such that the governing ODE may be solved numerically, enabling novel determination of the PDF at third and higher order. Successful comparisons with challenging data sets confirm accuracy. The methodology thus enables the PDF of the surface elevation to be determined numerically, and the asymptotic tail analytically, to any desired order. Results are worked out explicitly up to fifth order. The theoretical probability of extreme surface elevations (typical of rogue waves) may thus be assessed quantitatively for highly nonlinear irregular seas, requiring only relevant statistical quantities as input.

The influence of bottom disturbances on wave generation in a viscous liquid in the presence of uniform current

In the present paper, the effect of bottom disturbances on wave generation in a viscous liquid in the presence of uniform current is studied. The wave potential and Stokes stream function are used to formulate this problem. Multiple integrals representing the free surface elevation are obtained by mathematical analysis using the Laplace transform in time and the Fourier transform in space. This is divided into various multiple integrals, using the steepest descent method to evaluate them asymptotically for a large time and distance. There are three types of ground disturbances taken into consideration: D0(x)=e(−x2/2), D0(x)=e−|x|, and D0(x)=δ(x). The effect of uniform current speed (U) and viscosity (ν) on the free surface elevation is illustrated for the three forms of ground disturbances. It is observed that the presence of current often amplifies the energy of the propagating wave and also increases its amplitude. Moreover, as viscosity increases, the amplitude of free surface elevation decreases with respect to time, and further, the period of oscillation of surface elevation becomes smaller for a large time.

Modal analysis of a submerged elastic disk: A hypersingular integral equation approach

A method based on the hypersingular integral equation approach and the modal analysis is presented to consider the effects of the motion of a submerged elastic disk on the incoming waves. Initially, the governing boundary value problem is reduced to a two-dimensional integral equation with a hypersingular kernel. This integral equation is further reduced to a one-dimensional Fredholm integral equation of the second kind with the help of Fourier series expansions and a newly defined function. As a part of modal analysis, eigenfunction expansion based on natural modes of structural motion is considered to describe the motion of a thin circular elastic disk. Physical quantities, such as hydrodynamic force, added mass, damping coefficient, and surface elevation, are numerically evaluated. The computed numerical results are verified by comparing them with those for the rigid disk horizontally submerged in deep water. Apart from this, as a part of the analytical verification of our present analysis, the reciprocity relation has been included. The effects of different parameters (disk's rigidity, radius, submergence depth, and mode of vibrations) on the aforementioned physical quantities have been studied. The maximum hydrodynamic force occurs around Ka = 0.5, while the maximum added mass and damping coefficient occur around the wavenumber Ka = 0.3 and Ka = 0.5, respectively. The peaks of the hydrodynamic force and free surface elevation become sharper with the increasing values of the disk's size. The numerical results emphasize that the wave focusing can be controlled by changing the submergence depth, size, and rigidity of the disk.

Sea Surface Salinity Forecasting with a Comparison Studying Case of GMM-VSG and FB-Prophet Model

With the evolution of artificial intelligence, the utilization of machine learning algorithms for predicting hydrological data has gained popularity in scientific research, especially for the development and operational patterns of marine-related objects in coastal regions. Salinity analysis plays a crucial role in evaluating the resilience and health of marine ecosystems. Traditional numerical models, although accurate, require significant computational resources. Therefore, this study assesses the effectiveness of GMM-VSG proposed by Shanghai University and FB-Prophet created by Meta (Facebook) as rapid alternatives for simulating the nonlinear relationships between salinity and various parameters, like tide-induced free surface elevation, river flows, and wind speed. The algorithms were tested using an eight-year dataset collected at the MAREL buoy at the entrance to bay of Brest. Results indicate that, despite the simplicity of the input data, both algorithms successfully reproduced seasonal and semi-diurnal fluctuations in salinity. This underscores their potential as complementary tools for the ecological monitoring in estuarine environments.

Scale effect on wave planing performance of amphibious aircraft at constant speed

Scaled model testing is commonly recognized as a valuable approach for predicting aircraft performance in the aeronautical applications. However, challenges arise in the case of wave planing events for amphibious aircraft due to difficulties in satisfying the scaling laws of Reynolds number and Froude number simultaneously in a water tank. Therefore, it is important to evaluate the scale effect of regular wave planing process for amphibious aircraft. In this study, by fixing the Froude number, five geosim cases with different scale factors (1/1, 1/2, 1/4, 1/8 and 1/16) are carried out based on the Reynolds-Averaged Navier–Stokes equations (RANS) framework. The hydrodynamic and aerodynamic characteristics at different scales are respectively examined in detail through several physical results, including acceleration, pressure, shear force, velocity and free surface elevation. Comparative analyses among all scaled models reveal that the aerodynamic and hydrodynamic performance both monotonously change with the scale factor, yet the proportion of aerodynamic and hydrodynamic loads remains within a reasonably small range. Furthermore, the results indicate that the scale effect primarily stems from the lack of similarity in Reynolds number, thus resulting in the discrepancies of boundary layer, wave surface elevation and flow separation between the scale model and prototype.