Finite Water Research Articles

Linking parametric and water-balance models of the Budyko and Turc spaces

The Budyko and Turc frameworks have become very popular tools for the estimation of catchment-scale water balance. In their original definition, these frameworks and the resulting equations, which are considered equivalent, apply in the long-term to very large catchments, whose water balance is predominately driven by climatic factors. Several equations similar to Budyko’s and Turc’s have subsequently been proposed to account also for the effect of catchment characteristics, including parametric formulations as well as equations resulting from a simplified physical representation of the water balance. After highlighting their advantages and disadvantages, we show that models based on the water balance, which account for rainfall variability and feedback between water availability and evapotranspiration, are more versatile to describe catchment-scale rainfall partitioning. They include parameters that have clearer physical meaning and, therefore, can be estimated independently of streamflow and evapotranspiration, thereby making them more amenable to practical use in un-gaged catchments. They show that Budyko’s and Turc’s point of view are equivalent only for large catchments. Additionally, water balance models have limiting conditions for extremely dry and wet climates that differ from those of the Budyko equations and its parametric formulations, as expected in catchments with a finite water storage capacity; in these models, Budyko’s and Turc’s points of view become equivalent only for large catchments.

Application of the 3D time-domain Green's function for finite water depth in hydroelastic mechanics

Based on the boundary element method and the superposition principle of structural elastic modes, the three-dimensional time-domain Green's function in finite water depth is applied to hydroelasticity, and the theoretical basis of three-dimensional time-domain hydroelasticity is established. To address the difficulty and divergence of the three-dimensional time-domain Green's function in finite water depth, a numerical solution method that has high accuracy and good stability is developed using series expansion, asymptotic methods and fourth-order differential equations. Taking a large bulk carrier as an example, the corresponding predictions of resonance frequency, motion, wave load and hydroelastic response with speed in finite water depth are carried out. The numerical results are compared with the results of the three-dimensional frequency domain method and the time-domain method of inner and outer region matching and are verified by the towing model test. The three-dimensional time-domain hydroelastic theory and numerical method established in this paper are of great significance for fluid coupling analysis, structural dynamic response research and wave load prediction of complex floating bodies with speed.

Numerical and experimental study on the wave-body interaction problem with the effects of forward speed and finite water depth in regular waves

In this study, a time domain higher-order Rankine panel method is developed and applied to evaluate the wave-body interaction problem in shallow water and regular waves. The hydrodynamic effects of forward speed and finite water depth are accounted for. In order to verify the proposed numerical method, the Duisburg Test Case (DTC) container ship is chosen as a study object. The numerical results of the wave-induced ship motions and the added resistance are validated against the data of model tests, which were carried out in the Towing Tank for Manoeuvres in Confined Water at Flanders Hydraulics Research (FHR) in cooperation with Ghent University (UGent) as part of the SHOPERA project.

Numerical Study on Change of Added Resistance due to Incident Waves in Finite Water Depth

AbstractIn this study, the effect of water depth on vertical motion responses and added resistance of ships in waves was numerically examined. The applied numerical method corresponded to the time ...

Transient Axi-Symmetric Disturbances in Two-Layer Fluid

The present manuscript deals with the generation of flexural gravity waves due to transient axi-symmetric disturbances in two-layer fluid. Roles of structural rigidity and compressive force on the transient flexural gravity wave motion are analyzed under the assumption of small amplitude water wave theory and structural responses in the case of finite water depth. Using Laplace and Hankel transforms, integral forms of the velocity potentials, structural deflection, surface and interface elevations are derived for the flexural gravity wave motion. Asymptotic solutions for surface and interface elevations are derived in special cases using method of stationary phase for large time and space.

Wave scattering by vertical porous block placed over flat and elevated seabed

The present study addresses the hydrodynamic characteristics of the incident wave through porous structure for both finite and shallow water depth. The oblique wave transformation due to the porous block over flat and elevated seabed and the submerged rigid block is presented. Analytical direct formulae are proposed to determine the wave reflection and transmission coefficient for the porous structure considering different configurations like porous block, porous block backed by wall, vertical wall away from the porous block and semi-infinite porous block at flat and elevated seabed. The analytical results for wave interaction with porous structure are presented considering the mode-coupling relation and eigenfunction expansion technique. Further, the significance of the semi-infinite porous block placed on the flat and elevated seabed is studied in detail. The analytical results obtained in the present study are validated with the numerical results available in the literature for specific cases. The significance of the critical angle and skin depth for the semi-infinite structure is explored in the wave structure interaction problems. The comparative study between various structural configurations suggests that, if the ratio of wavelength and width of the structure is greater or equal to unity $$\left( {d/\lambda \, \ge \, 1} \right),$$ then the structure can be regarded as semi-infinite porous block for flat and elevated seabed. The derived analytical formulae will be helpful in the preliminary design and analysis of the porous blocks.

Wave transformation due to floating thick elastic plate over multiple stepped bottom topography

The wave transformation due to floating elastic plate is studied over multiple stepped bottom topography. The behaviour of the flexible floating plate is studied considering Timoshenko-Mindlin’s plate thick theory at finite water depth and the edge conditions for the floating plates are considered to be free-free support condition. The mathematical model is developed based on the eigenfunction expansion method to study the hydroelastic behaviour of a floating thick elastic plate at varying water depths, step thickness and plate sizes acted upon by ocean wave. The mode coupling relation is employed along with orthogonality relation and the continuity equations for velocity, pressure, deflection, bending moment, slope and shear force to determine the wave characteristics in reflection and transmission region due to variable bottom topography. The numerical computation is carried out to obtain the hydroelastic behaviour of floating elastic plate acted upon by ocean waves. Further, detail comparison of the numerical results is performed for different step bottom topography for the hydroelastic analysis of floating thick elastic plate. The present study will provide an insight into the effect of seabed profile due to the wave scattering from a large floating thick elastic plate at finite water depth.

Scale‐Dependent Patterning of Wetland Depressions in a Low‐Relief Karst Landscape

AbstractThousands of small wetland depression features (cypress domes) dot the low‐relief karst of Big Cypress National Preserve (BICY) in South Florida, USA. We hypothesized that these wetland depressions are organized in a regular pattern, which is atypical of wetlandscapes elsewhere. Regular patterning implies the existence of coupled feedbacks operating at different spatial scales, with local wetland depression expansion (facilitation via karst dissolution) limited by competition among adjacent depressions for finite water resources (inhibition). We sought to test the hypothesis that wetlands in BICY exhibit regular patterning, and to quantify pattern properties to evaluate competing genesis mechanisms. We tested four predictions about landscape structure and geometry using high‐resolution Light Detection and Ranging elevation data from six 2.25‐km2 domains across BICY. Specifically, we predicted (1) feature overdispersion resulting from competition between adjacent basins; (2) truncated wetland area distributions due to growth inhibition feedbacks; (3) periodicity in surface elevation indicating a characteristic pattern wavelength; and (4) elevation bimodality indicating distinct upland and wetland states. All four predictions were strongly supported. Depressions were significantly overdispersed and efficiently fill the landscape, generating hexagonal patterning. Wetland areas followed truncated power law scaling, indicating incremental constraints on basin expansion, in contrast to depression areas elsewhere. Variogram and radial spectrum analyses revealed clear periodicity (~150‐ to 250‐m wavelength) in surface elevations. Finally, surface elevations were consistently bimodal with elevation divergence of 10 to 40 cm. Regular patterning of wetland depressions across BICY is clear, implying long‐term biogeomorphic control on landform structure in this karst landscape.

Influence of Support Conditions on the Hydroelastic Behaviour of Floating Thick Elastic Plate

The hydroelastic response of very large floating structures (VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating thick elastic plate based on Timoshenko-Mindlin plate theory, and the analysis for the hydroelastic response is performed considering different edge boundary conditions. The numerical study is performed to analyse the wave reflection and transmission characteristics of the floating plate under the influence of different support conditions using eigenfunction expansion method along with the orthogonal mode-coupling relation in the case of finite water depth. Further, the analysis is extended for shallow water depth, and the continuity of energy and mass flux is applied along the edges of the plate to obtain the solution for the problem. The hydroelastic behaviour in terms of reflection and transmission coefficients, plate deflection, strain, bending moment and shear force of the floating thick elastic plate with support conditions is analysed and compared for finite and shallow water depth. The study reveals an interesting aspect in the analysis of thick floating elastic plate with support condition due to the presence of the rotary inertia and transverse shear deformation. The present study will be helpful for the design and analysis of the VLFS in the case of finite and shallow water depth.

Quantitative evaluation for variability characteristics of reflected sound waves from sea surface

Many kinds of hydroacoustic devices are used in the field of ocean development of resources and observations. In evaluating the effect of sound propagation in water, it is important to evaluate the characteristics of sound reflection on sea surface. Amplitude and phase of reflected sound waves often fluctuates because of the changing sea surface with waves. In this paper, we evaluated the amplitude and phase variability characteristics of reflected sound waves on sea surface by acoustic simulation with the finite difference time domain method and water tank test. It is revealed that the energy ratio γ for amplitude variability is uniquely determined by Rayleigh roughness parameter when the sea surface is sufficiently random or the number of surface waves included in the irradiation range of sound waves is large. In addition, the standard deviation of phase for the phase variability is determined by regardless of that is, sea surface spectrum.

Effects of finite water depth and lateral confinement on ships wakes and resistance

Wash waves produced by ships disintegrate river banks and coastal lines. This phenomenon of bank erosion is mainly due to the height of the waves. Various factors govern the formation of these waves and their amplitudes: the geometry of the water channel, the shape and the speed of the boat, etc.. These factors play an important role on the wave generation, in addition on the resistance of the ship and so on its fuel consumption. Whether to study the impact of wash waves on the ship's environment or its resistance, the analysis of the generated wake is essential. Hence a fine characterization of the wave field is necessary. This study proposes a comparison of wakes generated by two generic ships based on a Wigley hull with block coefficients 0.67 and 0.89 respectively representative of maritime and fluvial ships. The wakes generated in deep water and confined water configurations have been measured for different Froude numbers by a non-intrusive optical stereo-correlation method, giving access to a detailed and complete definition of the generated wave fields. The resistance of the ship hulls has been measured in deep and confined water configurations with a hydrodynamic balance. The results permit one to study the influence of both hull and water channel geometries on the ship wake, on the amplitude of the far-field generated waves and on the near-field hydrodynamic response. Moreover, resistance curves are obtained for both configurations and highlight the effect of both hull and water channel geometries on the resistance coefficient of the ship. A comparison of the resistance curves with or without the ship trim is conducted and shows the influence of the trim on the resistance coefficient in the different ship speed regimes.

Wave Interaction With Floating Elastic Plate Based on the Timoshenko–Mindlin Plate Theory

In the present study, the wave interaction with the very large floating structures (VLFSs) is analyzed considering the small amplitude wave theory. The VLFS is modeled as a 2D floating elastic plate with infinite width based on Timoshenko–Mindlin plate theory. The eigenfunction expansion method along with mode-coupling relation is used to analyze the hydroelastic behavior of VLFSs in finite water depth. The contour plots for the plate covered dispersion relation are presented to illustrate the complexity in the roots of the dispersion relation. The wave scattering behavior in the form of reflection and transmission coefficients are studied in detail. The hydroelastic performance of the elastic plate interacting with the ocean wave is analyzed for deflection, strain, bending moment, and shear force along the elastic plate. Further, the study is extended for shallow water approximation, and the results are compared for both Timoshenko–Mindlin plate theory and Kirchhoff’s plate theory. The significance and importance of rotary inertia and shear deformation in analyzing the hydroelastic characteristics of VLFSs are presented. The study will be helpful for scientists and engineers in the design and analysis of the VLFSs.

Water consumption, land use and production patterns of rice, wheat and potato in South Asia during 1988–2012

South Asia is home to over one-fifth of the global population where around 276 million people are chronically undernourished. This research analyzed the water consumption, agricultural land use and production patterns of three major cultivated crops in South Asia for the period 1988–2012, namely rice, wheat and potato. Data have been collected from AQUASTAT and FAOSTAT databases of the Food and Agriculture Organization. Results reveal that the majority of South Asian countries have managed to increase food production through intensive groundwater-based irrigation during the non-monsoon period. Food production in South Asia largely depends on high water-consuming crops such as rice and wheat. In recent years, potato-harvested area and volume of production both increased substantially compared to 1990s. However, to meet the demand of a growing population with finite land and water resources, South Asian countries should take a number of steps including promoting the cultivation of less water-consuming crops through diversification of cropping pattern, reducing high dependency on groundwater, increasing irrigation efficiencies and conjunctive use of water. These steps would help South Asian countries to promote sustainable agriculture in line with goal 2 of the Sustainable Development Goals.

Hydroelastic analysis of periodic arrays of multiple articulated floating elastic plate

ABSTRACTThe periodic array of multiple articulated floating elastic plate acted upon by ocean waves is analysed considering Timoshenko-Mindlin plate theory. The floating elastic plate is placed periodically and is interconnected with vertical linear and flexural rotational springs which acts as an articulated joint. The hydroelastic behaviour of multiple articulated floating elastic plate is analysed based on eigenfunction expansion method along with the orthogonal mode-coupling relation in finite water depth and the continuity of energy and mass flux are used in the hydroelastic analysis of floating plate at shallow water depth. Further, the application of the wide-spacing approximation (WSA) method is employed to analyse the hydroelastic characteristics of the multiple articulated floating elastic plate. The results obtained using the eigenfunction expansion method is compared with the results based on WSA at finite water depth and validated with the results available in the literature.

On the near resonances of collinear steady-state wave groups in finite water depth

In this paper, the role nearly resonant components play in collinear steady-state wave groups in finite water depth is investigated theoretically. Fully nonlinear water wave equations are solved when the resonance conditions are nearly satisfied. Convergent solutions are obtained for steady-state wave groups with multiple near resonances. Spectra analysis shows that, as water depth decreases from deep water to finite water depth, the four-wave nearly resonant interactions play a dominant role in nonlinear steady-state wave groups. Meanwhile the dispersion relation changes with the water depth and some low and high frequency components appear in the spectrum due to the three-wave nearly resonant interactions. Comparison between the linear and nonlinear wave groups are made in finite water depth when the mean rates of mass, momentum and energy fluxes are almost conserved. It is found that wave energy in nonlinear wave groups is redistributed as more components join the resonance when the nonlinearity increases. Besides, both the wave group steepness and magnitude of water particle horizontal velocities near the crests and troughs in nonlinear wave groups increase more rapidly with the nonlinearity. The significance of near resonances in finite water depth for collinear steady-state wave groups is demonstrated.

Coast/breakwater-integrated OWC: A theoretical model

Integrating wave energy converters into coastal structures such as breakwaters, seawalls or jetties not only offers benefits in terms of construction costs but also improves wave energy extraction. In this paper a novel theoretical model based on linear potential flow theory is developed to study the performance of an oscillating water column (OWC) integrated into a vertical structure in water of finite water depth. The model has three fundamental advantages relative to previous works: no thin-wall restriction (the thickness of the OWC chamber wall is considered), no singularities, and far fewer truncating terms in the eigen-function expansions. The OWC chamber is a vertical cylinder semi-embedded in the structure with a submerged, open bottom. As water waves impinge on the structure, the water column in the chamber oscillates and drives an air turbine installed at the chamber top to extract wave power. Using linear wave theory, the velocity potential in the water domain is decomposed into scattering and radiation potentials whose unknown coefficients are determined by the eigen-function matching method. Upon successful validation, the model is used to investigate the influence of the thickness of the chamber wall and the radius and submergence of the chamber on wave power absorption.

Finite-amplitude steady-state wave groups with multiple near-resonances in finite water depth

Finite-amplitude wave groups with multiple near-resonances are investigated to extend the existing results due to Liu et al. (J. Fluid Mech., vol. 835, 2018, pp. 624–653) from steady-state wave groups in deep water to steady-state wave groups in finite water depth. The slow convergence rate of the series solution in the homotopy analysis method and extra unpredictable high-frequency components in finite water depth make it hard to obtain finite-amplitude wave groups accurately. To overcome these difficulties, a solution procedure that combines the homotopy analysis method-based analytical approach and Galerkin method-based numerical approaches has been used. For weakly nonlinear wave groups, the continuum of steady-state resonance from deep water to finite water depth is established. As nonlinearity increases, the frequency bands broaden and more steady-state wave groups are obtained. Finite-amplitude wave groups with steepness no less than $0.20$ are obtained and the resonant sets configuration of steady-state wave groups are analysed in different water depths. For waves in deep water, the majority of non-trivial components appear around the primary ones due to four-wave, six-wave, eight-wave or even ten-wave resonant interactions. The dominant role of four-wave resonant interactions for steady-state wave groups in deep water is demonstrated. For waves in finite water depth, additional non-trivial high-frequency components appear in the spectra due to three-wave, four-wave, five-wave or even six-wave resonant interactions with the components around the primary ones. The amplitude of these high-frequency components increases further as the water depth decreases. Resonances composed by components only around the primary ones are suppressed while resonances composed by components around the primary ones and from the high-frequency domain are enhanced. The spectrum of steady-state resonant wave groups changes with the water depth and the significant role of three-wave resonant interactions in finite water depth is demonstrated.

On the Lagrangian Period in Steep Periodic Waves

We show that, for periodic steep waves at finite water depth, the excess Lagrangian period, $$\Delta T_\mathrm{{L}}$$, made nondimensional by the Eulerian period, $$T_0$$, is equal to the mean Lagrangian drift velocity, $$u_\mathrm{{L}}$$, made nondimensional by the wave speed, c. This result is exact within second-order theory. Measurements in wave tank obtain that the two quantities are approximately equal. The vertical mean of $$\Delta T_\mathrm{{L}}$$ and $$u_\mathrm{{L}}$$ are zero in the experiments. The vertically averaged Lagrangian period thus equals the Eulerian period. The experimental and theoretical vertical derivative of $$\Delta T_\mathrm{{L}}$$ are the same in the middle of the water column but strongly differ above the bottom and below the wave surface. These differences are due to the secondary streaming effect in the viscous boundary layers in the experiments, at the bottom and free surface. Fully nonlinear calculations complement the investigation.

Global solution for the 3D gravity water waves system above a flat bottom

Given any suitably small, localized, and smooth initial data, in this paper, we prove global regularity for the 3D finite depth gravity water wave system. As a byproduct, we rule out the small, localized traveling waves in 3D, which do exist for the same system in 2D.

Coupled BEM and FEM for the analysis of floating elastic plate with arbitrary shapes

ABSTRACTIn order to analyse the hydroelastic behaviour of the floating thin elastic plate, a numerical model has been developed by coupling higher-order boundary element method (BEM) and finite element method (FEM). The present model is capable of investigating the very large floating structure of arbitrary shapes at finite and infinite water depths. The developed hybrid model contains the same nodes maintaining the same order and basis function in both the methods. The novelty of this work can be seen in the newly developed modified Green’s function. Two geometrical configurations (triangle and trapezoidal) have been analysed. The time required for convergence and deflection of the geometrical model have been captured. Furthermore, the results obtained by Wang and Meylan [2004. A higher-order-coupled boundary element and finite element method for the wave forcing of a floating elastic plate. J Fluids Struct. 19(4):557–572] are used to validate the developed numerical model. It is concluded that the model works better in finite water depth for trapezoidal shape.