Uniform Bottom Research Articles

Effect of Sloping Bottom on Wave Interaction With Multiple Flexible Moored Breakwaters

Abstract An analytical framework is developed to analyze the interaction of oblique waves with multiple flexible porous breakwaters under the consideration of bottom undulation. The mathematical problem is tackled using the small amplitude water-wave theory, with Darcy’s law being applied to account for wave interaction with porous media. The bottom topography is considered to have a finite length, flanked by two semi-infinite sections of uniform bottom. The solution to the boundary value problem is approached by employing the eigenfunction expansion method within the uniform bottom regions. For the varying bottom topography, a modified mild-slope equation (MMSE) is utilized. To address the solution at the slope discontinuity at the bottom, a mass-conserving jump condition is applied. By matching solutions at the interfaces, a set of equations is derived. This system of equations encapsulates the behavior of reflection and transmission coefficients, as well as the force exerted on the breakwaters. These parameters are then investigated across various factors such as the length of the varying bottom, depth ratio, angle of the mooring line, angle of incidence, and flexural rigidity. Graphical representations of the reflection and transmission coefficients, along with the breakwater force, provide insights into the system’s behavior under different conditions. The water wave energy can be dissipated for the optimum values of flexural rigidity. The transmission coefficient is observed to be least for higher mooring angle.

Wave interaction with a rigid porous structure under the combined effect of refraction–diffraction

Water wave scattering, trapping, and generation by a thin porous structure placed on an uneven bottom are studied approximately. The classical eigenfunction expansion method is employed for the uniform bottom, whereas the Galerkin-Eigenfunction expansion method is employed for the uneven bottom. The solution is derived in the form of a system of algebraic equations through matching procedure. Wave reflection, transmission, and wave-induced forces on the porous structure and backwall are investigated under the combined refraction–diffraction effect. In the scattering problem with periodic bottom, Bragg resonance is minimized at the Bragg frequency, whereas the porous structure at other frequencies maximizes wave reflection. Consequently, wave transmission is very low for all wave frequencies in this situation. In the wave trapping problem, forces on the porous structure and the backwall are reduced substantially when the water depth ratio decreases. Feasible locations of the porous structure are shown at which wave reflection and forces on it and backwall are optimized. In the wave generation problem, the comparison of results for flat and uneven bottoms reveals that waves have a smaller amplitude at infinity as uniform bottom levels become farther for relatively small values of the reciprocal of the wave-effect parameter (C).

Attenuation in hydroelastic response of floating-elastic-plate by porous membrane in two-layer fluid with bottom undulation

The prime intention of this article is to study the effects of bottom undulation and a porous membrane barrier on the hydroelastic response of an elastic plate floating in a two-layer fluid with changing bottom topography assuming the small amplitude waves and potential flow theory. Finite and semi-infinite plates coupled with porous membrane barriers are considered in this study. As a mathematical technique, the eigenfunction expansion method along with an approximation method mild-slope are adopted for the uniform bottom and variable bottom topographies, respectively. In the variable bottom topography, a system of differential equations is solved. By using matching and jump conditions, the solution is expressed as a linear algebraic system, from which the unknown constants of interest are computed. The effects of fluid density ratio, water depth ratio, bottom topography, and porous membrane on the bending moment, shear force, and deflection of the elastic plate are studied. It is found that when the density ratio becomes closer to one, the bending moments and shear forces acting on the elastic plates tend to diminish. The variations in the bending moments, shear forces, and plate deflection with respect to changing density ratios are found to be in opposite trends caused by surface and interfacial waves, respectively. With higher tension and a less porous membrane, the bending moment, shear forces, and pate deflection are reduced. Concave-up bottoms reflect more surface wave energy, whereas concave-down bottoms reflect more interfacial wave energy. The observations made in this article may help in analyzing the response of very-large floating structures in the presence of an undulating seabed.

Wave interaction with an array of porous walls in a two-layer ocean of varying bottom topography

Oblique wave scattering by a breakwater consisting of an array of thin porous walls in a two-layer ocean with varying bottom topography is investigated by using linear wave theory. Further, wave trapping is studied by considering an impermeable seawall. The entire bottom profile is assumed to be a shelf-type comprising a varying bottom of finite length and two uniform bottoms of semi-infinite lengths. Porous walls extending from bottom to free-surface are assumed at a lower water-depth level (lee side). Impingement of waves, which approach from a deeper depth level (seaside), on walls is considered. The Fourier method or method of eigenfunction expansion is applied for the uniform bottom, whereas an approximation technique, called a mild-slope equation, is used for the varying bottom. Solutions from these two methods are matched at interfaces under physical conditions. An explicit solution is derived in the form of a system of algebraic equations. The effect of several bottom configurations on wave interaction with porous walls is analyzed. Reflection and transmission coefficients and wave force on porous walls and seawall are analyzed for the parameters related to waves, bottom, and porous medium. The study reveals that porous walls are very effective in reducing wave transmission for bottom profiles dominated by waves. Wave forces on porous walls are less in the two-layer ocean than in a homogeneous ocean. In wave trapping, seawall attains higher wave-force for incoming surface waves than for incoming interfacial waves. The ratio of water-depth levels and wave incident angles are also analyzed for the mitigation of wave forces. The force on seawall increases with the increased depth ratio in surface wave incidence, while the force decreases with the increased depth ratio in interface wave incidence. The findings may be useful for coastal engineers to understand wave scattering by multiple porous structures in the stratified ocean.

SURFACE WAVE SCATTERING BY AN ELASTIC PLATE SUBMERGED IN WATER WITH UNEVEN BOTTOM

Wave interaction with a vertical elastic plate in presence of undulating bottom topography is considered, assuming linear theory and utilizing simple perturbation analysis. First order correction to the velocity potential corresponding to the problem of scattering by a vertical elastic plate submerged in a fluid with a uniform bottom is obtained by invoking the Green’s integral theorem in a suitable manner. With sinusoidal undulation at the bottom, the first-order transmission coefficient (T1) vanishes identically. Behaviour of the first order reflection coefficient (R1) depending on the plate length, ripple number, ripple amplitude and flexural rigidity of the plate is depicted graphically. Also, the resonant nature of the first order reflection is observed at a particular value of the ratio of surface wavelength to that of the bottom undulations. The net reflection coefficient due to the joint effect of the plate and the bottom undulation is also presented for different flexural rigidity of the plate. When the rigidity parameter is made sufficiently large, the results for R1 reduce to the known results for a surface piercing rigid plate in water with bottom undulation.

Seismic characteristics and evolution of post-rift igneous complexes and hydrothermal vents in the Lingshui sag (Qiongdongnan basin), northwestern South China Sea

The study of morphology, distribution, and characteristics of igneous complexes has great significance to the understanding of magma plumbing processes, geodynamics, and tectonic evolution of continental margins. Previous studies concentrated partly on the magma-rich rifted basins, where the lateral magma transport mainly affects the igneous complexes' connection and distribution. However, due to seismic wave shielding effects of the large shallow magmatic bodies, the underlying igneous complexes and their corresponding magma plumbing systems in the magma-poor rifted margins are still in debate. In this study, 2D/3D seismic data and well data are utilized to describe the morphology, architecture, and spatial-temporal distribution of igneous complexes in the Lingshui sag of the Qiongdongnan basin, northwestern South China Sea margin. The identified igneous complexes include 98 intrusive sills and feeder dykes beneath some of the isolated sills. Twenty-six cone-shaped mounds that overlie intruded sills through internal disturbed conduits were also described. Drilled well samples and seismic expressions suggest that these mounds are hydrothermal vents. A uniform Bottom Mounds Horizon of these vents suggests that they probably formed at the same time. Constrained by biostratigraphic data and sedimentation rate of underlying and overlying sedimentary layers, the magma emplacement was dated to the middle Miocene (ca. 14.6 Ma). Most of the hydrothermal vents are distributed along the F2 fault zone and have direct linkage with the underlying sills, while the large sill complexes that are connected with limited vents are mainly present above the hyperextended continental crust, where the crust thins to 6–10 km. The sills intruded into different layers, from the lower Oligocene to the lower Miocene and the emplaced depth of sills is 1.2–6.3 km, whether or not they feed any vents above. Unlike most of the large volume and laterally linked sills found in the magma-rich rifted margins, the scattered distribution of sills at different levels indicates that dykes probably play an important role in magma transport, which might coexist with numerous polygonal or small faults and interference reflections. This work highlights the critical role of basin structures in controlling the distribution of post-rift igneous complexes in magma-poor margins, including thinned continental crust, sedimentary thickness, and faults.

Effect of a Floating Elastic Plate/Membrane on the Motion Due to a Ring Source in Water With Porous Bed

The velocity potentials due to the presence of a horizontal circular ring of wave sources of timedependent strength in water of finite constant depth with a floating elastic plate or a floating membrane are determined. The uniform bottom is composed of non-dissipative porous medium. The problems are formulated as the initial value problems and the Laplace transform method is used to solve these. For time-harmonic source strength, the steady-state analysis of the potentials reveals the existence of outgoing progressive waves. Graphs for the surface profiles are presented for different values of the tension parameter for the membrane, flexural rigidity of ice and the porous-effect parameter.

Highly Anisotropic Adhesive Film Made from Upside-Down, Flat, and Uniform Vertically Aligned CNTs.

We have created a multifunctional dry adhesive film with transferred vertically aligned carbon nanotubes (VA-CNTs). This unique VA-CNT film was fabricated by a multistep transfer process, converting the flat and uniform bottom of VA-CNTs grown on atomically flat silicon wafer substrates into the top surface of an adhesive layer. Unlike as-grown VA-CNTs, which have a nonuniform surface, randomly entangled CNT arrays, and a weak interface between the CNTs and substrates, this transferred VA-CNT film shows an extremely high coefficient of static friction (COF) of up to 60 and a shear adhesion force 30 times higher (12 N/cm2) than that of the as-grown VA-CNTs under a very small preloading of 0.2 N/cm2. Moreover, a near-zero normal adhesion force was observed with 20 mN/cm2 preloading and a maximum 100-μm displacement in a piezo scanner, demonstrating ideal properties for an artificial gecko foot. Using this unique structural feature and anisotropic adhesion properties, we also demonstrate effective removal and assembly of nanoparticles into organized micrometer-scale circular and line patterns by a single brushing of this flat and uniform VA-CNT film.

Analytical and numerical study of dual-chamber oscillating water columns on stepped bottom

The effect on the efficiency of the device of implementing a dual-chamber oscillating water column (OWC) placed over stepped bottom is analysed. The mathematical problem is formulated in the two dimensional Cartesian coordinate system under the linear water wave theory. Two different mathematical approaches are adopted to solve the associated boundary value problem (BVP), one is the method of matched eigenfunction expansion and the other is the boundary integral equation method (BIEM). The numerical results show good agreement with the analytical results. The performance of the proposed device is analysed and compared with the typical single chamber OWCs with/without step and with dual-chamber OWCs over uniform bottom profile. The present investigation shows that by considering dual-chamber OWC device on the stepped sea bottom the performance of the device can be improved significantly in wide range of frequencies, as compared with the single chamber case.

Dissolved Oxygen Dynamics at the Sediment–Water Column Interface in an Urbanized Stream

This manuscript reports findings on sediment oxygen demand (SOD), gross primary production (GPP), net daily metabolism (NDM), and stream reaeration in an urbanized stream, the Jordan River, in Utah. The river has two segments; the Lower Jordan River, which is impaired for dissolved oxygen (DO) and the Upper Jordan River, which is fast flowing with coarse sediments and has no DO impairment. Summer SOD values for the Lower Jordan River ranged from a high 2.2 g DO/m2 per day to a low of 0.97 g DO/m2 per day with most of the sampled sites in the Lower Jordan River having SOD values greater than 1 g DO/m2 per day. SOD values correlated well with volatile solids in surface sediments of the Lower Jordan River. The Upper Jordan River showed SOD values as high as 3.0 g DO/m2 per day, which was attributed to hyporheic exchanges or groundwater upwelling. All sampled sites exhibited high SOD values in winter. A modified chamber method was employed to estimate community respiration (CR24), GPP, and NDM, while characterizing both the water column and benthos. In summer 2010, the sediment tray primary production (TPP) ranged from 1.0 to 7.4 g DO/m2 per day. In winter 2011, TPP ranged from 0.7 g DO/m2 per day to a high value of 5.6 g DO/m2 per day. NDM values indicated that the Upper Jordan River is a year round source of in-stream produced organic matter to the downstream Lower Jordan River with the majority of organic matter produced in the benthos. Reaeration measurements showed that the potential for reaeration is much higher in the mid-sections of the Jordan River, where the river has increased flow velocities due to topography, decreased depths, and a less uniform bottom.

LAGRANGIAN BREAKER CHARACTERISTICS FOR NONLINEAR WATER WAVES PROPAGATING ON SLOPING BOTTOMS

In this paper, a new third-order Lagrangian asymptotic solution describing nonlinear water wave propagation on the surface of a uniform sloping bottom is presented. The model is formulated in the Lagrangian variables and we use a two-parameter perturbation method to develop a new mathematical derivation. The particle trajectories, wave pressure and Lagrangian velocity potential are obtained as a function of the nonlinear wave steepness ï¥ and the bottom slope ï¡ perturbed to third order. The analytical solution in Lagrangian form satisfies state of the normal pressure at the free surface. The condition of the conservation of mass flux is examined in detail for the first time. The two important properties in Lagrangian coordinates, Lagrangian wave frequency and Lagrangian mean level, are included in the third-order solution. The solution can also be used to estimate the mean return current for waves progressing over the sloping bottom. The Lagrangian solution untangle the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile and water particle trajectories leading to wave breaking. The proposed model has proved to be capable of a better description of non-linear wave effects than the corresponding approximation of the same order derived by using the Eulerian description. 
 The proposed solution has also been used to determine the wave shoaling process, and the comparisons between the experimental and theoretical results are presented in Fig.1a~1b. In addition, the basic wave-breaking criterion, namely the kinematical Stokes stability condition, has been investigated. The comparisons between the present theory, empirical formula of Goda (2004) and the experiments made by Iwagali et al.(1974), Deo et al.(2003) and Tsai et al.(2005) for the breaking index(Hb/L0) versus the relative water depth(d0/L0) under two different bottom slopes are depicted in Figs 2a~2b. It is found that the theoretical breaking index is well agreement with the experimental results for three bottom slopes. However,for steep slope of 1/3 shown in Fig 2b, the result of Goda's empirical formula gives a larger value in comparison with the experimental data and the present theory. Some of empirical formulas presented the breaking wave height in terms of deepwater wave condition, such as in Sunamura (1983) and in Rattanapitikon and Shibayama(2000). Base on the results depicted in Fig. 3a~3b, it showed that the theoretical results are in good agreement with the experimental data (Iwagali et al. 1974, Deo et al.2003 and Tsai et al. 2005) than the empirical formulas. The empirical formula of Sunamura (1983) always predicts an overestimation value.

Impact of stratification on internal waves and differential wearing of thermal inversions on the east coast of India

The surface layers of the Bay of Bengal along the east coast of India exhibit intricate stratification owing to the differential distribution of freshwaters. The winter (January–February) cooling of the salinity-induced stable layers results in the development of thermal inversions that deteriorate toward the end of the season. The study focuses on the behavior of the thermal inversions in the light of the variable stratification and the monsoon imposed reversing coastal current. To address the associated processes, a three-dimensional Princeton Ocean Model is applied for the east coast of India, and numerical experiments carried out to study the means by which the thermal inversions tend to perish with the passage of winter. The model domain with variable curvilinear grid uses input fields that comprise realistic bathymetry and initial temperature/salinity conforming to winter/specified stratification. The surface forcing comprises wind stress and diurnal pattern air–sea heat fluxes. The body forcing is derived from the periodic tidal elevations at the open boundaries. It has been found that the thermal inversions tend to sustain as the equator-ward flowing East India Coastal Current (EICC) traps the cool low saline waters between Paradip and Kakinada. The current off Paradip is weak and variable and is not a part of EICC. Consequently, in the absence of replenishment of cool and freshsurface waters, the temperature/salinity gradients get eroded steadily. No thermal inversions are noticed south of Kakinada because of relatively weak current with diminished vertical salinity gradient. As the nature of stratification encountered in the bay is highly variable due to diverse reasons, the behavior of internal waves under different stratification scenarios is also addressed. Numerical experiments indicate that the energy/amplitude of the internal waves are comparable in the surface layers for any stratification, where as it is certain orders exalted in the deeper waters of the strong stratification scenario. Further, it is found that the energies and pattern of the temperature oscillations conform to the nature of mixed tide at the corresponding latitude. The underneath stratification is found to be more responsible for the generation of internal waves compared to the local stratification. This implies that the body forcing emanating from below is the cardinal contributor for the generation of internal waves. The numerical experiment with a flat and uniform bottom showing weak manifestation of internal waves endorses the same. This connotes that the continental slopes are an effective generator of the internal waves and the energy flux conversion of the barotropic tide to internal waves seems to be heavily dependent on the shoaling bottom.

On Generating Uniform Bottom Shear Stress. Part II: Shear Stress Inducing Devices

On Generating Uniform Bottom Shear Stress. Part II: Shear Stress Inducing Devices

On Generating Uniform Bottom Shear Stress. Part I: A quantitative study of microcosm chambers

On Generating Uniform Bottom Shear Stress. Part I: A quantitative study of microcosm chambers

On Generating Uniform Bottom Shear Stress. Part II: Shear Stress Inducing Devices

Controlling and uniforming bottom shear stress is an important issue in many technical apparatus applied in biotechnology, chemical and process engineering, medicine and also in marine sciences. The device used in the latter application, has been referred to as microcosm, and was studied in detail in part I of this study (Khalili et al, Recent patents in Chem. Eng., 2008). The present investigation deals with quantification of the ability of shear stress uniformity achieved by two other devices known as shear stress inducers, which consist of a cone rotating in a fixed cylindrical container. In a detailed numerical study, the effect of all influencing parameters -cone angle, distance between the cone-tip and the the bottom disk, and Reynolds number- were investigated. The results confirm that the performance of shear stress inducers strongly depends on the input parameters, and that the inducers can not be regarded as a universal device to generate optimal uniformity. Keywords: Benthic chamber, microcosm chamber, viscosimeter, shear stress uniformity, rotating cone, linear and curved cone

On Generating Uniform Bottom Shear Stress. Part I: A quantitative study of microcosm chambers

Generating uniform shear stress planes finds a variety of applications in different disciplines such as process engineering, medicine and marine sciences. The focus of this study is to quantify the potential of microcosm chambers, applied in marine applications, in producing shear stress uniformity at the chamber bottom. To do this, computational fluid dynamics was used to simulate the flow pattern, velocity profiles, and shear stress distribution at chamber bottom. The study revealed that the microcosm chambers, such as those presented in the patent of Gust, produce a fully vortical flow, containing acceleration-deceleration zones near the central axis and the outer wall. The results show that the presence of these acceleration-deceleration zones is the major reasons for non-uniform shear stress formation at the chamber bottom. Utilizing a suction-injection mechanism and-or attached skirt provides better bottom shear stress profiles compared to a conventional disk-cylinder. In spite of this partial improvement, the addition of a suction-injection device or a skirt attached to the disk provide a partial shear stress uniformity only over the 72% of the bottom area, and are therefore of limited use.

Effects of channel morphology and sensor spatial resolution on image-derived depth estimates

The utility of remote sensing in the study of fluvial systems depends upon the extent to which image data can be used to derive quantitative information of sufficient accuracy and precision for specific applications. In this study, we evaluate the effects of channel morphology on depth retrieval by coupling a radiative transfer model to various morphologic scenarios. Upwelling radiance L u spectra generated for a range of depths (2–150 cm) and benthic cover types (limestone, periphyton, and gravel) were linearly mixed to simulate sub-pixel bed topography and substrate heterogeneity. For sloping bottoms, solar–streambed geometry modified L u relative to a level bottom, especially for beds sloping steeply away from the sun. Aggregate pixel scale L u spectra were compared to a database of simulated spectra to determine the radiance-equivalent depth of a uniform bottom ( REDUB). REDUB spectra for hypothetical stepped streambeds indicated underestimation of the actual area-weighted mean depth, but the ln ( L u ,560 / L u ,690 ) REDUB ratio consistently reproduced the pixel-scale mean for beta distributions of depths. Similarly, when both dark periphyton and bright limestone substrates occurred within a pixel, REDUB spectra produced large errors while the ratio proved robust. Along channel banks, pixels will inevitably be mixed, and our simulations indicated that although bank fractions estimated by spectral mixture analysis were highly accurate for vegetated cutbanks, gravel bars were sensitive to the selection of both aquatic and terrestrial end members and subject to relatively large fraction errors. These theoretical results were tested using a ratio-based relative depth map and two-end member mixture models derived from a hyperspectral image of the Lamar River in Yellowstone National Park, which also served to illustrate the importance and applicability of our simulations. The primary conclusions of this study are that 1) the ratio-based algorithm is well-suited to complex river channels; 2) channel morphology and sensor spatial resolution must be considered jointly during data collection and analysis; and 3) the accuracy and precision of depth estimates are influenced by channel morphology and thus vary spatially.

Integration of Poultry with Aquaculture in Seasonal Tank

An experiment was conducted for short-term culture of carps involving marginal farmers in a seasonal tank with area of 15 ha at Budhemanahalli in Bengalore district. A rectangular pen of size 60 m x 22 m was installed in the tank using a close meshed HDPE cloth in a pre-selected area with uniform bottom. A low cost thatched poultry shed of size 10 m x 6 m was constructed within the pen enclosure, perching 2 m above the water surface at full tank level. A total of 260 chicks (Giriraja) of average weight of 200 g were reared in the shed. The pen was stocked with 1500 fingerlings of common carp (av. wt. 5 g) during July. No manuring or feeding was adopted. After rearing period of 80 days, the birds attained an average weight of one kilogram and 182 kg of birds were disposed off. A total of 277 kg of fish was harvested from the pen in 150 days of culture. The size of the fish ranged between 238-350 mm (av. 254 mm) in length and 260-840 g (av. 346.6 g) in weight. The results indicated the feasibility of integrating aquaculture with poultry rearing in short seasonal tanks or watersheds.

Visual Image Retrieval by Multiscale Description of User Sketches

This paper describes an application allowing content-based retrieval. The application may be called ‘sketch-based database retrieval’ since the user interacts with the database by means of sketches. The user draws his request with a pencil: the request image is then a binary image that comprises a contour on a uniform bottom. The image-retrieval based on user-provided information such as hand-drawn sketches is a challenging problem in multimedia applications. A human's perception of shape can be rather subjective and has a large variance. In this paper, we propose to represent a sketch and a contours in image database by curvature scale space (CSS) description, which define an invariant distance in the shapes space. In theoretical aspect, the invariance, the completeness and the stability properties of CSS description imply the definition of a metric on the shape space. This distance allows us to compare a sketch to images in database. A prototype system has been developed for image retrieval by sketch. This system takes into account spatial relationships between objects in multi-objects queries.

Intratidal variations in stratification and mixing in the Hudson estuary

This study represents a detailed examination of intratidal variations in boundary‐layer structure in a relatively narrow, straight section of the Hudson river estuary during high river discharge. The presence of active mixing is inferred from estimates of the Richardson number. The maximum height above bed to which mixing occurs is comparable during flood and ebb; however, the regions of mixing differ in density structure. During the flood, active mixing is confined to a well‐mixed near‐bed layer, whereas during the ebb, active mixing occurs throughout regions of significant stratification. Tidal straining maintains stratification during the ebb, while it promotes the growth of a uniform bottom, mixed layer during the flood. In general, maximum and minimum near‐bed stratification occur during late ebb and flood, respectively, reflecting the dominant role played by tidal straining in determining intratidal variation. Vertical stretching was also found to be an important term in the stratification balance during the ebb.