High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom

High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).

Statistical Analyses of Wave Height Distribution for Multidirectional Irregular Waves over A Sloping Bottom

The main objective of this paper is to examine the influences of both the principal wave direction and the directional spreading parameter of the wave energy on the wave height evolution of multidirectional irregular waves over an impermeable sloping bottom and to propose an improved wave height distribution model based on an existing classical formula.The numerical model FUNWAVE 2.0,based on a fully nonlinear Boussinesq equation,is employed to simulate the propagation of multidirectional irregular waves over the sloping bottom.Comparisons of wave heights derived from wave trains with various principal wave directions and different directional spreading parameters are conducted.Results show that both the principal wave direction and the wave directional spread have significant influences on the wave height evolution on a varying coastal topography.The shoaling effect for the wave height is obviously weakened with the increase of the principal wave direction and with the decrease of the directional spreading parameter.With the simulated data,the classical Klopman wave height distribution model is improved by considering the influences of both factors.It is found that the improved model performs better in describing the wave height distribution for the multidirectional irregular waves in shallow water.

EFFECTS OF SLOPING BOTTOM ON THE DEEPCROSS-EQUATORIAL BOUNDARY CURRENT

This paper reports study focusing on the effects of sloping bottom on the deep cross-equatorial boundary current, and discusses model and laboratory experiment results showing that the southward that the southward intrusion distance and flow speed of the western boundary current depend on the bottom slope variation rate,the difference between and and are the current thickness at eastward edge and westward edge, respectively), and the net mass transport.

Coupled Perturbed Modes over Sloping Penetrable Bottom

In environments with water depth variations, one-way modal solutions involve mode coupling. Higham and Tindle developed an accurate and fast approach using perturbation theory to locally determine the change in mode functions at steps. The method of Higham and Tindle is limited to low frequency （≤250 Hz）. We extend the coupled perturbation method, thus it can be applied to higher frequencies. The approach is described and some examples are given.

Effect of the sloping seabed on 3D soil-spudcan interaction using a material point-finite element(MPM-FEM)model

The sloping seabed affects the bearing capacity and failure mechanism of soil,which may compromise the stability and safety of offshore structures such as jack-up platforms.This paper employs a coupled model combining the material point method and finite element method(MPM-FEM)to analyze the impact of sloping seabeds on the three-dimensional soil-spudcan interaction.The MPM-FEM model implements the B¯approach to solve the challenge of volumetric locking due to the incompressibility constraints imposed by yield criterion.It is validated against the centrifuge results.The effects of sloping seabeds on penetration resistance,soil flow pattern,lateral response,stress distribution,and failure mechanism are discussed.The soil mainly undergoes overall failure when the ratio of penetration depth to spudcan diameter(i.e.D P/D)is between 0 and 0.25.As the slope angle increases,the soil on the side of lower slope is expelled further,resulting in an asymmetric stress distribution and a larger horizontal sliding force of soil.When D P/D increases to 0.75,the soil transitions to localized plastic flow failure,and the range of soil flow affected by the spudcan penetration decreases.The results show that,when the slope angle increases,the lateral displacement and stress distribution on the lower slope of a sloping seabed is significantly larger than that of a horizontal seabed,impacting the spudcan and surrounding soil behavior.The study suggests that the seabed slope significantly affects the range of soil flow and failure at shallow penetration,indicating that the slope angle should be taken into account in the design and installation of offshore jack-up rigs,particularly in areas with sloping seabeds.

Heat-Generating Effects Involving Multiple Nanofluids in a Hybrid Convective Boundary Layer Flow on the Sloping Plate in a Porous Medium

The hybrid convective boundary layer circulation involving multiple nanofluids via a medium with pores is approaching a sloping plate. An investigation regarding the heat-generating effects upon the examined nanofluid flows has been carried out through computational analysis. A mathematical framework employing governing differential equations that are partial has been implemented to produce an ensemble of ordinary differential equations, which happen to be nonlinear that incorporate nanofluid flows by utilizing acceptable transformations. Through the combination of the Nachtsheim-Swigert shooting method and the Runge-Kutta method, the group of resulting non-dimensionalized equations is solved computationally. In a few special, confined cases, the corresponding numeric output is thereafter satisfactorily matched with the existing available research. The consequences of heat generation regarding local skin friction coefficient and rate of heat in conjunction with mass transfer have been investigated, evaluated, and reported on the basis of multiple nanofluid flows.

Error Analysis on Gradient Information of Sloping Land Derived from the Low-resolution DEM

With digital elevation model （DEM）,sloping data were extracted automatically and soil erosion situation was also investigated. Compared with field survey and the related studies,the results showed that parallel range-gorge landform in Three Gorges reservoir area,the inter-bedded structures formed by Jurassic purple clay （page） rocks and human activities were the key controlling factors for small-scale sloping terrain.

Effect of Soil Erosion on Productivity of Sloping Field in a Micro-plot Experiment

[Objective] This study aimed to explore the effects of soil erosion on the productivity of sloping field. [Method] Through removing of and covering with topsoil in a micro-plot experiment, the effect of soil erosion on productivity of sloping field was studied. [Result] The results showed that there was extremely significantly posi- tive correlation between the thicknesses of covered topsoil with either the yield of maize seeds or the yield of maize stalks, which indicated that the yields of maize seeds and maize stalks decreased extremely significantly with the increase of the amount of surface soil loss caused by erosion on the sloping field. The yields of maize seeds and maize stalks decreased by 29.62% and 24.46% respectively in the treatment with removal of a 15 cm thick layer of mature topsoil in the plow layer; the yields of maize seeds and maize stalks decreased by 17.31% and 20.14% re- spectively in the treatment with removal of a 10 cm thick layer of mature topsoil in the plow layer; the yields of maize seeds and maize stalks decreased by 12.69% and 11.51% respectively in the treatment with removal of a 5 cm thick layer of ma- ture topsoil in the plow layer; the yields of maize seeds and maize stalks increased by 10.00% and 9.35% respectively in the treatment with covering with a 5 cm thick layer of mature topsoil in the plow layer; the yields of maize seeds and maize stalks increased by 15.77% and 16.19% respectively in the treatment with covering with a 10 cm thick layer of mature topsoil in the plow layer; the yields of maize seeds and maize stalks increased by 17.69% and 25.18% respectively in the treat- ment with covering with a 15 cm thick layer of mature topsoil in the plow layer. [Conclusion] This study provides a basis for assessing the effect of soil erosion on sloping field.

Weathering Characteristics of Sloping Fields in the Three Gorges Reservoir Area, China

For the purpose of understanding the weathering characteristics of surface layers in purple mudstone sloping fields of the Three Gorges Reservoir area of China, oxide content of major elements, composition of clay minerals, magnetic susceptibility, and difference in weathering characteristics of surface layers under different slope gradients were determined. The results showed that the oxide content of Si, Al, and Fe ranged from 60% to 75% and the weathering coefficient with depth showed no trend along the slope gradient. Also, for gentle (10° and 15°) and intermediate (25° and 40°) slopes the clay relative diffraction peak for kaolinite at the surface between 0-10 cm and 10-20 cm declined with an increase in slope gradient, while the relative diffraction peak for kaolinite in weathered layers on steep slopes (50° and 60°) disappeared altogether. Magnetic susceptibility decreased with increasing depth and, for a given depth layer, decreased with an increase in slope gradient. Analysis of the oxide content, weathering coefficients, clay minerals, and magnetic susceptibility showed that in the Three Gorges Reservoir area, the pedogenesis of the weathering layer in purple mudstone sloping fields was weak with weaker soil formation going from gentle slope to steep slope.

Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived. The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool, such as mass flow rates, flow coefficients, effiux angles and steady state flow forces under different operating conditions. At last, the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test. It is presented that the bottom arc of sloping U-shape notch （ABU） should not be omitted when it is required to accurately calculate the orifice area of ABU. Although the theoretical flow area of plain bottom sloping U-shape notch （PBU） is larger than that of ABU at the same opening, the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening, while the simulated flow force of PBU is larger than that of ABU at the same opening. Therefore, it should be prior to adapt the ABU when designing the spool with proportional character.

Three-dimensional analysis of the modified sloping cooling/shearing process

A self-designed setup of modified sloping cooling/shearing process was made to prepare the semisolid Al-3wt%Mg alloy. A three-dimensional simulation model was established for the analysis of preparing the semisolid Al-3wt%Mg alloy. Through simulation and experiment, it is shown that the sloping angle of the plate greatly affects temperature and velocity distributions, and the temperature and velocity of the alloy at the exit of the sloping plate increase with the increase of the sloping angle. The alloy temperature decreases linearly from the pouring mouth to the exit. The alloy temperature at the exit increases obviously with the increase of pouring temperature. To prepare the semisolid Al-3wt%Mg alloy with good quality, the sloping angle θ=45° is reasonable, and the pouring temperature is suggested to be designed above 650-660℃ but under 700℃.

Effectiveness of sloping agricultural land technology on soil fertility status of mid-hills in Nepal

Hedgerows with intercropping systems were established at the ICIMOD test and demonstration site at Godawari to assess the effective- ness of Sloping Agricultural Land Technology （SALT） in reducing run- off water volume, controlling soil loss, increasing crop production, and improving soil fertility in the mid-hills of Nepal. Runoff water volume （1996-2002）, soil loss （1996-2002） and maize yield （1995-2001）, and soil fertility-related parameters were assessed on SALT models with three factors： the type of nitrogen-fixing plant, the farmers＇ practice, and fertilizer use. Results showed a significant effect of Alnus nepalensis and/or Indigofera dosua on runoff water volume, soil loss, crop produc- tion, soil water retention, and soil nutrients （NPK）. Farmers＇ practice and fertilization did not play a significant role in reducing runoff water and soil loss. However, farmers＇ practice significantly increased crop produc- tion. Therefore, integrating soil conservation approaches on SALT sys- tems enhances stable economic output to hills and mountain farmers.

Bottom Currents Observed in and Around a Submarine Valley on the Continental Slope of the Northern South China Sea

Bottom currents at about 1000m depth in and around a submarine valley on the continental slope of the northern South China Sea were studied by a 14-month long experiment from July 2013 to September 2014. The observations reveal that bottom currents are strongly influenced by the topography, being along valley axis or isobaths. Power density spectrum analysis shows that all the currents have significant peaks at diurnal and semi-diurnal frequencies. Diurnal energy is dominant at the open slope site, which is consistent with many previous studies. However, at the site inside the valley the semi-diurnal energy dominates, although the distance between the two sites of observation is quite small （11 kin） compared to a typical horizontal first-mode internal tide wavelength （200 km）. We found this phenomenon is caused by the focusing of internal waves of certain frequencies in the valley. The inertial peak is found only at the open slope site in the first deployment but missing at the inside valley site and the rest of the de- ployments. Monthly averaged residual currents reveal that the near-bottom currents on the slope flow southwestward throughout the year except in August and September, 2013, from which we speculate that this is a result of the interaction between a mesoscale eddy and the canyon/sag topography. Currents inside the valley within about 10mab basically flow along slope and in the layers above the 10mab the currents are northwestward, that is, from the deep ocean to the shelf. The monthly mean current vectors manifest an Ek- man layer-like vertical structure at both sites, which rotate counter-clockwise looking from above.

Assessment of bearing capacity of interfering strip footings located near sloping surface considering artificial neural network technique

The bearing capacity of interfering footings located near the slope face suffers from reduced bearing capacity due to the formation of the curtailed passive zone. Depending upon the position of the footing, their spacing and steepness of the slope different extents of bearing capacity reduction can be exhibited. A series of finite element investigation has been done with the aid of Plaxis 3 D v AE.01 to elucidate the influence of various geotechnical and geometrical parameters on the ultimate bearing capacity of interfering surface strip footings located at the crest of the natural soil slope. Based on the large database obtained from the numerical simulation, a6-8-1 Artificial Neural Network architecture has been considered for the assessment of the ultimate bearing capacity of interfering strip footings placed on the crest of natural soil slope. Sensitivity analyses have been conducted to establish the relative significance of the contributory parameters, which exhibited that for the stated problem, apart from shear strength parameters, the setback ratio and spacing of footing are the prime contributory parameters.

Observational Study of Surface Wind along a Sloping Surface over Mountainous Terrain during Winter

The 2018 Winter Olympic and Paralympic Games will be held in Pyeongchang, Korea, during February and March. We examined the near surface winds and wind gusts along the sloping surface at two outdoor venues in Pyeongchang during February and March using surface wind data. The outdoor venues are located in a complex, mountainous terrain, and hence the near-surface winds form intricate patterns due to the interplay between large-scale and locally forced winds. During February and March, the dominant wind at the ridge level is westerly; however, a significant wind direction change is ob- served along the sloping surface at the venues. The winds on the sloping surface are also influenced by thermal forcing, showing increased upslope flow during daytime. When neutral air flows over the hill, the windward and leeward flows show a significantly different behavior. A higher correlation of the wind speed between upper- and lower-level stations is shown in the windward region compared with the leeward region. The strong synoptic wind, small width of the ridge, and steep leeward ridge slope angle provide favorable conditions for flow separation at the leeward toot of the ridge. The gust factor increases with decreasing surface elevation and is larger during daytime than nighttime. A significantly large gust factor is also observed in the leeward region.

Experimental Study on Mean Overtopping of Sloping Seawall Under Oblique Irregular Waves

In this paper, domestic and abroad research progresses and related calculation formulae of the mean overtopping discharge are summarized. Through integral physical model experiments, the relation between the wave direction and the overtopping discharge on the top of the sloping dike is focused on and put into analysis and discussion; and a modified formula for mean overtopping discharges under oblique irregular waves is proposed. The study shows that the mean overtopping discharge generally goes down as the relative wave obliquity fl increases for a fixed measurement point and the mean overtopping discharge generally increases as the wave steepness H/L decreases （the cycle increases） for a fixed relative wave obliquity.

Fate of Urea Applied to Peanut (Arachis hypogaea L.) on a Sloping Udic Ferrosol in Subtropical China

A field experiment was conducted to study the outcome of N using isotope-labeled urea with a peanut cropping system in a Udic Ferrosol on a 7% slope at the Ecological Experimental Station of Red Soil, Chinese Academy of Sciences. The micro-plots were designed in two sets with three replicates and four N treatments. An iron frame with its edge 10 cm above the ground was used to control soil erosion and runoff in set A, but in set B the upper edge of the frame was level with the ground. Randomly positioned 15…

Effects of Contour Hedgerow Intercropping on Nutrient Losses from the Sloping Farmland in the Three Gorges Area,China

Eutrophication is recognized as one of the major environmental problems in the Three Gorges Reservoir.Contour hedgerows have been used as a major soil and water conservation measure in this area.Accordingly,a two-year study was conducted to investigate the effects of contour hedgerow intercropping on nutrient loss from sloping farmland in this area.Four treatments were applied:(1) Maize + Soybean,(2) Maize,(3) Maize + Alfalfa,and(4) Maize + Hemerocallis citrina Baroni.Results indicated that nutrient loss in the control treatment(Maize) was serious,especially the average loss flux of total nitrogen(2245.8 mg) and total phosphate(2434.2 mg) in a typical rainfall event.However,the nutrient losses by runoff in the other three treatments with contour hedgerow intercropping showed significant reduction.Compared with the control treatment,the total nitrogen loss in the Alfalfa and Hemerocallis citrina Baroni decreased by 80.9% and 85.0%,respectively,and the total phosphorus loss in the two treatments decreased by 91.2% and 92.5%,respectively.Therefore,it is concluded that nutrient losses could be reduced by using contour hedgerows in the Three Gorges Region.Reducing runoff volume and sediment loss was the main mechanisms of contour hedgerow intercropping to reduce nutrient loss.

Kinematic analysis of geosynthetics-reinforced steep slopes with curved sloping surfaces and under earthquake regions

A procedure of kinematic analysis is presented in this study to assess the reinforcement force of geosynthetics required under seismic loadings, particularly for steep slopes which are hardly able to maintain its stability. Note that curved sloping surfaces widely exist in natural slopes, but existing literatures were mainly focusing on a planar surface in theoretical derivation, due to complicated calculations. Moreover, the non-uniform soil properties cannot be accounted for in conventional upper bound analysis. Pseudo-dynamic approach is used to represent horizontal and vertical accelerations which vary with time and space. In an effort to resolve the above problems, the discretization technique is developed to generate a discretized failure mechanism, decomposing the whole failure block into various components. An elementary analysis permits calculations of rates of work done by external and internal forces. Finally, the upper bound solution of the required reinforcement force is formulated based on the work rate-based balance equation. A parametric study is carried out to give insights on the implication of influential factors on the performance of geosynthetic-reinforced steep slopes.

Study of Spatial and Temporal Processes of Soil Erosion on Sloping Land Using Rare Earth Elements As Tracers

Rare earth elements (REE) were used to study the temporal and spatial processes of soil erosion from different depths and sections of a slope. Two simulated rainfall events were applied to a prepared plot with a slope of 22°. The total runoff and sediment yield were collected every minute during the rainfall events. During the first twenty minutes of the first rainfall event, the average rate of rill erosion and the accumulated sediment yield due to rill erosion was 0.5 and 0.3 times higher than for sheet erosion. During this time, most of the erosion occurred on the lower one third of the plot. After 20 min, rill erosion became the dominant process on the slope. The average acceleration in the rate of rill erosion, the rate of rill erosion and the accumulated sediment yield due to rill erosion were 42, 6 and 4 times higher than that of sheet erosion, respectively. During the first 35 minutes of the second rainfall event, the average acceleration in the rate of rill erosion was 6～9 times higher than that of sheet erosion. Afterwards, the slope became nearly stable with little change in either rill or sheet erosion rates. Initially, most of the rill erosion occurred in the lower third of the slope but later the preexisting rillhead in the middle section of the slope became reactivated and erosion in this section of the slope increased rapidly. These results indicate that REE tracer technology is a valuable tool for quantifying spatial and temporal changes in erosion from a soil slope.