Reflection Of Long Waves Research Articles

HARMONIC WAVES ON AN ABRUPT TRANSITION

A simple long-wave reflection and transmission over an abrupt depth change with constant channel width are presented. Firstly, the wave propagation is modeled on a two-step abrupt transition, and the waves are reflected and transmitted only once. The model is extended to include more than one re-reflection and retransmission as well as depth-limited breaking-wave height criteria. The Dean beach profile is also modeled. The profile is a function of the median grain size of the beach material. It is found that the wave energy is conserved when the waves are re-reflected and retransmitted more than five times. The breaking waves reduce the reflection coefficient by 30%. The results are compared with other research on the reflection coefficient occurring in a smooth sloping beach model. On a small sloping beach, an abrupt depth change gives a significant difference in the value of the reflection coefficient. The reflection coefficient on the smooth small sloping beach is close to zero, while the abrupt depth change can increase the reflectioncoefficient to about 60% in this case.

Quantifying the impact of urban climate by extending the boundaries of urban energy system modeling

Rapid growth of cities, concerns on global warming and depletion of fossil fuel resources call for sustainable energy solutions for cities. Distributed energy systems such as energy hubs offer promising solutions in this context. Evaluating the energy demand at urban scale is vital to support the design of energy hubs. However, most of the recent studies are based on bottom-up models and do not consider the energy demand in detail. More specifically, the influence of the urban climate on urban energy demand has not been considered so far in the energy system design process. In order to address this research gap, a novel computational platform is developed in the first part of this study, combining an urban climate model with a building simulation tool and an energy system optimization model. The second part of the manuscript is devoted to quantifying the impact of urban climate on energy system design and assessing the consequences of neglecting this specific aspect on energy system performance. Three case studies are conducted considering three building densities for the city of Nablus (building density at the periphery, center and future center of the city) in Palestine. Three scenarios representing (1) standalone buildings (present practice) (2) shadowing and longwave reflection (radiation heat transfer from the walls and the roofs of the buildings to the urban climate and to the sky) of neighboring buildings and (3) urban climate are considered for each case study when computing the energy demand. Subsequently, the energy system is optimized considering Net Present Value (NPV) and system autonomy level as the objective functions (Pareto optimization). The results of the study reveal that the urban climate has a notable impact on the energy demand and energy system design. More importantly, it is shown that the influence of urban climate results in higher fluctuations in the energy demand, which in turn results in a notable increase in the NPV (by up to 40%). This further magnifies the increase in annual or peak demand. The study reveals that neglecting the influence of urban climate in the energy system design process can result in a performance gap in NPV, grid integration level, and greenhouse gas emissions and can impose reliability issues. The design tool introduced in this study can be used for urban planning to mitigate the aforementioned adverse effects.

Optimization of parabolic bars for maximum Bragg resonant reflection of long waves

This paper presents an analytical solution for the problem of the long wave reflection by a series of artificial bars with parabolic configuration in terms of the associated Legendre functions. It is shown that both the reflection and transmission coefficients depend solely upon the number of bars, the dimensionless bar height, the dimensionless bar width and the dimensionless bar distance. Particularly, under the Bragg resonance condition, i.e., the distance between two adjacent bars is about half of the wavelength of the normal incident waves, the analytical solution for the peak Bragg resonant reflection is obtained, which reveals that the peak Bragg resonance depends upon the number of bars, the dimensionless bar height and the dimensionless bar width. Based on this solution, the optimization of the parabolic bars is made to obtain the maximum Bragg resonance and a group of optimal curves, which may be very useful in the design of Bragg breakwaters with parabolic bars.

Experimental studies of the local reflection of long waves from an underwater slope

The regularities of the local reflection of long waves from underwater slopes with different inclinations were investigated using the data of a laboratory experiment that was performed at a scale of 1 : 20 compared to the full-scale conditions. It is shown that the coefficient of the local reflection of waves decreases with the distance from the coast. The dissipation of the wave energy significantly reduces the local reflection coefficient near the shoreline and at the most remote sea point of the underwater slope. This leads to the existence of maximum of the local reflection coefficient at the boundary of the wave breaking. The presence of peculiarities of the bottom topography, such as an underwater bar or trench, can also significantly change the local reflection coefficient and influence its values in the offshore part of the underwater slope.

Experimental Investigation of Local Reflection of Long Wave from Sloping Underwater Bottom

Experimental Investigation of Local Reflection of Long Wave from Sloping Underwater Bottom

Optimal Collocation of Three Kinds of Bragg Breakwaters for Bragg Resonant Reflection by Long Waves

AbstractIt is well known that, for a series of submerged artificial bars uniformly distributed in the coastal region parallel to the coastline, if the wavelength of the incident wave train is twice that of the bar distance, Bragg resonant reflection occurs. In this paper, three closed-form analytical solutions for linear long-wave reflection for bars with triangular shape, rectified cosinoidal shape, and idealized trapezoidal shape are presented. These analytical solutions show that the magnitude of the peak Bragg resonant reflection still depends on three bar parameters, which are the bar number, the dimensionless bar height, and the dimensionless bar width. Based on intensive analysis of the relations among these parameters, three sets of optimal curves to determine the optimal collocation of the three types of artificial bars are established, which may be very significant in the study of Bragg resonance and in the fundamental design of Bragg breakwaters.

Analytical Solution for Long-Wave Reflection by a General Breakwater or Trench with Curvilinear Slopes

AbstractIn the first part of this paper, an exact analytical solution in closed form for linear long-wave reflection by a submerged idealized breakwater or trench with various curvilinear slopes is given. The solution obtained finds almost all previous long-wave analytical solutions for wave reflection by idealized bathymetries to be its special cases, including the wave reflection by an infinite step, a continental shelf with a parabolic slope, a continental shelf with a linear slope, a rectangular obstacle, an obstacle of general trapezoidal shape with linear slopes, and a trench of general trapezoidal shape with linear slopes. In the second part, an exact analytical solution in the form of a Taylor series for linear long-wave reflection by a submerged quasi-idealized breakwater or trench is also constructed. It is shown by convergence analysis that the series solution converges in the entire physical domain. Based on the present analytical solutions, the reflection coefficients for long waves reflected...

Reflection of a long wave from an underwater slope

Reflection of long sea waves from an underwater slope described by a power law is studied within the shallow water theory. The slope is connected with the flat bottom. This model allows us to estimate the roles of a pointwise reflection from the inflection point of the bottom profile and distributed reflection at the underwater slope. The case of the underwater slope described by the so-called nonreflecting beach (h(x) ∼ x 4/3, where h is the depth of the basin and x is the coordinate) when the wave is reflected only from the inflection point (pointwise reflection) is specially considered. The reflection and transmission coefficients over the bottom topography were calculated, and it was shown that the sum of the squared absolute values of these values differs from unity for all profiles except the nonreflecting one. This difference is related to the distributed re-reflections (resonances) over the underwater slope that lead to the deviations in the wave height from the known Green’s law.

Analytical Solution for Long-Wave Reflection by a Rectangular Obstacle with Two Scour Trenches

In this paper, linear long-wave reflection by a rectangular obstacle with two scour trenches of power function profile is explored. A closed-form analytical solution in terms of the first and second kinds of Bessel functions is obtained, which finds two classic analytical solutions as its special cases, i.e., the wave reflection from a rectangular obstacle and from an infinite step. The phenomenon of zero reflection coefficient for a single rectangular obstacle with the same depths in front of and behind the obstacle still remains for a rectangular obstacle with two scour trenches as long as the bathymetry is symmetrical about the obstacle. The periodicity of the reflection coefficient as a function of the relative length of the middle rectangular obstacle disappears if two scour trenches are attached to the middle rectangular obstacle. Finally, the wave reflection by a rectangular obstacle with two scour trenches generally increases when the trenches become wide and deep. The wave reflection by a degener...

Experimental study of long wave generation on sloping bottoms

Low-frequency waves generated on steep (1:10) and mild (1:40) slopes by six series of bichromatic wave groups are studied experimentally. The shorelines for both slopes are replaced by horizontal reaches of small depth. This reduces the reflection of long waves near the shoreline significantly, which for the first time makes possible the explicit observation of outgoing breakpoint forced long waves. The breakpoint and released bound long wave mechanisms on the different slopes are compared. Generally, the breakpoint forced long waves dominate the low-frequency wave field on the steep slope, while the released bound long waves are found to be more significant on the mild slope. Two parameters indexing the effectiveness of the breakpoint mechanism are compared and the normalized slope tends to give more realistic results. Shoaling of bound long waves is analyzed and the shallow-water equilibrium limit ~ h −5/2 exhibits a good prediction of the variation of the bound long waves on both slopes.

Assessing the diurnal evolution of surface radiation balance over the western region of Tropical Atlantic Ocean using in situ measurements carried out during the FluTuA Project

AbstractIn this work, the diurnal evolution of the radiation balance components over the tropical Atlantic Ocean is described and analysed. The analysis is based on measurements carried out on board a Brazilian Navy ship during the observational campaign of the FluTuA Project (‘Fluxos Turbulentos sobre o Atlântico’), from 15 to 23 May 2002. The observations indicated that the albedo responds as expected to atmospheric attenuation effects with a diurnal evolution similar to the Fresnel albedo. In general, the observed longwave radiation values agreed better with the estimated values obtained without longwave reflection. In agreement with the literature, the average surface emissivity was around 0.97. The net radiation, estimated from published equations for albedo, atmospheric transmissivity and surface emissivity, agreed with the observations, indicating that these parameters are representative of the radiometric properties of the air‐sea interface in the region between Natal (6°S, 35.2°W) and the São Pedro and São Paulo Archipelago (1°N, 29.3°W). Copyright © 2008 Royal Meteorological Society

Long wave reflection from submerged trapezoidal breakwaters

This study addresses the reflection and transmission of long waves from a trapezoidal breakwater and a series of trapezoidal breakwaters, using the matching method. A systematic shape transfer is derived to determine wave reflection and transmission. The peak Bragg reflection of long waves from a series of trapezoidal breakwaters is shifted toward low frequency. In spite of the spacing between any pair of breakwaters, the top plane width and the arrangement of the series of breakwaters are found to be the two major parameters in designing multiply composite Bragg breakwaters.

Propagation of Long Water Waves through Branching Channels

This paper investigates the fundamental behavior of long water waves propagating through branching channels of uniform depth and width. Numerical simulations based on the Boussinesq long wave model were carried out to investigate the effects of channel width b, effective wavelength λe, wave amplitude α, and angle θ between channel branches on wave transmission and reflection. Our results showed that the transmission and reflection of long waves through branching channels are dominantly governed by a single dimensionless parameter b∕λe, whereas other parameters such as the angle between channel branches are less important. Detailed quantitative results for predicting long wave transmission and reflection in different branching channels based on the similarity parameter b∕λe were determined. From these results, we have discovered some very interesting and distinct long wave behaviors in narrow and wide branching channels. To verify the numerical results, experiments were conducted in a right-angled branching channel, and the experimental results showed good agreement with the numerical predictions.

Analytical Study of Linear Long-Wave Reflection by a Two-Dimensional Obstacle of General Trapezoidal Shape

In this paper, an analytical solution for linear long-wave reflection by an obstacle of general trapezoidal shape is explored. A closed-form expression in terms of first and second kinds of Bessel functions is obtained for the wave reflection coefficient, which depends on the relative lengths of the two slopes and top of the obstacle as well as the depth ratios in front of and behind the obstacle versus that above the obstacle. The analytical solution obtained in this study finds a few well-known analytical solutions to be its special cases, which include the wave reflection from a rectangular obstacle, an infinite step, and an infinite step behind a linear slope. The present analytical solution, however, covers a much wider range of problems. It is found that the periodicity of the wave reflection coefficient as the function of the relative length of the obstacle remains when two slopes are present but with a reduced magnitude. The phenomenon of zero wave reflection from the structure is special to a rectangular obstacle only, which disappears with the addition of a slope in front or at the rear. The new solution may be very useful in some engineering applications, for example, the design of a submerged breakwater of trapezoidal shape.

CRYPTIC DICHROMATISM AND SEASONAL COLOR VARIATION IN THE DIADEMED TANAGER

Abstract We studied the patterns of sexual dichromatism and seasonal variation in plumage color in the Diademed Tanager (Stephanophorus diadematus), a species previously considered devoid of variation in adult plumage. The general coloration of this species is dark blue-violet, with a white-blue and red crown. Plumage reflectance of seven body regions from 33 study skins belonging to adults of both sexes was measured. Reflectance values were used in a principal components analysis (PCA) and hue, short-wave chroma, and UV chroma were also measured directly on the spectra. Both PCA factor scores and these latter variables were subjected to two-way ANCOVAs with sex and season as main factors and the year of capture as a covariate. We found that crowns of males were significantly brighter than those of females. In addition, the nape, chest, and belly showed significant differences in spectral shape, with relatively greater short-wave reflectance and less long-wave reflectance in males than in females. Althoug...

Tunneling and reflection of long waves

We investigate tunneling through a barrier and reflection over a step potential in the limit of long waves, i.e., near the base of the barrier, or for barriers with a small action integral over the forbidden region, and at the top of the ramp where the usual semiclassical approximation breaks down systematically. General approximations of the probability of transmission and reflection are given and compared to competing ones showing that the present approach based on the comparison method can give far better results.

Oblique Long Waves on Beach and Induced Longshore Current

This study considers the 3D runup of long waves on a uniform beach of constant or variable downward slope that is connected to an open ocean of uniform depth. An inviscid linear long-wave theory is applied to obtain the fundamental solution for a uniform train of sinusoidal waves obliquely incident upon a uniform beach of variable downward slope without wave breaking. For waves at nearly grazing incidence, runup is significant only for the waves in a set of eigenmodes being trapped within the beach at resonance with the exterior ocean waves. Fourier synthesis is employed to analyze a solitary wave and a train of cnoidal waves obliquely incident upon a sloping beach, with the nonlinear and dispersive effects neglected at this stage. Comparison is made between the present theory and the ray theory to ascertain a criterion of validity. The wave-induced longshore current is evaluated by finding the Stokes drift of the fluid particles carried by the momentum of the waves obliquely incident upon a sloping beach. Currents of significant velocities are produced by waves at incidence angles about 45 [degrees] and by grazing waves trapped on the beach. Also explored are the effects of the variable downward slope and curvature of a uniform beach on 3D runup and reflection of long waves.

Propagation of solitary waves through significantly curved shallow water channels

Propagation of solitary waves in curved shallow water channels of constant depth and width is investigated by carrying out numerical simulations based on the generalized weakly nonlinear and weakly dispersive Boussinesq model. The objective is to investigate the effects of channel width and bending sharpness on the transmission and reflection of long waves propagating through significantly curved channels. Our numerical results show that, when travelling through narrow channel bends including both smooth and sharp-cornered 90°-bends, a solitary wave is transmitted almost completely with little reflection and scattering. For wide channel bends, we find that, if the bend is rounded and smooth, a solitary wave is still fully transmitted with little backward reflection, but the transmitted wave will no longer preserve the shape of the original solitary wave but will disintegrate into several smaller waves. For solitary waves travelling through wide sharp-cornered 90°-bends, wave reflection is seen to be very significant, and the wider the channel bend, the stronger the reflected wave amplitude. Our numerical results for waves in sharp-cornered 90°-bends revealed a similarity relationship which indicates that the ratios of the transmitted and reflected wave amplitude, excess mass and energy to the original wave amplitude, mass and energy all depend on one single dimensionless parameter, namely the ratio of the channel width b to the effective wavelength λe. Quantitative results for predicting wave transmission and reflection based on b/λe are presented.

Modeling the effect of mulch optical properties and mulch-soil contact resistance on soil heating under plastic mulch culture

A numerical model was developed to simulate the effect of plastic mulches on the field energy balance and soil temperature regime. Newton-Raphson methods were used to solve the energy balances of the soil and mulch simultaneously. The resultant temperature of the soil surface was used as a boundary condition for an implicit finite difference model of soil heat flow. The model contained a detailed radiation section to account for mulch optical properties in shortwave and longwave bands. Heat transfer between the mulch and soil surface was modeled using a thermal contact resistance, and transport in the boundary layer was quantified using flux profile theory. The effect of evaporation and condensation on the underside of the mulch was not considered. The accuracy of the model was verified by comparing simulated soil temperatures with field data collected under five commercially available mulches. Simulated average daily temperatures were within ±1.3°C of the observed values and root mean square errors were less than 2.5°C in all cases. The model showed that mulch optical properties strongly influenced the way energy was partitioned at the surface. Complete characterization of the mulches in the longwave spectrum was required for realistic simulation. Changing longwave reflectance by only 0.3, for example, caused maximum soil temperature to change by 5°C under some mulches. Thermal contact resistance between the mulch and soil affected temperatures by up to 20°C beneath mulches that strongly transmitted or absorbed radiation. However, contact resistance was not an important factor for mulches that had nearly equal shortwave transmittance and absorptance. Results demonstrate that a complex relationship exists between mulch optical properties and thermal contact resistance. Modification of mulch longwave properties during manufacturing and control of thermal contact resistance during mulch installation appear to be two promising areas for research. An alternative numerical scheme was evaluated that utilized linear forms of the energy balance equations. The linearized model produced results almost identical to the original model, but required less computing time and could be adapted easily to simulate multiple mulch layers.

Simulation of Surface Energy Balance and Soil Temperature under Strip Tillage: I. Model Description

AbstractConservation‐tillage practices that reduce soil erosion and conserve moisture are becoming more widespread. In northern latitudes, germination and early crop development may be hindered due to slower soil warming under mulched surfaces. Strip tillage, in which mulch or stubble strips alternate with bare planting strips, represents a compromise between conservation of soil and water by mulch or stubble and more rapid spring warming of bare soil. The object of our research was to identify the processes that determine surface energy‐balance components and soil temperatures under strip tillage and simulate them using a physically based numerical model, which consists of soil‐temperature and surface‐energy‐balance submodels. Dynamic inputs to the model are solar irradiances, air temperatures, water‐vapor densities, and wind speeds measured above the surface. The energy‐balance model determines radiation, heat, and water‐vapor transfers within the mulch and between the mulch surface and atmosphere, as well as the surface energy balance in the bare strip, including shading, shortwave and longwave reflection, and emission effects of the mulch sides. An explicit finite‐difference numerical technique is used to predict soil temperatures and heat fluxes. The soil‐temperature model was in excellent agreement with analytical solutions to periodic heat‐transfer problems in one‐dimensional nonbomogeneous and two‐dimensional homogeneous semi‐infinite soils with surface boundary conditions of the third kind (linear combination of soil heat flux and temperature specified at the surface).