Water waves generated by instantaneous disturbances at the bed of a sloping beach

The two-dimensional problem of the generation of water waves due to instantaneous disturbances prescribed at the bed of a beach sloping at an arbitrary angle is studied here. It is formulated in terms of an initial-boundary-value problem for the velocity potential describing the motion in the fluid region assuming the linear theory. Using the Laplace transform in time and the Mellin transform in distance, the problem is reduced to solving a difference equation whose method of solution is of considerable importance in the literature. The form of the free surface is obtained in terms of a multiple infinite integral that is evaluated by the method of steepest-descent. For some prescribed forms of the disturbance at the bed of the beach, the free surface is depicted in a number of figures for different beach angles. It is observed that as the beach angle decreases, the maximum wave height increases, which is plausible.     

Two-dimensional approximation for tide-induced watertable fluctuations in a sloping sandy beach

The prediction of watertable fluctuations in a coastal aquifer is important for coastal management. However, most previous approaches have based on the one-dimensional Boussinesq equation, neglecting variations in the coastline and beach slope. In this paper, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer bounded by a rhythmic coastline is derived. In the new model, the effect of beach slope is also included, a feature that has not been considered in previous two-dimensional approximations. Three small parameters, the shallow water parameter (ε), the amplitude parameter (α) and coastline parameter (β) are used in the perturbation approximation. The numerical results demonstrate the significant influence of both the coastline shape and beach slopes on tide-driven coastal groundwater fluctuations.     

The relation between the mean vector surface wind and the mean vector pressure gradient over the oceans

Summary Mean values of the angle of inclination between the mean vector surface wind and the mean isobars have been calculated as a function of latitude for a number of independent Marsden squares over the ocean. Mean values of the ratio between the mean vector surface wind velocity and the calculated geostrophic wind velocity have been computed in the same way. Some general inferences about the general circulation have been drawn from the results.     

Berm formation and dynamics on a gently sloping beach; the effect of water level and swash overtopping

Berm formation and morphological development of the beach face have been observed during a neap–neap tidal cycle on the gently sloping and accreting beach at Vejers, Denmark. During the field campaign, an intertidal bar migrated onshore and stabilized as a berm on the foreshore. A new intertidal bar occurred on the lower beach face, migrated onshore on the rising tide and finally merged with the pre‐existing berm. As the tide continued to rise, the new berm translated further onshore as an intertidal bar to the uppermost part of the foreshore. The sediment transport during the berm transition was onshore directed in the upper swash and offshore directed in the lower swash. This berm development can be described through both the neap‐berm, ridge‐and‐runnel and berm‐ridge development concepts proposed by Hine (Sedimentology 1979; 26: 333–351), and all three stages were observed during only three tidal cycles. The main factors controlling this fast transformation were the gentle slope of the cross‐shore profile, rapid water level translation rates, substantial swash overtopping of the berm, and low infiltration rates. Despite the onshore migration of intertidal bars and berm formation, no net foreshore accretion took place during the field campaign. This was largely due to the formation of rip channels with strong rip currents cutting through the intertidal bars and the berm, which acted as a sediment drain in the profile. Copyright © 2009 John Wiley & Sons, Ltd.     

Geoelectromagnetic variations over a sloping ocean floor up to and including the coastline

Summary The electric and magnetic field variations over an arbitrarily sloping ocean floor are represented in series of Bessel functions forH-polarized uniform plane wave excitation. Calculation of the spatial variations of electric eurrents and apparent resistivity near a coastline will determine the usefulness of the magnetotelluric method in this application.The work presented herein was conducted at the Institute for Applied Mathematics of the University of Oslo, Oslo, Norway.     

Projected changes in mean and interannual variability of surface water over continental China

Five General Circulation Model(GCM) climate projections under the RCP8.5 emission scenario were used to drive the Variable Infiltration Capacity(VIC) hydrologic model to investigate the impacts of climate change on hydrologic cycle over continental China in the 21 st century. The bias-corrected climatic variables were generated for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change(IPCC AR5) by the Inter-Sectoral Impact Model Intercomparison Project(ISIMIP). Results showed much larger fractional changes of annual mean Evapotranspiration(ET) per unit warming than the corresponding fractional changes of Precipitation(P) per unit warming across the country, especially for South China, which led to a notable decrease of surface water variability(P-E). Specifically, negative trends for annual mean runoff up to -0.33%/ year and soil moisture trends varying between -0.02% to -0.13%/year were found for most river basins across China. Coincidentally, interannual variability for both runoff and soil moisture exhibited significant positive trends for almost all river basins across China, implying an increase in extremes relative to the mean conditions. Noticeably, the largest positive trends for runoff variability and soil moisture variability, which were up to 0.41%/year and 0.90%/year, both occurred in Southwest China. In addition to the regional contrast, intra-seasonal variation was also large for the runoff mean and runoff variability changes, but small for the soil moisture mean and variability changes. Our results suggest that future climate change could further exacerbate existing water-related risks(e.g., floods and droughts) across China as indicated by the marked decrease of surface water amounts combined with a steady increase of interannual variability throughout the 21 st century. This study highlights the regional contrast and intra-seasonal variations for the projected hydrologic changes and could provide a multi-scale guidance for assessing effective adaptation strategies for China on a river basin, regional, or as a whole.     

Beach erosion and recovery during consecutive storms at a steep‐sloping,meso‐tidal beach

This study analyses beach morphological change during six consecutive storms acting on the meso‐tidal Faro Beach (south Portugal) between 15 December 2009 and 7 January 2010. Morphological change of the sub‐aerial beach profile was monitored through frequent topographic surveys across 11 transects. Measurements of the surf/swash zone dimensions, nearshore bar dynamics, and wave run‐up were extracted from time averaged and timestack coastal images, and wave and tidal data were obtained from offshore stations. All the information combined suggests that during consecutive storm events, the antecedent morphological state can initially be the dominant controlling factor of beach response; while the hydrodynamic forcing, and especially the tide and surge levels, become more important during the later stages of a storm period. The dataset also reveals the dynamic nature of steep‐sloping beaches, since sub‐aerial beach volume reductions up to 30 m³/m were followed by intertidal area recovery (–2 < z < 3 m) with rates reaching ~10 m³/m. However, the observed cumulative dune erosion and profile pivoting imply that storms, even of regular intensity, can have a dramatic impact when they occur in groups. Nearshore bars seemed to respond to temporal scales more related to storm sequences than to individual events. The formation of a prominent crescentic offshore bar at ~200 m from the shoreline appeared to reverse the previous offshore migration trend of the inner bar, which was gradually shifted close to the seaward swash zone boundary. The partially understood nearshore bar processes appeared to be critical for storm wave attenuation in the surf zone; and were considered mainly responsible for the poor interpretation of the observed beach behaviour on the grounds of standard, non‐dimensional, morphological parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

On the mean atmospheric circulation over Antarctica

Abstract

The south-easterly surface flow down the slopes of Antarctica induces a transfer of westerly angular momentum to the atmosphere, which must be removed from the Antarctic domain by atmospheric transports. It is suggested that synoptic eddies protruding from the northern baroclinic zone into the polar regions are modified by the topography such that they are able to perform these meridional transports. A simple linear two-layer model of the axisymmetric circulation of Antarctica is presented where the eddy effects are incorporated via a K-ansatz. It is shown that qualitatively realistic mean flow patterns can be obtained with this model. The limitations of this approach are exposed.     

Equilibrium modeling of the beach profile on a macrotidal embayed low tide terrace beach

Eleven-year long time series of monthly beach profile surveys and hourly incident wave conditions are analyzed for a macrotidal Low Tide Terrace beach. The lower intertidal zone of the beach has a pluriannual cycle, whereas the upper beach profile has a predominantly seasonal cycle. An equilibrium model is applied to study the variation of the contour elevation positions in the intertidal zone as a function of the wave energy, wave power, and water level. When forcing the model with wave energy, the predictive ability of the equilibrium model is around 60% in the upper intertidal zone but decreases to 40% in the lower intertidal zone. Using wave power increases the predictive ability up to 70% in both the upper and lower intertidal zones. However, changes around the inflection point are not well predicted. The equilibrium model is then extended to take into account the effects of the tide level. The initial results do not show an increase in the predictive capacity of the model, but do allow the model free parameters to represent more accurately the values expected in a macrotidal environment. This allows comparing the empirical model calibration in different tidal environment. The interpretation of the model free parameter variation across the intertidal zone highlights the behavior of the different zones along the intertidal beach profile. This contributes to a global interpretation of the four model parameters for beaches with different tidal ranges, and therefore to a global model applicable at a wide variety sites.     

Transmission of Rayleigh waves over the surface of a heterogeneous medium

Summary The frequency equation of Rayleigh waves propagating over the free surface of an isotropic, perfectly elastic, heterogeneous semi-infinite medium with material properties varying as = ₀ e ^az , = ₀ e ^az , = ₀ e ^az (a>0) has been obtained. Solution of the frequency equation in closed form is obtained in two cases (i) =0, (ii) =, and the Rayleigh wave dispersion curves for phase and group velocities drawn. In both the cases the medium yields single Rayleigh modes which cannot propagate below certain cut-off frequencies. It is found that in case (i), <c<c ₀ and 0.87500 <c _g <c ₀, and in case (ii), 1.03082 <c<c ₁ and 0.90850 <c _g <c ₁, wherec andc _g denote phase nad group velocities respectively, is the constant shear wave velocity of the mediumc ₀ andc ₁ are the corresponding Rayleigh wave velocities of the homogeneous medium of the same Poisson's ratio. The motion of the surface particles is found to be retrograde elliptical as in the homogeneous case, but the ratic of the major and minor axes now becomes frequency dependent and is plotted against frequency. In both the cases (i) and (ii), the ratio starts at a lower value at the cut-off frequency and approaches the corresponding value of the homogeneous medium at high frequencies.     

The effects of surface moisture on aeolian sediment transport threshold and mass flux on a beach

This paper presents results from a study designed to explore the effects of beach surface moisture and fetch effects on the threshold of movement, intensity of sand transport by wind and mass flux. The experiment was carried out over a period of five weeks at Greenwich Dunes, Prince Edward Island, Canada in May and June 2002. Moisture content was measured with a Delta‐T moisture probe over a 50 m by 25 m grid established on the beach. Measurements of wind speed and direction were made with arrays of cup anemometers and a two‐dimensional sonic anemometer. Transport intensity was measured at a height of 2–4 cm above the bed using omnidirectional saltation probes which count the impact of saltating grains on a piezoelectric crystal. Anemometers and saltation probes were sampled at 1 Hz. Sand transport was measured with vertical integrating sand traps over periods of 10–20 minutes. Results show that where there is a considerable supply of dry sand the saltation system responds very rapidly (1–2 s) to fluctuations in wind speed, i.e. to wind gusts. Where sand supply from the surface is limited by moisture, mean transport rates are much lower and this reflects in both a reduction in the instantaneous transport rate and in a transport system that becomes increasingly intermittent. Threshold wind speed is significantly correlated with an increase in surface moisture content near the upwind end of the beach fetch, but the relationship is not significant at the downwind end where sediment transport is initiated primarily by saltation impact from upwind. Mass flux increases with increasing fetch length and the relationship is described best by a power function. Further work is necessary to develop a theoretical function to predict the increase in transport with fetch distance as well as the critical fetch distance. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental investigation of the velocity of a sand cloud blowing over a sandy surface

The velocity of a wind‐blown sand cloud is important for studying its kinetic energy, related erosion, and control measures. PDA (particle dynamics analyser) measurement technology is used in a wind tunnel to study the probability distribution of particle velocity, variations with height of the mean velocity and particle turbulence in a sand cloud blowing over a sandy surface. The results suggest that the probability distribution of the particle velocity in a blowing sand cloud is stochastic. The probability distribution of the downwind velocity complies with a Gaussian function, while that of the vertical velocity is greatly complicated by grain impact with the bed and particle–particle collisions in the air. The probability distribution of the vertical velocity of ?ne particles (0·1–0·3 mm sands) can be expressed as a Lorentzian function while that of coarse particles (0·3–0·6 mm sands) cannot be expressed by a simple distribution function. The mean downwind velocity is generally one or two orders greater than the mean vertical velocity, but the particle turbulence in the vertical direction is at least two orders greater than that in the downwind direction. In general, the mean downwind velocity increases with height and free‐stream wind velocity, but decreases with grain size. The variation with height of the mean downwind velocity can be expressed by a power function. The particle turbulence of a blowing sand cloud in the downwind direction decreases with height. The variations with height of the mean velocity and particle turbulence in the vertical direction are very complex. It can be concluded that the velocity of a sand cloud blowing over a sandy surface is mainly in?uenced by wind velocity, grain impact with the bed and particle–particle collisions in the air. Wind velocity is the primary factor in?uencing the downwind velocity of a blowing sand cloud, while the grain impact with the bed and particle–particle collisions in the air are the primary factors responsible for the vertical velocity. Copyright © 2004 John Wiley & Sons, Ltd.     

SPH simulation of free surface flow over a sharp-crested weir

In this paper the numerical simulation of a free surface flow over a sharp-crested weir is presented. Since in this case the usual shallow water assumptions are not satisfied, we propose to solve the problem using the full weakly compressible Navier–Stokes equations with the Tait equation of state for water. The numerical method used consists of the new meshless Smooth Particle Hydrodynamics (SPH) formulation proposed by Ferrari et al. (2009) [8], that accurately tracks the free surface profile and provides monotone pressure fields. Thus, the unsteady evolution of the complex moving material interface (free surface) can been properly solved. The simulations involving about half a million of fluid particles have been run in parallel on two of the most powerful High Performance Computing (HPC) facilities in Europe. The validation of the results has been carried out analysing the pressure field and comparing the free surface profiles obtained with the SPH scheme with experimental measurements available in literature [18]. A very good quantitative agreement has been obtained.     

Barotropic instability of a boundary jet on a sloping bottom

Abstract

The stability of a shear flow on a sloping bottom in a homogeneous, rotating system was investigated by means of a laboratory experiment.

The basic flow was driven near a vertical wall of a circular container by a ring-shaped plate that contacted with a free surface of the working fluid and rotated relative to the fluid container. The velocity profile was asymmetric in the radial direction and had only one inflection point. The velocity profile was well expressed by a linear theory for the vertical shear layer.

The effect of the circular geometry was checked by comparing experimental results obtained in two fluid systems in which only the sign of the curvature was opposite and it was confirmed that circular geometry was not essential for the shear flow on the sloping bottom in this experiment.

It was found that the sloping bottom stabilizes the basic flow only when the drift direction of the topographic Rossby wave is opposite to that of the basic flow. The viscous dissipation in both the Ekman layer and the interior region was also important in determining the critical Rossby number.

The eddy fields caused by the instability can be classified into two types: One is the stationary eddy field in which a row of eddies moves along the basic flow without changing form. The other is the flow pattern in which eddies have finite life times and their configuration is not well organized. When the sloping bottom does not stabilize the basic flow, the former flow pattern is realized, otherwise the latter flow pattern appears.

The wave numbers of the eddies in the regular flow pattern were observed as a function of the Rossby number. The relation did not fit to linear preferred modes predicted by an eigenvalue problem.     

Magnetotelluric response of a two-dimensional sloping contact by the finite element method

Summary The finite element method, with triangular elements, is used to study the effect of a two-dimensional sloping contact on the surface electromagnetic fields. It is found in the case ofH-polarization and small slopes that the electric field and the apparent resistivity near the contact, on the conductive side, are higher than their asymptotic values. In the case ofE-polarization the apparent resistivity and phase values on the conductive side fall off less rapidly to their asymptotic values with decreasing slope resulting in higher apparent resistivity and phase values on the conductive side, than those expected for a vertical contact. The peak in the amplitude and phase of the normalized vertical magnetic field shifts from the resistive side for a vertical contact to the conductive side for a sloping contact. Far from the sloping contact, on the conductive side, higher values are observed for the normalized vertical magnetic field than in the case of a vertical contact.     

Preliminary hydrodynamic results of a field experiment on a barred beach, Truc Vert beach on October 2001

A field experiment conducted on a sandy barred beach, situated on the southern part of the French Atlantic coastline, allowed us to investigate the impact of the intertidal bar on the wave-energy dissipation on the beach face in presence of a high-energy long-incoming swell (significant wave height of about 1.7 to 3.0 m in 56 m water depth and significant wave period about 12 s). Data were collected along three parallel cross-shore transects deployed along an intertidal ridge and runnel system. Wave heights in the inner surf zone are depth-limited, consistent with previous works, and the wave-energy dissipation in the inner surf zone appears to be relatively independent of the offshore energy level. On the other hand, the presence of the bar seems to scatter the data. In models of surf-zone hydrodynamics, wave-energy dissipation is often parameterized in terms of , the ratio of the sea-swell significant wave height to the local mean water depth. The observed values of are not constant along a cross-shore transect, and increase onshore. Furthermore, the observed values observed onshore the intertidal bar are higher than those observed outside the influence of the intertidal bar, and this cannot be fully explained by the different local beach slope.Responsible Editor: Iris Grabemann