A note on specific variability of long surface gravity waves and drag coefficient in coastal upwelling zone

In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. UsingGent andTaylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.     

Determining drag coefficients and their application in modelling of turbulent flow with submerged vegetation

Vegetation is a key aspect of water resources and ecology in natural rivers, floodplains and irrigation channels. The hydraulic resistance of the water flow is greatly changed when submerged vegetation is present. Three kinds of drag coefficients, i.e., the drag coefficient for an isolated cylinder, the bulk drag coefficient of an array of cylinders and the vertically distributed or local drag coefficient, have been commonly used as parameters to represent the vegetation drag force. In this paper, a comprehensive experimental study of submerged stems in an open channel flow is presented. Empirical formulae for the three drag coefficients were obtained based on our experimental results and on data from previous studies. A two-layer model was developed to solve the mean momentum equation, which was used to evaluate the vertical mean velocity profile with each of the drag coefficients. By comparing the velocity distribution model predictions and the measurement results, we found that the model with the drag coefficient for an isolated cylinder and the local drag coefficient was good fit. In addition, the model with the bulk drag coefficient gave much larger velocity values than measurements, but it could be improved by adding the bed friction effect and making choice of the depth-averaged velocity within the canopy layer.     

Analysis of key parameters in a diffusion type beach profile evolution model

Diffusion type formulations are commonly used in beach profile evolution models. The practical idea behind that is to map the behaviour of the beach profile onto a simple mathematical model that exhibits the same behaviour under defined operating conditions. The success of this approach is based on the accurate determination of key parameters in the diffusion model that govern its behaviour, using observed beach behaviour in the field. In order to determine these parameters, i.e. diffusion coefficient and a time and space varying source function, we used observations of historic beach profiles at Milford-on-Sea beach in Christchurch Bay, Dorset, United Kingdom. The relationship between the diffusion coefficient and Dean's equilibrium profile was investigated, leading to a new interpretation of the diffusion coefficient in terms of the sediment characteristics. The analysis also shows the significance of the diffusion process in the medium to long term evolution of the beach profile. A canonical correlation analysis (CCA) was undertaken in order to identify patterns of behaviour between wave conditions and source terms, and the possible correlations between them. The analysis provides strong evidence of a useful link between the source term in the simple dynamical equation and the distribution of wave steepness.     

Charnock dynamics: a model for the velocity structure in the wave boundary layer of the air–sea interface

We present a unified model of the air–sea boundary layer, which takes account of the air–sea momentum exchange across the sea surface. The recognition of the importance of the velocity shears in the water (which comprise a frictional shear and the Stokes shear due to the wave motion) in determining the sea surface roughness is a distinctive feature of the analysis, which leads to a prediction of the Charnock constant (α) in terms of two independent parameters, namely the wave age and the ratio of the Stokes shear to the Eulerian shear in the water. This expression is used to interpret the large observational variability of the Charnock constant. The 10-m drag coefficient can also be expressed using similar reasoning, and the introduction of a relation in which the ratio of the frictional shear in the water to the frictional shear in the air decreases with the friction velocity yields predictive relations for the variation of the 10-m drag coefficient at very high wind speeds both in the open ocean and in wind–wave tanks. The physical interpretation of this relation is that the production of spray essentially returns momentum from the ocean to the atmosphere, and this process becomes progressively more important as the wind speed increases.     

转换波AVO反演速度比各横波反射系数

Based on the empirical Gardner equation describing the relationship between density and compressional wave velocity, the converted wave reflection coefficient extrema attributes for AVO analysis are proposed and the relations between the extrema position and amplitude, average velocity ratio across the interface, and shear wave reflection coefficient are derived. The extrema position is a monotonically decreasing function of average velocity ratio, and the extrema amplitude is a function of average velocity ratio and shear wave reflection coefficient. For theoretical models, the average velocity ratio and shear wave reflection coefficient are inverted from the extrema position and amplitude obtained from fitting a power function to converted wave AVO curves. Shear wave reflection coefficient sections have clearer physical meaning than conventional converted wave stacked sections and establish the theoretical foundation for geological structural interpretation and event correlation. ＂The method of inverting average velocity ratio and shear wave reflection coefficient from the extrema position and amplitude obtained from fitting a power function is applied to real CCP gathers. The inverted average velocity ratios are consistent with those computed from compressional and shear wave well logs.     

Modeling deposition by wave-supported gravity flows on the Po River prodelta: From seasonal floods to prograding clinoforms

A simple model for wave-supported gravity flows is applied to sediment deposition off the mouth of the Po River at time scales ranging from a single major flood to steady-state clinoform progradation. Wave-supported gravity flows are a newly appreciated class of turbidity currents, which rely on the velocity shear produced by waves near the seabed to keep sediment in suspension. The modeling approach used here, which limits the gravity flow's sediment load via a critical Richardson number, is applicable to fine sediment transport near river mouths wherever wave energy is available to move abundant sediment offshore during floods. Results suggest this phenomenon can account for the majority of the fall 2000 flood deposit mapped by EuroSTRATAFORM investigators in the vicinity of the Po River prodelta and also for the rate of prodelta progradation observed off the dominant Pila outlet of the Po over a century time-scale. Model results predict that convergence of down-slope sediment transport by wave-supported gravity flows increases with bed slope but decreases with slope gradient, such that greatest deposition occurs near where steep slopes first stop increasing with distance offshore. Thus on profiles which reach maximum steepness near shore, like those off Tolle–Gnocca–Goro mouths today or off the Pila mouth 150 y ago, gravity-driven deposition occurs in shallower water. Over time, if deposition overwhelms subsidence, the prodelta becomes less steep near shore and steeper offshore, and the locus of deposition moves progressively into deeper water. If the prodelta is prograding across a relatively flat shelf, the shape of the prodelta eventually reaches a stable form which progrades seaward as a unit. This has occurred off the Pila; but subsidence has likely overwhelmed deposition off the Tolle–Gnocca–Goro, keeping steepest slopes and maximum deposition in shallower water.     

On the variability of the Charnock constant and the functional dependence of the drag coefficient on wind speed

A model for the air–sea interface, based on the coupled pair of similarity relations for “aerodynamically” rough flow in both fluids, is presented, which is applied to fetch-limited and high wind speed conditions which occur, for example, in hurricanes. It is shown that the specification of the maximum 10-m drag coefficient and the 10-m wind speed and the peak wave speed at which it occurs are sufficient to uniquely determine the drag law, which asymptotes at low wind speeds to a Charnock constant similar to that for the fully developed wind wave sea and is almost independent of the peak wave speed at the maximum in drag coefficient. A feature of the drag law is that it is of Charnock form, almost independent of the wave age, consistent with the transfer of momentum to the wave spectrum being due to the smaller rather than the dominant wavelengths. The analysis is also applied to a variable sea state in which either the surface wind or the surface Stokes drift vary, but the peak wave speed is kept constant. The corresponding variability in the Charnock constant is in general accord with observations.     

Prediction of the drag law for air–sea momentum exchange

In this paper, we use the inertial coupling relation as a similarity model for the air–sea boundary layer, to predict the 10-m drag coefficient. Excellent agreement with the commonly used statistical relationship of Garratt (1992) is found for a fully developed growing wind wave sea with a constant inertial drag coefficient, K_I = 1.5 × 10^–3. This suggests that the inertial coupling model can be used to realistically predict the 10 m drag coefficient under more general wind wave conditions.Acknowledgements The paper was completed while JATB was a Fellow at the Hanse-Wissenschaftskolleg in Delmenhorst, Germany, in July and August 2004. The comments of two anonymous reviewers are gratefully acknowledged.     

Similarity analysis and scaling: An application to soil infiltration properties

Similarity and scaling theory are applied to soil physics, specifically to several parameters of unsaturated soil water movement. Following a dimensional analysis of Richards' equation, a mechanical similarity criterion of the hydraulic parameters is developed. Dimensionless factors which conform to assumptions of kinematic and dynamic mechanical similarity in the flow system are converted to relations using the scale factor a derived under the assumption of geometric similarity. As an example, the infiltration process is assessed through scaling of the parameters in Philip's equation, using experimental data from double-ring infiltration measurements at 54 locations in a study catchment as the scaling test.     

基于储层砂岩微观孔隙结构特征的弹性波频散响应分析

储层砂岩微观孔隙结构特征不仅影响干燥岩石的弹性波传播速度,也决定了岩石介质中与流体流动相关的速度频散与衰减作用.依据储层砂岩微观结构特征及速度随有效压力变化的非线性特征,将其孔隙体系理想化为不同形状的硬孔隙(纵横比α0.01)与软孔隙(纵横比α0.01)的组合(双孔隙结构).基于孔弹性理论,给出软孔隙最小初始纵横比值(一定压力下所有未闭合软孔隙在零压力时的纵横比最小值)的解析表达式,并在此基础上利用岩石速度-压力实验观测结果给出求取介质中两类孔隙纵横比及其含量分布特征的方法.通过逐步迭代加入软孔隙的方法对基于特征纵横比的"喷射流"(squirt fluid)模型进行了扩展,以考虑复杂孔隙分布特征对岩石喷射流作用的影响及其可能引起的速度频散特征.相较于典型的喷射流作用速度频散模式,对于岩石中软孔隙纵横比及其对应含量在较宽的范围呈谱分布的一般情况,其速度频散曲线不存在明显的低频段和中间频段,速度随频率的增大呈递增趋势直至高频极限.这说明即使在地震频段,微观尺度下的喷射流作用仍起一定作用,同样会造成流体饱和岩石介质的地震速度与Gassmann方程预测结果有不可忽略的差异.本文是对现有喷射流模型的重要补充,也为利用实验数据建立不同频段间岩石弹性波传播速度的可能联系提供了理论依据.     

Fission of a weakly nonlinear interfacial solitary wave at a step

The transformation of a weakly nonlinear interfacial solitary wave in an ideal two-layer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a weak transformation for propagation into deeper water. Far from the step, the wave dynamics is described by the Korteweg-de Vries equation which is fully integrable. In the vicinity of the step, the reflected and transmitted waves have soliton-like shapes, but their parameters do not satisfy the steady-state soliton solutions. Using the inverse scattering technique it is shown that the reflected wave evolves into a single soliton and dispersing radiation if the wave propagates from deep to shallow water, and only dispersing radiation if the wave propagates from shallow to deep water. The dynamics of the transmitted wave is more complicated. In particular, if the coefficient of the nonlinear quadratic term in the Korteweg-de Vries equation is not changed in sign in the region after the step, the transmitted wave evolves into a group of solitons and radiation, a process similar to soliton fission for surface gravity waves at a step. But if the coefficient of the nonlinear term changes sign, the soliton is destroyed completely and transforms into radiation. The effects of cubic nonlinearity are studied in the framework of the extended Korteweg-de Vries (Gardner) equation which is also integrable. The higher-order nonlinear effects influence the amplitudes of the generated solitons if the amplitude of the transformed wave is comparable with the thickness of lower layer, but otherwise the process of soliton fission is qualitatively the same as in the framework of the Korteweg-de Vries equation.     

Statistical distribution of nonlinear random wave height in shallow water

Here we present a statistical model of random wave,using Stokes wave theory of water wave dynamics,as well as a new nonlinear probability distribution function of wave height in shallow water.It is more physically logical to use the wave steepness of shallow water and the factor of shallow water as the parameters in the wave height distribution.The results indicate that the two parameters not only could be parameters of the distribution function of wave height but also could reflect the degree of wave heigh...     

Measurements of Reynolds stress in a wind-driven lagoonal estuary

Acoustic Doppler current profilers (ADCPs) have been used to measure Reynolds stresses in tidally dominated environments where wave action was minimal. In this paper, we examine observations from a microtidal estuary where the effects of wind stress and surface waves dominate the velocity variance. Reynolds stress measurements in this setting require a technique for addressing surface gravity wave contamination. We present here a method of reducing the effect of wave motion on Reynolds stresses by subtracting coincident observations along the axis of the ADCP beam. Linear wave theory is used to account for the attenuation of wave orbital velocities with depth. Using this method, Reynolds stress values are brought in line with those predicted by drag laws at the surface and bottom. The apparent Reynolds stress that is removed by the along-axis subtraction is shown to be largely due to the interaction of a slight tilt (1°) in the ADCP and the wave orbital velocity. During periods of stronger wind and waves, there is evidence of enhanced near-surface turbulence and momentum flux, presumably due to breaking waves. During these events, our calculated Reynolds stress magnitudes still appear reasonable, although the directions are suspect. We develop a diagnostic technique that clearly demarcates this region when it occurs. Coincident density profile measurements are used with the ADCP data to compute gradient Richardson numbers throughout the water column. Enhanced Reynolds stresses appear to correspond to Richardson numbers less than one. Responsible editor: Alejandro Souza     

A comparison of methods for low streamflow estimation from spot measurements

Low streamflow statistic estimators at ungauged river sites generally have large errors and uncertainties. This can be due to many reasons, including lack of data, complex hydrologic processes, and the inadequate or improper characterization of watershed hydrogeology. One potential solution is to take a small number of streamflow measurements at an ungauged site to either estimate hydrogeologic indices or transfer information from a nearby site using concurrent streamflow measurements. An analysis of four low streamflow estimation techniques, regional regression, regional plus hydrogeologic indices, baseflow correlation, and scaling, was performed within the Apalachicola–Chattahoochee–Flint watershed, a U.S. Geological Survey WaterSMART region in the south‐eastern United States. The latter three methods employ a nominal number of spot measurements at the ungauged site to improve low streamflow estimation. Results indicate that baseflow correlation and scaling methods, which transfer information from a donor site, can produce improved low streamflow estimators when spot measurements are available. Estimation of hydrogeologic indices from spot measurements improves regional regression models, with the baseflow recession constant having more explanatory power than the aquifer time constant, but these models are generally outperformed by baseflow correlation and scaling.     

Modelling soil solute release and transport in run‐off on a loessial slope with and without surface stones

Stone covers on loessial slopes can increase the time of infiltration by slowing the velocity of the overland flow, which reduces the transport of solutes, but few mechanistic models have been tested under water‐scouring conditions. We carried out field experiments to test a previously proposed, physically based model of water and solute transport. The area of soil infiltration was calculated from the uncovered surface area, and Richards' equation and the kinematic wave equation were used to describe water infiltration and flow along slopes with stone covers. The transport of chemicals into the run‐off from the surface soil, presumably by diffusion, and their movement in the soil profile could be described by the convection–diffusion equations of the model. The simulated and measured data correlated well. The stones on the soil surface reduced the area available for infiltration but increased the Manning coefficient, eventually leading to increased water infiltration and decreased solute loss with run‐off. Our results indicated that the traditional model of water movement and solute migration could be used to simulate water transport and solute migration for stone‐covered soil on loessial slopes.     

Variable power‐law scaling of hillslope Hortonian rainfall–runoff processes

Hydrological studies focused on Hortonian rainfall–run‐off scaling have found that the run‐off depth generally declines with the plot length in power‐law scaling. Both the power‐law proportional coefficient and the scaling exponent show great variability for specific conditions, but why and how they vary remain unclear. In the present study, the scaling of hillslope Hortonian rainfall–run‐off processes is investigated for different rainfall, soil infiltration, and hillslope surface characteristics using the physically based cell‐based rainfall‐infiltration‐run‐off model. The results show that both temporally intermittent and steady rainfalls can result in prominent power‐law scaling at the initial stage of run‐off generation. Then, the magnitude of the power‐law scaling decreases gradually due to the decreasing run‐on effect. The power‐law scaling is most sensitive to the rainfall and soil infiltration parameters. When the ratio of rainfall to infiltration exceeds a critical value, the magnitude of the power‐law scaling tends to decrease notably. For different intermittent rainfall patterns, the power‐law exponent varies in the range of ?1.0 to ?0.113, which shows an approximately logarithmic increasing trend for the proportional coefficient as a function of the run‐off coefficient. The scaling is also sensitive to the surface roughness, soil sealing, slope angle, and hillslope geometry because these factors control the run‐off routing and run‐on infiltration processes. These results provide insights into the variable scaling of the Hortonian rainfall–run‐off process, which are expected to benefit modelling of large‐scale hydrological and ecological processes.     

Statistical distribution of nonlinear random wave height

1 Introduction The probability distribution of ocean wave element is one of the results of application of random process theory to the ocean wave study. A great amount of outcome has obtained in this field[1,2]. In fact, a great deal of research on linear…     

Thermoconvective instabilities in a vertical cylinder of water with maximum density effects part 1. Experiments

Abstract

Thermoconvective instabilities were investigated in cylindrical water layers under a 0-4° C vertical temperature gradient. For aspect ratios (height/diameter) ranging from 0.3 to 5.7. angular flow patterns were deduced from thermocouple measurements. The first two diametrically antisymmetrical modes (n=l,2) were detected in the steady and unsteady regime. Slow oscillatory motions with a characteristic time of severals hours were found for aspect ratios (height/diameter) larger than 2. The Fourier analysis of the angular temperature distribution at regular time intervals yields the result that the vertical nodal planes rotate around the cylinder axis in the oscillatory regime. A physical mechanism is suggested to explain the occurrence of such oscillatory instability.     

Effects of pore fluid pressure on the seismic response of a fractured carbonate reservoir

An effective medium model for the stress-dependent seismic properties of fractured reservoirs is developed here on the basis of a combination of a general theory of viscoelastic waves in rock-like composites with recently published formulae for deformation of communicating and interacting cavities (interconnected pores/cracks and fractures at finite concentration) under drained loading. The inclusion-based model operates with spheroidal cavities at two different length scales; namely, the microscopic scale of the pores and (grain-boundary) cracks, and the mesoscopic scale of the fractures (controlling the flow of fluid). The different cavity types can in principle have any orientation and aspect ratio, but the microscopic pores/cracks and mesoscopic fractures were here assumed to be randomly and vertically oriented, respectively. By using three different aspect ratios for the relatively round pores (representing the stiff part of the pore space) and a distribution of aspect ratios for the relatively flat cracks (representing the compliant part of the pore space), we obtained a good fit between theoretical predictions and ultrasonic laboratory measurements on an unfractured rock sample under dry conditions. By using a single aspect ratio for the mesoscopic fractures, we arrived at a higher-order microstructural model of fractured porous media which represents a generalization of the first-order model developed by Chapman et al. (2002,2003). The effect of cavity size was here modelled under the assumption that the characteristic time for wave-induced (squirt) flow at the scale of a particular cavity (pore/crack vs. fracture) is proportional with the relevant scale-size. In the modelling, we investigate the effect of a decreasing pore pressure with constant confining pressure (fixed depth), and hence, increasing effective pressure. The analysis shows that the attenuation-peak due to the mesoscopic fractures in the reservoir will move downward in frequency as the effective pressure increases. In the range of seismic frequencies, our modelling indicates that the P-wave velocities may change by more than 20% perpendicular to the fractures and close to 10% parallel to the fractures. In comparison, the vertical S-wave velocities change by only about 5% for both polarization directions (perpendicular and parallel to the fractures) when the effective pressure increases from 0 to 15 MPa. This change is mainly due to the overall change in porosity with pressure. The weak pressure dependence is a consequence of the fact that the S waves will only sense if the fractures are open or not, and since all the fractures have the same aspect ratio, they will close at the same effective pressure (which is outside the analysed interval). Approximate reflection coefficients were computed for a model consisting of the fractured reservoir embedded as a layer in an isotropic shale and analysed with respect to variations in Amplitude Versus Offset and aZimuth (AVOZ) properties at seismic frequencies for increasing effective pressure. For the P-P reflections at the top of the reservoir, it is found that there is a significant dependence on effective pressure, but that the variations with azimuth and offset are small. The lack of azimuthal dependence may be explained from the approximate reflection coefficient formula as a result of cancellation of terms related to the S-wave velocity and the Thomson’s anisotropy parameter δ. For the P-S reflection, the azimuthal dependence is larger, but the pressure dependence is weaker (due to a single aspect ratio for the fractures). Finally, using the effective stiffness tensor for the fractured reservoir model with a visco-elastic finite-difference code, synthetic seismograms and hodograms were computed. From the seismograms, attenuation changes in the P wave reflected at the bottom of the reservoir can be observed as the effective pressure increases. S waves are not much affected by the fractures with respect to attenuation, but azimuthal dependence is stronger than for P waves, and S-wave splitting in the bottom reservoir P-S reflection is clearly seen both in the seismograms and hodograms. From the hodograms, some variation in the P-S reflection with effective pressure can also be observed.     

High-altitude data assimilation system experiments for the northern summer mesosphere season of 2007

A global numerical weather prediction system is extended to the mesosphere and lower thermosphere (MLT) and used to assimilate high-altitude satellite measurements of temperature, water vapor and ozone from MLS and SABER during May–July 2007. Assimilated temperature and humidity from 100 to 0.001 hPa show minimal biases compared to satellite data and existing analysis fields. Saturation ratios derived diagnostically from these assimilated temperature and water vapor fields at PMC altitudes and latitudes compare well with seasonal variations in PMC frequency measured from the aeronomy of ice in the mesosphere (AIM) satellite. Synoptic maps of these diagnostic saturation ratios correlate geographically with three independent transient mesospheric cloud events observed at midlatitudes by SHIMMER on STPSat-1 and by ground observers during June 2007. Assimilated temperatures and winds reveal broadly realistic amplitudes of the quasi 5-day wave and migrating tides as a function of latitude and height. For example, analyzed winds capture the dominant semidiurnal MLT wind patterns at 55°N in June 2007 measured independently by a meteor radar. The 5-day wave and migrating diurnal tide also modulate water vapor mixing ratios in the polar summer MLT. Possible origins of this variability are discussed.