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1.
Based on the full water-wave equation,a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper.For special case of slope angle β=π/2,this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline.Interactions between two edge waves including progressive,standing and partially reflected standing waves are also discussed.The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given.The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated,and the corresponding theoretical autocorrelation and spectral density functions of the first and the second orders are derived.The boundary conditions for the determination of the parameters of short edge wave are suggested,that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory.Finally some computation results are demonstrated. 相似文献
2.
Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a constant plane sloping bottom is presented in this paper. For special case of slope angle b=p/2, this solution can be reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves were also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves were also discussed. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoretical autocorrelation and spectral density functions of the first and second orders are derived. The boundary conditions for the determining determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated. 相似文献
3.
《Ocean Modelling》2008,20(1):35-60
The generalized Langrangian mean theory provides exact equations for general wave–turbulence–mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here an approximate closure is obtained under the hypotheses of small surface slope, weak horizontal gradients of the water depth and mean current, and weak curvature of the mean current profile. These assumptions yield analytical expressions for the mean momentum and pressure forcing terms that can be expressed in terms of the wave spectrum. A vertical change of coordinate is then applied to obtain glm2z-RANS equations with non-divergent mass transport in cartesian coordinates. To lowest order, agreement is found with Eulerian mean theories, and the present approximation provides an explicit extension of known wave-averaged equations to short-scale variations of the wave field, and vertically varying currents only limited to weak or localized profile curvatures. Further, the underlying exact equations provide a natural framework for extensions to finite wave amplitudes and any realistic situation. The accuracy of the approximations is discussed using comparisons with exact numerical solutions for linear waves over arbitrary bottom slopes, for which the equations are still exact when properly accounting for partial standing waves. For finite amplitude waves it is found that the approximate solutions are probably accurate for ocean mixed layer modelling and shoaling waves, provided that an adequate turbulent closure is designed. However, for surf zone applications the approximations are expected to give only qualitative results due to the large influence of wave nonlinearity on the vertical profiles of wave forcing terms. 相似文献
4.
The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced
currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth.
In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers
in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling
approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing
equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its
magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due
to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme
is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves
over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory
wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the
vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom
beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful
demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient
incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics
beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and
morphology evolution. 相似文献
5.
The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress. 相似文献
6.
Numerical simulation based on the Princeton Ocean Model (POM) was performed for a region of the Southeast Baltic in order to compare data on the spatial distribution of velocity and bottom sediments. Special attention was focused on the influence of western and northeastern winds, which generate intense quasi-geostrophic currents can may cause very high velocities in the near bottom layer, which results in the elution of bottom sediments and transport of their fine fractions. An abrupt change in wind velocity intensifies the effect of elution due to generation of inertial internal waves that penetrate into the bottom layer. The spatial distributions of the velocity in the surface and near bottom layers are compared with data on bottom sediments. It turned out that areas with the highest velocities that formed under the effect of western and northeastern winds in most cases coincide with areas where bottom sediments are represented by coarse-grain fractions of gravel and sands. 相似文献
7.
The highest short-crested waves have been studied analytically and numerically by several workers, but without a conclusive view. An efficient numerical scheme is proposed in this paper which retains the water-surface elevations in an implicit form in the governing equations, rather than using a series approximation, thus improving the accuracy of the numerical results. Convergence of the numerical scheme is verified. The almost highest short-crested waves in deep water are then evaluated, which are defined for the condition with the largest wave energies. It is found that the critical angle for wave frequency reversal also demarcates the wave characteristics near breaking, for either kinematic or dynamic prominence. The known results available for the limiting two-dimensional cases of standing and progressive waves are compared favourably. 相似文献
8.
Alan M. Davies Jiuxing Xing John M. Huthnance Philip Hall Laurenz Thomsen 《Progress in Oceanography》2002,52(2-4)
A three dimensional time-dependent baroclinic hydrodynamic model, including sediment transport and incorporating a turbulence energy sub-model, is used in cross sectional form to examine sediment movement at the shelf edge off North West Iberia at 42°40.5’N where measurements were made as part of the OMEX-II programme. These calculations are complemented by a simpler, in essence time-independent model, which is used to examine the sensitivity of the sediment distribution over the slope (from a shelf-break source) to changes in the specified values of horizontal and vertical diffusion coefficients. The philosophy of the paper is to use idealized tidal, wind and wind wave forcing to examine changes in sediment distribution resulting from these processes. Calculations with the time-dependent and steady state models give insight into both the role of events and long-term effects. The steady state model focuses on the off-shelf region, whilst the time-dependent model considers on-shelf events.Tidal calculations showed that for the stratification used here the internal tide in the OMEX region was primarily confined to the shelf edge and ocean. A mean on-shelf sediment transport in the surface layer and off-shelf transport at the bed was found. Across-shelf circulations produced by up-welling/down-welling favourable winds gave rise to on-shelf/off-shelf currents in the bottom boundary layer with an opposite flow in the surface layer. In the case of an up-welling favourable wind, sediment suspension was at a maximum in the near coastal region, with sediment being advected off shore in the surface layer. With a down-welling favourable wind, surface sediment was advected towards the shore, but there was offshore transport at the bed. Near the shelf edge any upwelling flow had the tendency to return this sediment to the surface layer from whence it was transported on-shore. So in essence the sediment was trapped within an on-shelf circulation cell. Wind waves effects increased the total bed stress and hence the sediment concentration and its transport, although its pattern was determined by tidal and wind forcing.The time independent model with increased/decreased lateral diffusivity gave an enhanced/reduced horizontal sediment distribution for a given settling velocity. As the settling velocity increases, the down-slope movement of sediment is increased, with a reduction in the thickness of the near-bed sediment layer, but with little change in its horizontal extent. 相似文献
9.
The mass transport in a thin layer of non-Newtonian bed mud under surface waves is examined with a two-fluid Stokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for small-applied stresses, but flows readily when the yield stress is exceeded. Asymptotic expansions suitable for shallow lluid layers are applied, and the second-order solutions for the mass transport induced by surface progressive waves are obtained numeri-cally. It is found that the stronger the non-Newtonian behavior of the mud, the more pronounced intermittency of the flow. Consequently, the mass transport velocity is diminished in magnitude, and can even become negative (i. e. , oppo-site to wave propagation) for a certain range of yield stress. 相似文献
10.
Takashi Ichiye 《Journal of Oceanography》1970,26(6):340-353
Scaling of the equations of motion of the Antarctic Circumpolar Current indicates that the Rossby number and the Ekman number
are 10−4 to 10−5 but the vertical Ekman number may reach unity in the bottom boundary layer. The equations of motion are integrated vertically
from the surface to the bottom and averaged over a latitude circle. The resulting equation in the meridional direction is
predominantly geostrophic, whereas the main terms of the equation in the zonal direction are the wind stress and the bottom
stress. When the vertical eddy viscosity near the bottom is of the order of 102cm2/sec, the total zonal transport through the Drake Passage computed from the balance of the wind stress and the bottom stress
equals 260×106m3/sec, the amount determined byReid andNowlin (1970) from observations.
The northward transport reduces the eastward transport corresponding to the wind stress of the westerlies in the A. C. C.
through the Coriolis' term in the vertically integrated equation of motion of the zonal direction. South of the Drake Passage,
such reduction reaches about ten percent of the wind-driven transport mainly due to the peripheral water discharge. North
of the Drake Passage, the northward transport may be generated by the effect of the South American coast which prevents free
eastward movement of the A. C. C., causing a wake to the east. This transport may contribute to a part of the northward transport
of the bottom water postulated byMunk (1966). The effect of the horizontal eddy viscosity in the zonal transport equation is negligible except near the Antarctic
coast, if the eddy viscosity is less than 109cm2/sec. 相似文献
11.
The determination of the characteristics of a standing wave boundary layer, such as water particle velocities and shear stresses, is a vital issue in the prediction of sediment transport rate. Thus, an accurate measure of boundary layer characteristics is a key factor in the study of the wave boundary layer. In this study, a fiber-optic laser Doppler velocimeter (FLDV) is applied to directly measure the velocity profile in the standing wave boundary layer. As the experimental data presented in this paper, the antinode points of standing waves are found to move in the temporal domain. The previous second-order solution for a standing wave boundary layer is insufficient for the prediction of larger Ursell numbers. 相似文献
12.
The conditions for energy flux, momentum flux and the resulting streaming velocity are analysed for standing waves formed in front of a fully reflecting wall. The exchange of energy between the outer wave motion and the near bed oscillatory boundary layer is considered, determining the horizontal energy flux inside and outside the boundary layer. The momentum balance, the mean shear stress and the resulting time averaged streaming velocities are determined. For a laminar bed boundary layer the analysis of the wave drift gives results similar to the original work of Longuet–Higgins from 1953. The work is extended to turbulent bed boundary layers by application of a numerical model. The similarities and differences between laminar and turbulent flow conditions are discussed, and quantitative results for the magnitude of the mean shear stress and drift velocity are presented. Full two-dimensional simulations of standing waves have also been made by application of a general purpose Navier–Stokes solver. The results agree well with those obtained by the boundary layer analysis. Wave reflection from a plane sloping wall is also investigated by using the same numerical model and by physical laboratory experiments. The phase shift of the reflected wave train is compared with theoretical and empirical models. 相似文献
13.
Numerical simulation of breaking wave generated sediment suspension and transport process based on CLSVOF algorithm 总被引：1，自引：0，他引：1
The sediment suspension and transport process under complex breaking wave situation is investigated using large eddy simulation （abbreviated as LES hereafter） method. The coupled level set （LS） and volume of fluid （VOF） method is used to accurately capture the evolution of air？water interface. The wall effect at the bottom is modeled based on the wave friction term while the complicate bottom boundary condition for sediment is tackled using Chou and Fringer’s sediment erosion and deposition flux method. A simulation is carried out to study the sediment suspension and transport process under periodic plunging breaking waves. The comparison between the results by CLSVOF method and those obtained by the LS method is given. It shows that the latter performs as well as the CLSVOF method in the pre-breaking weak-surface deformation situation. However, a serious mass conservation problem in the later stages of wave breaking makes it inappropriate for this study by use of the LS method and thus the CLSVOF method is suggested. The flow field and the distribution of suspended sediment concentration are then analyzed in detail. At the early stage of breaking, the sediment is mainly concentrated near the bottom area. During the wave breaking process, when the entrapped large-scale air bubble travels downward to approach the bottom, strong shear is induced and the sediment is highly entrained. 相似文献
14.
The transport of a chemical species under the pure action of surface progressive waves in the benthic boundary layer which is loaded with dense suspended sediments is studied theoretically. The flow structure of the boundary layer is approximated by that of a two-layer Stokes boundary layer with a sharp interface between clear water and a heavy fluid. The simplest model of constant eddy diffusivities is adopted and the exchange of matter with the bed is ignored. For a thin layer of heavy fluid, whose thickness is comparable to the surface wave amplitude and the Stokes boundary layer thickness, effective transport equations are deduced using an averaging technique based on the method of homogenization. The effective advection velocity is found to be equal to the depth-averaged mass transport velocity, while the dispersion coefficient can be shown to be positive definite. Explicit expressions for the transport coefficients are obtained as functions of fluid properties and flow kinematics. Physical discussions on their relations are also presented. 相似文献
15.
This paper presents an investigation of the roughness effects in the turbulent boundary layer for asymmetric waves by using the baseline (BSL) k–ω model. This model is validated by a set of the experimental data with different wave non-linearity index, Ni (namely, Ni = 0.67, Ni = 0.60 and Ni = 0.58). It is further used to simulate asymmetric wave velocity flows with several values of the roughness parameter (am/ks) which increase gradually, namely from am/ks = 35 to am/ks = 963. The effect of the roughness tends to increase the turbulent kinetic energy and to decrease the mean velocity distribution in the inner boundary layer, whereas in the outer boundary layer, the roughness alters the turbulent kinetic energy and the mean velocity distribution is relatively unaffected. A new simple calculation method of bottom shear stress based on incorporating velocity and acceleration terms is proposed and applied into the calculation of the rate of bed-load transport induced by asymmetric waves. And further, the effect of bed roughness on the bottom shear stress and bed-load sediment transport under asymmetric waves is examined with the turbulent model, the newly proposed method, and the existing calculation method. It is found that the higher roughness elements increase the magnitude of bottom shear stress along a wave cycle and consequently, the potential net sediment transport rate. Moreover, the wave non-linearity also shows a big impact on the bottom shear stress and the net sediment transport. 相似文献
16.
The objectives of this study are carried out a series of controlled large wave flume experiments using fine-grained sediment from the Huanghe River Delta, exploring the complete sequence of sediment behavior in the bottom boundary layer(BBL) during wave-induced liquefaction. The results show that:(1) The BBL in silty seabed is exposed to a progressive wave, goes through a number of different stages including compaction before liquefaction, sediment liquefaction, and compaction after liquefaction, which determines the range and thickness of BBL.(2) With the introduction of waves, first, the sediment surface has settled by an amount S(S=1–2 cm) in the course of wave loadings with an insufficient accumulation of pore water pressure. And a thin high concentration layer formed the near-bed bottom.(3) Once the liquefaction sets in, the liquefied sediment with an ‘orbital motion' and the sub-liquefied sediment form a two-layer-sediment region. The range of BBL extends downwards and stopped at a certain depth, subsequently, develops upwards with the compaction process. Meanwhile, resuspended sediments diffuse to the upper water column.(4) During the dynamics process of the BBL beneath progressive waves, the re-suspended sediment increment ranked as sediment liquefaction erosion before liquefaction compaction after liquefaction. 相似文献
17.
Internal inlet for wave generation and absorption treatment 总被引：1，自引：0，他引：1
A new method of implementing, in two-dimensional (2-D) Navier–Stokes equations, a numerical internal wave generation in the finite volume formulation is developed. To our knowledge, the originality of this model is on the specification of an internal inlet velocity defined as a source line for the generation of linear and non-linear waves. The use of a single cell to represent the source line and its transformation to an internal boundary condition proved to be an interesting alternative to the common procedure of adding a mass source term to the continuity equation within a multi-cell rectangular region. Given the reduction of the source domain to a one-dimensional region, this simple new type of source introduced less perturbation than the 2-D source type. This model was successfully implemented in the PHOENICS code (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series). In addition, the volume of fluid (VOF) fraction was used to describe the free surface displacements. A friction force term was added to the momentum transport equation in the vertical direction, in order to enhance wave damping, within relatively limited number of cells representing the sponge layers at the open boundaries. For monochromatic wave, propagating on constant water depth, numerical and analytical results showed good agreements for free surface profiles and vertical distribution of velocity components. For solitary wave simulation, the wave shape and velocity were preserved; while, small discrepancy in the tailing edge of the free surface profiles was observed. The suitability of this new numerical wave generation model for a two source lines extension was investigated and proven to be innovative. The comparisons between numerical, analytical and experimental results showed that the height of the merging waves was correctly reproduced and that the reflected waves do not interact with the source lines. 相似文献
18.
Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves 总被引：1，自引：0，他引：1
In this paper, the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed of 1/15 uniform slope, is experimentally investigated. Flow visualization technique with thin-layered fluorescent dye was first used to observe the variation of the flow structure, and a laser Doppler velocimeter was then employed to measure the horizontal velocity, U.The bottom boundary layer flow is found to be laminar except within a small region near the breaking point. The vertical distribution of the phase-averaged velocity U at each phase is non-uniform, which is directly affected by the mean velocity,
. The magnitude of
increases from zero at the bottom to a local positive maximum at about z/δ2.02.5 (where z is the height above the sloping bottom and δ is the Stokes layer thickness), then decreases gradually to zero at z/δ6.07.0 approximately, and finally becomes negative as z/δ increases further. Moreover, as waves propagate towards shallower water, the rate of increase in the maximum onshore oscillating velocity component
is greater than that of the offshore counterpart
except near the breaking point. The free stream velocities in the profiles of the maximum onshore and offshore oscillating velocity components,
and
are found to appear at z/δ≥6.0. This implies that, if the Stokes layer thickness is used as a length scale, the non-dimensionalized boundary layer thickness remains constant in the pre-breaking zone. Although
is greater than
and the asymmetry of the maximum free stream velocities (i.e.
) increases with decrease of water depth, a universal similar profile can be established by plotting z/δ versus (
) or (
). The final non-dimensional profile is symmetric and unique for the distributions of the maximum onshore and offshore oscillating velocity components within the bottom boundary layer, which are induced by nonlinear, asymmetric shoaling waves crossing the pre-breaking zone. 相似文献
19.
A simple numerical model, based on the Reynolds stress equations and k–ε turbulence closure scheme, is developed for the coastal wave and current bottom boundary layer. The current friction velocity is introduced to account for the effect of currents on waves. The implicit Crank–Nicolson finite difference method discretizes the governing equations. Vertical changing step grids with the constant ratio for two adjacent spatial steps are used together with the equal time steps in the modeling. Vertical profiles of mean current velocity and wave velocity amplitude are obtained. These modeled results are compared with the laboratory experimental data of Van Doorn [1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands]. It has been shown that modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands; 1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands) mean velocity profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled and observed (Van Doorn, T., 1981. Experimental investigation of near bottom velocities in water waves with and without a current. Report M1423, Delft Hydraulics Laboratory, Delft, The Netherlands) wave velocity amplitude profiles within the wave and current bottom boundary layer are in better agreement than outside. Modeled wave velocity amplitudes are in good agreement with the laboratory experimental data of Van Doorn [1982. Experimenteel onderzoek naar het snelheidsveld in de turbulente bodemgrenslaag in een oscillerende stroming in een golftunnel. Report M1562, Delft Hydraulics Laboratory, Delft, The Netherlands]. 相似文献
20.
《Coastal Engineering》1999,36(1):59-85
Simple theoretical models to determine the equilibrium profile shape under breaking and non-breaking waves are presented. For the case of breaking waves, it is assumed that the seaward transport in the undertow is locally balanced by a net vertical sedimentation, so that no bottom changes occur at equilibrium. The parameterization of the water and sediment flux in the surf zone yields a power curve for the equilibrium profile with a power of 2/3, which is in agreement with previous field investigations on surf zone profile shapes. Three different models were developed to derive the profile shape under non-breaking waves, namely (1) a variational formulation where the wave energy dissipation in the bottom boundary layer is minimized over the part of the profile affected by non-breaking waves, (2) an integration of a small-scale sediment transport formula over a wave period where the slope conditions that yield zero net transport determine equilibrium, and (3) a conceptual formulation of mechanisms for onshore and offshore sediment transport where a balance between the mechanisms defines equilibrium conditions. All three models produced equilibrium profile shapes of power-type with the power typically in the range 0.15–0.30. Comparison with field data supported the results obtained indicating different powers for the equilibrium profile shape under breaking and non-breaking waves. 相似文献