近岸波浪引起的水流及长波研究进展

从现场观测、理论分析和数值计算、试验室研究三个方面回顾了近岸波浪引起水流以及长波的研究进展，并对今后着重研究的几个方向提出看法。     

关于二阶伴随模型的理论研究

Hesse矩阵-目标函数关于控制变量的二阶偏导数形成的矩阵,在变分数据同化过程中以及敏感性分析等方面起着重要的作用;它可以通过建立数学模型的一阶和二阶伴随模型求得.以浅水方程模型为例,利用泛函的Gâteaux微分和Hilbert空间上伴随算子的概念,导出了一阶和二阶伴随模型并由此得到Hesse矩阵.改进了Zhi Wang等(1992)建立的二阶伴随模型理论.     

A fast convolution approach to the transformation of surface gravity waves: Linear waves in 1DH

The transformation of irrotational surface gravity waves in an inviscid fluid can be studied by time stepping the kinematic and dynamic surface boundary conditions. This requires a closure providing the normal surface particle velocity in terms of the surface velocity potential or its tangential derivative. A convolution integral giving this closure as an explicit expression is derived for linear 1D waves over a mildly sloping bottom. The model has exact linear dispersion and shoaling properties. A discrete numerical model is developed for a spatially staggered uniform grid. The model involves a spatial derivative which is discretized by an arbitrary-order finite-difference scheme. Error control is attained by solving the discrete dispersion relation a priori and model results make a perfect match to this prediction. A procedure is developed by which the computational effort is minimized for a specific physical problem while adapting the numerical parameters under the constraint of a predefined tolerance of damping and dispersion error. Two computational examples show that accurate irregular-wave transformation on the kilometre scale can be computed in seconds. Thus, the method makes up a highly efficient basis for a forthcoming extension that includes nonlinearity at arbitrary order. The relation to Boussinesq equations, mild-slope wave equations, boundary integral equations and spectral methods is briefly discussed.     

A simple analytical model for surface water waves on a depth-varying current

A perturbation analysis is presented in which a series of small amplitude regular waves co-exist with an arbitrarily sheared current, U(z). Assuming that the current velocity is weak, i.e. U(z)/c=O(ε), the solution is extended to O(ε²), where c is the phase velocity and ε=ak the wave steepness. This provides a first approximation to the non-linear wave-current interaction, and allows simple explicit solutions for both the modified dispersion relation and the water-particle kinematics to be derived. These solutions differ from the existing irrotational models commonly used in design and, in particular, highlight the importance of the near-surface vorticity distribution. These results are shown to be in good agreement with laboratory data provided by Swan et. al. [J. Fluid Mech (2001, in press)]. Perhaps more surprisingly, good agreement is also achieved in a number of strongly non-linear wave-current combinations, where the results of the present analytical solution are compared with a fully non-linear numerical wave-current model.     

A second order random wave model for predicting the power performances of a wave energy converter

The power performances of a point absorber wave energy converter(WEC) operating in a nonlinear multidirectional random sea are rigorously investigated. The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter. This is a new approach, and, as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea, avoids the inaccuracies resulting from using a first order linear wave model in the simulation process. The predicted results have been systematically analyzed and compared, and the advantages of using this new approach have been convincingly substantiated.     

Pollution — a French perspective

A summary of the various forms of pollution control discussed at an international Anti-Pollution Course held at the French Merchant Marine School in Marseilles on 13–25 June 1977.     

On the distribution of second order pressure on a vertical circular cylinder

This paper shows how the second order wave pressure on the submerged surface of a body may be obtained without solving the boundary value problem for the second order velocity potential. The corresponding analytical solution for a vertical circular cylinder is developed, and selected results are presented which illustrate a number of novel phenomena not occurring in first order diffraction analysis.     

Spatial variation in river runoff into a coastal area — An ecological approach

Carbon and nitrogen stable isotopes were used to investigate spatial variation in terrestrial particulate organic matter (POM) input to a coastal area off the Tagus river estuary. Isotopic variation in higher trophic level organisms was also examined, along the coast. This study was carried out in late summer, after a period of 3 months of low river flow. The overall aim was to determine if under such conditions the coastal area is enriched by the river plume and, particularly, if lower secondary productivity should be expected in some areas. Spatial variation was detected as a gradient of decreasing terrestrial input with increasing distance from the river. It was concluded that terrestrial carbon input was also incorporated into higher trophic levels and that organisms with lower mobility are more sensitive to the gradient in terrestrial input. Even in low flow conditions the whole fishing area remained under the influence of the river plume, which still accounted for 24% of the total POM 30 km from the river mouth. Additionally, δ¹⁵N values indicated pollution input from the river Tagus.     

Energy dissipation in sloshing waves in a rolling rectangular tank — III. Results and applications

The hydrodynamic aspects of the motion of a viscous fluid having a free surface in a rolling tank have been investigated. In a sequence of three papers, an analytical technique together with a numerical solution method will be presented to describe the sloshing phenomenon accurately and efficiently. This first paper introduces a linear theory of viscous liquid sloshing and formulates a boundary value problem subject to appropriate conditions. Viscosity is included in the problem formulation and its effects are properly accounted for. The second paper will describe a solution of the problem in function space by the truncation of infinite series. Boundary conditions are satisfied through the use of Fourier series expansions. However, the no-slip condition at the side walls can also be treated in a least-squares sense.Among the results that will be reported in the third paper are the effects of viscosity on liquid sloshing phenomenon and the dependence of viscous dissipation on the Reynolds and Froude numbers. Furthermore, the influence of the tank aspect ratio on viscous dissipation has been explored. These results demonstrate some unknown features of the functional relationships that exist between the dissipated energy and the Reynolds and Froude numbers. Similarly, the dependence of the dissipated energy on the aspect ratio has been analytically studied. The results obtained agree with the physical laws for the range of parameters investigated.     

A second approximation to the time-mean lagrangian drift beneath a series of progressive gravity waves

A fourth-order solution is derived for the mean drift induced by a steady train of waves in water of constant depth. New measurements are carried out of the drift in the body of the fluid and the drift velocity gradient at the free surface. Comparison of theory and experiment shows significantly better agreement with the present fourth-order solution than with the previous second-order solution of Longuet-Higgins, M.S., 1953 [Phil. Trans. R. Soc.245, 535–581]. In particular, the present solution reproduces the observed tendency of the surface drift velocity to rise in shallow water and to level-off in very deep water.     

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).     

A model for the propagation of nonlinear surface waves over viscous muds

The effect of a thin viscous fluid–mud layer on nearshore nonlinear wave–wave interactions is studied using a parabolic frequency-domain nonlinear wave model, modified to incorporate a bottom dissipation mechanism based on a viscous boundary layer approach. The boundary-layer formulation allows for explicit calculation of the mud-induced wave damping rate. The model performed well in tests based on laboratory data. Numerical tests show that damping of high frequency waves occurs, mediated by “difference” nonlinear interactions. Simulations of 2-dimensional wave propagation over a mud “patch” of finite extent show that the wave dissipation causes significant downwave diffraction effects.     

An analysis of second order waves in a wave tank by 3-probe correlation analysis and by square-low operation

Two methods are presented for analysis of second order waves in a wave tank. The first method is by placing three wave probes in a line parallel to the line of propagation of long-crested irregular waves. By correlation analysis the spectra of set-down, parasitic waves and reflected waves of the second order are separated. The second method is to apply the square-law operation as proposed by Bendat and Piersol, to the spectral analysis of this particular non-linear system. The results of the two methods seem to agree reasonably well. A practical application of the present analysis is to analyse low frequency responses of a moored structure in a wave tank, where it is recognized that simulation of second order waves and the structure's responses are often accompanied by parasitic second order waves and reflected waves in the tank. These adulterations may be regarded as noises, and the proper information regarding non-linear second order responses extracted from the raw output.     

Bioaccumulation in marine food chains—A kinetic approach

The risk of bioaccumulation of persistent liposoluble pollutants in marine food chains was highlighted by work done on organochlorine residues in marine organisms in the early 1960s. In one study, concentrations of DDE and dieldrin were determined in species from different trophic levels of the Farne Island ecosystem.¹ Concentrations of pollutants were related to trophic levels, with the highest levels occurring in predators such as the cormorant (Phalacrocorax carbo) and the shag (Phalacrocorax aristotelis). This paper will consider model systems which may be used to predict bioaccumulation risks from simple in vitro data. Emphasis will be upon persistent liposoluble pollutants with relatively simple patterns of metabolism, and upon the problem of bioaccumulation by marine predators.     

On a near-optimal control approach for a wave energy converter in irregular waves

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers–Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal (one being odd and other even), full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this difficulty and the non-causality of the exciting force impulse response function, this paper investigates the use of propagating-wave surface elevation up-wave of the device to synthesize the necessary forces. Long-crested waves are assumed, and the approach is based on the formulations of Naito and Nakamura [2] and Falnes [22]. A predominantly heaving submerged device comprised of three vertically stacked discs driving a linear power take-off is studied. The overall formulation leads to smooth control that is near-optimal, given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. Absorbed power performance with the near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results for wave spectra over a range of energy periods and significant wave heights are compared for the three situations studied. While practical implementation presents engineering challenges, in terms of time-averaged absorbed power, unconstrained near-optimal control is found to perform significantly better than single-frequency tuning in the spectra with longer energy periods (>10 s for the present device), and somewhat better in the spectra with shorter energy periods (here ≤10 s).     

A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves

A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave.     

A novel synthetic aperture radar scattering model for sea surface with breaking waves

In this study a novel synthetic aperture radar(SAR) scattering model for sea surface with breaking waves is proposed. Compared with existing models, the proposed model considers an empirical relationship between wind speed and wave breaking scattering to present the contribution of wave breaking. Moreover, the scattering weight factor p, and wave breaking rate q, are performed to present the contribution of the quasi-specular scattering term, Bragg scattering term, and wave breaking scattering t...