Methods for retrieval of sea wave spectra from aerospace image spectra

An approach to the retrieval of sea wave spatial spectra based on satellite optical imagery in linear and nonlinear approximations is described. Physical mechanisms of the formation of disturbed sea surface brightness fields recorded by remote sensing equipment are analyzed. Wave spectra retrieval methods using brightness field formation models that consider linear and nonlinear dependencies on sea surface slopes are suggested. A method for the construction of operators that retrieve the spatial spectra of surface wave slopes and elevations from aerospace imagery and take into account nonlinear modulations of disturbed sea surface brightness fields is developed. This method is based on the numerical simulation of sea surface images and the construction of a retrieving operator with respect to a set of parameters determined by aerospace imaging conditions. Examples of the use of the developed methods are given.     

Ozone Temporal Variability in the Subarctic Region: Comparison of Satellite Measurements with Numerical Simulations

Fourier and wavelet spectra of time series for the ozone column abundance in the atmospheric 0–25 and 25–60 km layers are analyzed from SBUV satellite observations and from numerical simulations based on the RSHU and EMAC models. The analysis uses datasets for three subarctic locations (St. Petersburg, Harestua, and Kiruna) for 2000–2014. The Fourier and wavelet spectra show periodicities in the range from ~10 days to ~10 years and from ~1 day to ~2 years, respectively. The comparison of the spectra shows overall agreement between the observational and modeled datasets. However, the analysis has revealed differences both between the measurements and the models and between the models themselves. The differences primarily concern the Rossby wave period region and the 11-year and semiannual periodicities. Possible reasons are given for the differences between the models and the measurements.     

Interaction of ocean waves with floating and submerged horizontal flexible structures in three-dimensions

A three-dimensional general mathematical hydroelastic model dealing with the problem of wave interaction with a floating and a submerged flexible structure is developed based on small amplitude wave theory and linear structural response. The horizontal floating and submerged flexible structures are modelled with a thin plate theory. The linearized long wave equations based on shallow water approximations are derived and results are compared. Three-dimensional Green’s functions are derived using fundamental source potentials in water of finite and infinite depths. The expansion formulae associated with orthogonal mode-coupling relations are derived based on the application of Fourier transform in finite and infinite depths in case of finite width in three-dimensions. The usefulness of the expansion formula is demonstrated by analysing a physical problem of surface gravity wave interaction with a moored finite floating elastic plate in the presence of a finite submerged flexible membrane in three-dimensions. The numerical accuracy of the method is demonstrated by computing the complex values of reflected wave amplitudes for different modes of oscillation and mooring stiffness. Further, the effect of compressive force and modes of oscillations on a free oscillation hydroelastic waves in a closed channel of finite width and length for floating and submerged elastic plate system is analysed.     

CABARET in the ocean gyres

A new high-resolution Eulerian numerical method is proposed for modelling quasigeostrophic ocean dynamics in eddying regimes. The method is based on a novel, second-order non-dissipative and low-dispersive conservative advection scheme called CABARET. The properties of the new method are compared with those of several high-resolution Eulerian methods for linear advection and gas dynamics. Then, the CABARET method is applied to the classical model of the double-gyre ocean circulation and its performance is contrasted against that of the common vorticity-preserving Arakawa method. In turbulent regimes, the new method permits credible numerical simulations on much coarser computational grids.     

大洋环流模式中Boussinesq近似与静压近似问题的讨论

改进环流模式中的Boussinesq近似与静压近似是当前海洋环流模式的主要研究方向之一。虽然目前已提出一些在模式中包含非Boussinesq效应和静压效应的方法,但是仍有很多关键问题亟待解决。系统地回顾了改进这2个基本近似的理论分析和数值模式的研究进展,介绍了不同方法的理论基础及其数值分析结果,并分析了这些方法中所存在的缺陷和问题,指出了开展进一步研究需要首先分析的几个关键问题。     

Stochastic simulations of ocean waves: An uncertainty quantification study

The primary objective of this study is to introduce a stochastic framework based on generalized polynomial chaos (gPC) for uncertainty quantification in numerical ocean wave simulations. The techniques we present can be easily extended to other numerical ocean simulation applications. We perform stochastic simulations using a relatively new numerical method to simulate the HISWA (Hindcasting Shallow Water Waves) laboratory experiment for directional near-shore wave propagation and induced currents in a shallow-water wave basin. We solve the phased-averaged equation with hybrid discretization based on discontinuous Galerkin projections, spectral elements, and Fourier expansions. We first validate the deterministic solver by comparing our simulation results against the HISWA experimental data as well as against the numerical model SWAN (Simulating Waves Nearshore). We then perform sensitivity analysis to assess the effects of the parametrized source terms, current field, and boundary conditions. We employ an efficient sparse-grid stochastic collocation method that can treat many uncertain parameters simultaneously. We find that the depth-induced wave-breaking coefficient is the most important parameter compared to other tunable parameters in the source terms. The current field is modeled as random process with large variation but it does not seem to have a significant effect. Uncertainty in the source terms does not influence significantly the region before the submerged breaker whereas uncertainty in the incoming boundary conditions does. Considering simultaneously the uncertainties from the source terms and boundary conditions, we obtain numerical error bars that contain almost all experimental data, hence identifying the proper range of parameters in the action balance equation.     

跳点法在风暴潮数值预报模型中的应用

将跳点法的基本思想应用于求解二维水位抛物型方程，从而构造了一种用于风暴潮数值预报的高效率差分格式。文中给出了这一格式的稳定性证明，并通过对实际风暴潮过程的模拟，证实了这一格式的稳定性和时效性     

Enhanced predictions of wave impact pressure by improved incompressible SPH methods

A new criterion is proposed for a more efficient assessment of free-surface particles in a particle-based simulation. Enhanced wave impact simulations are carried out by improved Incompressible SPH (ISPH) methods. The first improvement is the same as that in the Corrected ISPH (CISPH; [Khayyer A, Gotoh, H, Shao SD. Corrected incompressible SPH method for accurate water-surface tracking in breaking waves, Coast Eng 2008; 55 (3): 236–250]) method and is proposed for the improvement of momentum conservation. The second improvement is achieved by deriving and employing a higher order source term based on a more accurate differentiation to obtain a less fluctuating and more accurate pressure field. The enhanced performance of improved ISPH methods is demonstrated through the simulation of several fluid impact simulations in comparison with the experimental data and simulation results by other numerical methods.     

Numerical and experimental study on seakeeping performance of a SWATH vehicle in head waves

The seakeeping characteristics of a Small Waterplane Area Twin Hull (SWATH) vehicle equipped with fixed stabilizing fins was investigated by experimental and numerical methods The calculation methods range from viscous CFD simulation based on an unsteady RANS approach to Boundary Element Method (BEM) based on Three Dimensional Translating-pulsating Source Green Function (3DTP). Responses of ship motions in head regular waves and nonlinear effects on motion responses with increasing wave amplitude were analyzed. Numerical simulations have been validated by comparisons with experimental tests. The results indicate that the heave and pitch transfer functions depict two peaks with the increase of wave length. Comparisons amongst experimental data and different numerical calculations illustrate that the RANS method predicts ship motions with higher accuracy and allows the detection of nonlinear effects. The heave and pitch transfer functions see a downward trend with the increasing wave amplitude in the resonant zone at low speed.     

Truss Spar平台垂荡响应频域分析

利用已有水动力试验和数值模拟结果及Morison方程,简化估计了Truss Spar平台垂荡方向水动力贡献,快速有效地预报了平台极端海况下的垂荡响应.在频域内分别采用数值迭代计算和粘滞阻尼线性化方法得到了平台在不同数量垂荡板配置下的垂荡响应幅值算子.在墨西哥湾、西非和中国南海等3种不同地区极端海况以及墨西哥湾工作状态海况下计算了平台的响应极值,分析发现平台波频垂荡响应对入射波浪周期非常敏感.采用JONSWAP波能谱得到了Truss Spar平台垂荡响应谱.通过比较和参数分析,验证了平台在设计上的合理性与实际海况下良好的垂荡运动性能.     

Analysis of correlations between time series with the use of the phase spectrum

In connection with the problem of revealing cause-effect relations among different climatic characteristics, methods for determining the dependence between time series on the basis of selected auto-and cross-covariance functions and periodograms expressed in terms of the Fourier coefficients of the initial series are discussed. Real time series do not always satisfy the conditions of statistical stationarity, so that their analysis requires a combination of statistical and deterministic approaches. The possibility of using the above numerical characteristics in relation to such series is considered. Characteristic features of describing finite segments of time series with the use of their Fourier coefficients is studied in detail. The main emphasis is on the determination of the time shifts (delays) at which the covariance between the series is maximal. The problems that appear during a practical implementation of the periodogram method for shift estimation are discussed. A previously unknown formula that is necessary for further studies and relates the Fourier transform of a selected correlation function to the periodogram of the series is derived.     

Response cumulant analysis of a linear oscillator driven by Morison force

A frequency-domain cumulant spectral analysis method is developed in this study to estimate the higher-order statistics of the linear oscillator responses driven by Morison wave force. The fourth-order cumulant function of the nonlinear drag force is formulated in terms of the autocorrelation functions of water particle velocity. Price's theorem is applied to evaluate the associated higher-order joint moments. Three-dimensional Fourier Transforms are employed to obtain the trispectra of Morison force and oscillator responses. The estimated force and response kurtosis are in good agreement with those obtained from time-domain simulations; while the proposed method is found to be much more efficient. The numerical results also show that the drag force cubicization based on the least square approximation results in an overestimation of the kurtosis values; in addition, it is necessary to include the joint moments of order higher than eighth.     

Rational approximations in the parabolic equation method for water waves

Approximations based on minimax principles are developed in order to allow for large-angle propagation in the parabolic equation method. Numerical studies show that the minimax approximations do not cause any significant degradation of accuracy at small angles of incidence when compared with an existing model based on a (1,1) Padé approximant, and that they allow for much more successful treatment of large angles of incidence than is possible using the previously available methods.     

A coupled-mode system with application to nonlinear water waves propagating in finite water depth and in variable bathymetry regions

A non-linear coupled-mode system of horizontal equations is presented, modelling the evolution of nonlinear water waves in finite depth over a general bottom topography. The vertical structure of the wave field is represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional terms, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The present coupled-mode system fully accounts for the effects of non-linearity and dispersion, and the local-mode series exhibits fast convergence. Thus, a small number of modes (up to 5–6) are usually enough for precise numerical solution. In the present work, the coupled-mode system is applied to the numerical investigation of families of steady travelling wave solutions in constant depth, corresponding to a wide range of water depths, ranging from intermediate depth to shallow-water wave conditions, and its results are compared vs. Stokes and cnoidal wave theories, as well as with fully nonlinear Fourier methods. Furthermore, numerical results are presented for waves propagating over variable bathymetry regions and compared with nonlinear methods based on boundary integral formulation and experimental data, showing good agreement.     

Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary I. A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

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Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary Ⅰ.A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

A 3-D numerical model is set up in a large domain covering the Hang zhou Bay and the Changjiang Estuary based on the ECOM model in orthogonal curvilinear coordinates.The numerical schemes for baroclinic pressure gradient (BPG) terms and convective terms are improved in the paper according to the characteristics of velocity field and mass transport in the area.The model is validated by the simulations of residual current and salinity transport in the Hangzhou Bay and the Changjiang Estuary.     

Study of Seabed Pullout Resistance on a Quadrate Foundation Using Adaptive Time-Stepping Method

We developed a solid-fluid analysis procedure that can simulate the seabed pullout resistance based on two adaptive time-stepping methods. One is heuristic time stepping, and the other is based on the truncation error estimation in temporal discretization. The pullout resistance is investigated through experiments and numerical simulations. The results show that the proposed adaptive stepping methods can deal with the un-convergence problems caused by the time increment and can improve the calculation efficiency. The base suction, related to the area of the negative pore water pressure, is generated under the structure and provides the pullout resistance.     

基于纵横波保幅分离的粘弹介质弹性波正演模拟

地下介质往往表现为粘弹特性,研究基于粘弹假设的数值模拟方法对于正确认识地震波的传播规律和提高地震勘探精度具有重要意义。波动方程正演过程中纵横波的保幅解耦是研究准确的粘弹介质中地震波传播机理的前提,基于散度和旋度算子的纵横波解耦方法会使波场的相位和振幅产生畸变,且解耦后的波场在极性反转位置上无法与分离前混合波场各分量对应。在散度和旋度算子上再做一次梯度和旋度运算的波场分离方法虽然能够克服上述缺陷,但存在保幅性差等问题。本文从粘弹介质中的一阶速度-应力方程出发,推导了矢量纵横波分离的波数域表达式,结合有限差分思路给出了其在空间域的求解方法。本文方法利用纵横波的传播速度对现有的矢量波场分离方法进行振幅校正,并将校正结果分别作为纵波与横波对时间的二阶偏导,实现了粘弹介质中的纵横波分离。模型试算结果表明,本文方法能够克服现有方法的缺陷,获得更具保幅性的波场分离结果。     

A three-dimensional wake impingement model and applications on tandem oscillating foils

Potential flow based vortex numerical methods have been widely used in aerodynamics and hydrodynamics. In these methods, vortices shed from lifting bodies are traced by using vortex filaments or dipole panels. When the wake elements encounter a downstream body, such as a rudder behind a propeller or a stator behind a rotor, a treatment is necessary to divert the wake elements to pass by the body. This treatment is vital to make wake simulations realistic and to satisfy the non-penetration condition during wake body interaction. It also helps to avoid pure numerical disturbances such as when a vortex filament or an edge of a dipole panel passes through the collection point of a body element; this is a singularity for induced velocity and it will introduce a large numerical disturbance. This necessary treatment for three-dimensional problems with geometrical complexity has not been found to date. In this study, a wake impingement model was developed to divert wake elements to slip over the body surface, model the vortex/body interaction, and predict forces on fluctuating components. The model was also tested on configurations of oscillating foils in tandem with an existing panel method code. Simulation results with the wake impingement model are shown to be in closer agreement with limited published experimental data than those without the model. With the established wake impingement model, force fluctuations on the after body due to the wake vortex impingement were investigated based on a series of simulations. The series varied several parameters including distance between two foils, oscillating frequency, span, rear foil pitch angle, swap angle and vertical position.     

Use of genetic algorithm in new approach to modeling of flood routing

The hydrological models and simpli?ed methods of Saint-venant equations are used extensively in hydrological modeling, in particular for the simulation of the ?ood routing. These models require speci?c and extensive data that usually makes the study of ?ood propagation an arduous practice. We present in this work a new model, based on a transfer function, this function is a function of parametric probability density, having a physical meaning with respect to the propagation of a hydrological signal. The inversion of the model is carried out by an optimization technique called Genetic Algorithm. It consists of evolving a population of parameters based primarily on genetic recombination operators and natural selection to?nd the minimum of an objective function that measures the distance between observed and simulated data. The precision of the simulations of the proposed model is compared with the response of the Hayami model and the applicability of the model is tested on a real case, the N'Fis basin river, located in the High Atlas Occidental, which presents elements that appear favorable to the study of the propagation. The results obtained are very satisfactory and the simulation of the proposed model is very close to the response of the Hayami model.