Decomposing damped incident and reflected waves using correlation and quasi-linearization methods

Water waves propagating over a layer of soft mud or submerged aquatic vegetation can drastically attenuate over distances comparable to several wave lengths. The attenuation in the case of mud has been found previously to be reasonably described by an exponential decay. Waves reflect from beaches and any structures that they impact. The reflected waves affect wave heights measured in the field or laboratory wave basins.Decomposition of small amplitude waves into incident and reflected waves is a linear problem. However, the presence of the exponential damping introduces nonlinearity to the decomposition problem and requires an iterative process for solving the problem. Despite considerable experimental research on attenuation of waves over mud, none of the existing methods for decomposition of incident and reflected waves have accounted for this case.Here, the Newton Algorithm was used to account for the effect of wave decay over mud by quasi-linearizing the nonlinear equations. Also, a second method using a new error function and a commercial nonlinear solver was proposed in both time and frequency domain. The performance of both methods has been verified using artificial as well as laboratory data.     

Theoretical and experimental study on wave damping inside a rubble mound breakwater

Wave decay in a rubble mound breakwater has been analysed theoretically for various types of damping functions (linear, quadratic and polynomial). The applicability of these damping functions for wave decay in the landward part of the breakwater core has been investigated in large scale model tests. The properties of the rock materials that have been used in the model tests have been determined to provide a rational basis for the damping coefficients. The analysis is based on detailed measurements of wave conditions and pressure distributions inside the breakwater. The theoretical approaches have been validated and where necessary extended by empirical means. The wave decay inside the breakwater can be reasonably approximated by the commonly applied linear damping model (resulting in exponential wave height attenuation). An extended polynomial approach provides a slightly better fit to the experimental results and reflects more clearly the governing physical processes inside the structure.     

Vertical structure of the upper ocean from profiles fitted to physically consistent functional forms

A method for characterizing the upper ocean structure is developed. Each temperature (density) profile is fitted by an ideal function based on the assumption that the permanent and seasonal thermoclines can be approximated respectively by steady state and transients of turbulent-diffusive processes and that the mixed layer can advance sharply under external forcing. The ideal profile is composed of two pieces joined at the mixed layer depth (MLD). The upper part is a constant; the part below the MLD is a product of an exponential decay and a Gaussian, representing the seasonal thermocline and decaying asymptotically to a straight line that describes the permanent thermocline. The composition of an exponential decay and a Gaussian accurately fits a wide family of solutions of the diffusion equation and includes the case of a shift of the boundary. The ideal fit for each profile relies on six adjustable parameters including the MLD. As the function is non-linear and non-differentiable, a Differential Evolution optimization algorithm is proposed to make the fitting. The solution gives a good estimate of the MLD based on the topology of the profile. It also provides a measure of the gradient and the shape of each profile, which are intuitive parameters for characterizing the upper ocean structure with direct applicability in ecosystem models. The algorithm is applied to a time series of monthly conductivity–temperature–depth (CTD) profiles from a hydrographical station in the southern Bay of Biscay. The construction of a local climatology of the vertical structure evolution (mixed layer development) is presented as a practical application. Other potential uses of the method are also discussed.     

半参数回归在测量平差中的应用

针对测量平差中的实际问题,引入半参数回归模型,分析了它在测量平差中应用的可能性,并以实例与经典测量平差方法进行精度分析,说明该方法的有效性。对含有系统误差的测量平差问题进行了试算,为进一步研究半参数回归模型在测量平差中的应用具有一定的意义。     

Air-Sea Interactions under the Existence of Opposing Swell

Data of a comprehensive laboratory study on the coexistent system of wind waves and opposing swell (Mitsuyasu and Yoshida, 1989) have been reanalyzed to clarify the air-sea interaction phenomena under the coexistence of wind waves and swell. It is shown that the magnitude of the decay rate of swell due to an opposing wind is almost the same as that of the growth rate of swell caused by a following wind, as measured by Mitsuyasu and Honda (1982). The decay rate is much smaller than that obtained recently by Peirson et al. (2003), but the reason for the disagreement is not clear at present. The effect of an opposing swell on wind waves is very different from that of a following swell; wind waves are intensified by an opposing swell while they are attenuated by a following one. The phenomenon contradicts the model of Phillips and Banner (1974), but the reason for this is not clear at this time. The high-frequency spectrum of wind waves shows a small increase of the spectral density. Wind shear stress increases a little due to the effect of opposing swell. The intensification of wind waves by opposing swell and the small increase of the spectral density in a high-frequency region can be attributed to the increase of wind shear stress. Such organized phenomena lead to the conclusion that the hypothesis of local equilibrium for pure wind waves (Toba, 1972) can also be satisfied for wind waves that coexist with opposing swell. The recent finding of Hanson and Phillips (1999) can be explained by this mechanism.     

Why a corrugated coast only influences a longshore current within a wave length of the coast

An inviscid zone of influence is postulated from a physical model to occur when a steady homogeneous fluid flows by a two-dimensional corrugated wall with small slopes. The thickness of the influence zone is calculated to be a constant times the wave length of the wall. The method used involves balancing pressure differences between extreme points along the wall and between the wall and the outer edge of the influence zone but does not involve the irrotational assumption. An influence zone forms because the curvature of the boundary induces cross-stream accelerations and pressure gradients in the fluid. The result for the thickness of the influence zone agrees qualitatively with the exponential decay scale of an available potential flow solution to a similar problem, which suggests that the influence zone may occur in some rotational (as well as irrotational) flows.     

Nonlinear output feedback control of underwater vehicle propellersusing feedback form estimated axial flow velocity

Accurate propeller shaft speed controllers can be designed by using nonlinear control theory and feedback from the axial water velocity in the propeller disc. In this paper, an output feedback controller is derived, reconstructing the axial flow velocity from vehicle speed measurements, using a three-state model of propeller shaft speed, forward (surge) speed of the vehicle, and the axial flow velocity. Lyapunov stability theory is used to prove that a nonlinear observer combined with an output feedback integral controller provide exponential stability. The output feedback controller compensates for variations in thrust due to time variations in advance speed. This is a major problem when applying conventional vehicle-propeller control systems. The proposed controller is simulated for an underwater vehicle equipped with a single propeller. The simulations demonstrate that the axial water velocity can be estimated with good accuracy. In addition, the output feedback integral controller shows superior performance and robustness compared to a conventional shaft speed controller     

适用于海洋动态观测设备嵌入式系统的低功耗管理预测模型

能耗是制约海洋设备在水下工作时长的关键因素。为进一步降低海洋动态观测设备嵌入式系统的动态功耗, 本文针对前人提出的用于预测空闲时间的指数平滑算法所存在的权重系数基于凑数法确定、算法难以适应大波动等问题, 设计了一种新的权重系数, 并构建了一种自适应的低功耗管理预测模型。当模型检测到预测的空闲时间超过工作和休眠状态切换的时间阈值后, 中央处理器关停系统的部分外设, 使系统进入低功耗休眠状态。仿真和单片机实验均表明,本文提出的低功耗管理预测模型能够有效地提高对处理器工作的空闲时间预测的准确性, 且面对突发状况具有良好的自适应性, 可显著降低嵌入式系统的功耗, 有效延长设备的工作时间。     

Groundwater response to the tide in wetlands: Observations from the Gillman Marshes,South Australia

We present results from a series of piezometers installed in the foreshore flat and mangrove environments of the Gillman Marshes, South Australia in an interdisciplinary study of the propagation of the ocean tide into the coastal aquifers. A unique feature of the analysis is that all water level records were harmonically analysed so that the behaviour of the four major tidal constituents could be independently examined. The main findings were that: (1) the decay of the groundwater tide in the coastal aquifers was greater than that predicted by the Ferris solution. A theoretical model has been developed and applied to the study site. The model suggests that this behaviour is due to the occurrence of a time delay in the Darcian response in the shelly and muddy sand substrate; (2) when the tide is incident over a gently sloping bank, the time delay in response gives rise to a spiked signal in which high water is confined to a small fraction of the tidal cycle; and (3) at the coastal interface tidal propagation across a sloping bank causes a rise in the water table relative to mean sea level which is proportional to the variance of tidal elevation and inversely proportional to the decay constant of the groundwater tide. The model developed in this study is also applicable to other coastal groundwater systems with tidal influence.     

Determination of residence time and mixing processes of the Ubatuba,Brazil, inner shelf waters using natural Ra isotopes

Coastal waters contain elevated dissolved activities of short-lived radium isotopes, ²²³Ra and ²²⁴Ra, having half-lives of 11.4 and 3.66 days, respectively. The input of these isotopes near the coast must be balanced by decay and mixing into the open ocean, where excess activities are zero. Since the decay rate is known, in the ideal case the mixing rate may be determined from the offshore distribution of these isotopes. This study found that samples collected in June 2000 followed the expected exponential decrease with distance offshore. We assign a dispersion coefficient of 28–39 m² s⁻¹ for this study. During January 2002 and November 2003, there was not a consistent decrease of activity with distance offshore. This is likely due to the ruggedness of the coastline, where many bays and small islands interrupt simple mixing patterns. To estimate exchange rates during 2002 and 2003, we used a model based on the decrease in the ²²⁴Ra/²²³Ra activity ratio (AR) with time for samples isolated from fresh inputs of Ra. This model yielded residence times of 1–2 weeks for samples collected within 20 km of the coast. We used this residence time to calculate the flux of ²²⁸Ra (half-life = 5.7 years) to the study area necessary to maintain the enrichment relative to ocean water. This enrichment is a factor of ten greater than the flux of ²²⁸Ra expected from submarine groundwater discharge (SGD) occurring within 50 m of shore.     

模态分离的环流模式POM的垂向速度算法的误差估计

A time splitting technique is common to many free surface ocean models. The different truncation errors in the equations of the internal and external modes require a numerical adjustment to make sure that algorithms correctly satisfy continuity equations and conserve tracers quantities. The princeton ocean model （POM） has applied a simple method of adjusting the vertical mean of internal velocities to external velocities at each internal time step. However, due to the Asselin time filter method adopted to prevent the numerical instability, the method of velocity adjustment used in POM can no longer guarantee the satisfaction of the continuity equation in the internal mode, though a special treatment is used to relate the surface elevation of the internal mode with that of the external mode. The error is proved to be a second-order term of the coefficient in the Asselin filter. One influence of this error in the numerical model is the failure of the kinetic boundary condition at the sea floor. By a regional experiment and a quasi-global experiment, the magni- tudes of this error are evaluated, and several sensitivity tests of this error are performed. The characteristic of this error is analyzed and two alternative algorithms are suggested to reduce the error.     

基于叠前时间偏移速度扫描的四维建模技术及应用

速度建模是做好叠前偏移的关键。主要介绍一种基于叠前时间偏移（PreSTM）的百分比速度扫描的四维速度建模技术。该技术通过对分析点的百分比速度扫描,得到一组不同百分比速度的偏移叠加剖面,经速度建模交互软件包形成四维数据体,通过速度模型的多次迭代和修正,形成最终偏移速度模型。这种速度建模技术在地质结构比较复杂的条件下也可以根据偏移成像结果提取速度函数以满足叠前时间偏移对复杂地质构造正确成像的需要。该技术在海上三维叠前时间偏移处理中得到了成功应用,并取得了较好的地质效果。     

Analytical convolution model for shipping water evolution on a fixed structure

The shipping of water is a problem that affects naval and offshore structures. Estimating its propagation on the decks of these structures by using analytical methods has been a main concern of projects. However, classical approaches disregard the decay tendency of water elevation time series and tend to overestimate the resultant water on deck. This paper is concerned with estimating the evolution of water along the deck of a fixed structure due to shipping water events. An analytical convolution model is proposed to estimate water elevations. The model considers the freeboard exceedance time series and the mean shipping flow velocity as inputs and the frictional effects of the bottom by resistance coefficients, which enables an approximated representation of the water elevation time series over the deck. It was validated with experiments of isolated shipping water events that were generated with the wet dam-break approach. The results obtained with the proposed model captured the experimental results, approximating the peak values and the decay trend of time series. Improvement of the proposed approach over classical models to represent shipping water elevations was demonstrated by comparing the results obtained with those of the dam-break model of Stoker.     

On the decay of layered structures in a stratified shear flow

The effect of a vertical velocity shear on the decay of small-scale perturbations in an unbounded thermally-stratified fluid is considered. The behaviour of perturbations at the final stage is shown to be controlled by the combined effects of viscosity, thermal conductivity, collapse, and material line stretching due to velocity shear. The behaviour of density and velocity perturbations has been analysed for the case of dominating viscosity forces and a velocity shear.UDK 532.529+532.517.4Translated by Vladimir A. Puchkin.     

长江口泥质区18#柱样的现代沉积速率及其环境 指示意义

通过对长江口泥质区18#柱样进行137Cs和210Pb同位素测年分析,得到了柱样站点的现代沉积速率。结果表明,近50多年来沉积速率较大,且呈现阶段性差异：由137Cs时标计年法得到柱样1954—1964年的沉积速率为5.9 cm/yr,1964—2006年减小为 3.36 cm/yr;沉积柱样的210Pb剖面呈两段分布,由此得到沉积速率120～225 cm为5.47 cm/yr,对应于18～100 cm减小为4.58 cm/yr。对比分析两种方法得出沉积速率开始减小的时间为1968—1972年,并且采样点区域表层可能出现侵蚀现象,为研究长江口泥质区环境演变提供了依据。     

Linear dynamics of hydrostatic adjustment to horizontally homogeneous heating

The process of hydrostatic adjustment to horizontally homogeneous heating in a stably stratified atmosphere of arbitrary thermal structure is investigated in the limit of small perturbations. A linear differential equation is derived for the vertical pressure distribution in the final balanced state. Solutions of this equation are compared with the time dependent solution which is found by numerically integrating the equations in time. During the process of hydrostatic adjustment acoustic‐buoyancy oscillations are generated. The amplitudes of these oscillations become so great that static instability is generated at heights above 100 km, depending on where and how abruptly the heat is added. As a crude representation of the unstable breakdown and damping of these waves, Rayleigh damping is introduced. If the associated damping coefficient in the upper atmosphere is sufficiently large (greater than the Brunt Väisälä frequency), the oscillations vanish. Below a height of about 50 km the steady state predicted by the above mentioned differential equation is reached approximately in 10 min.     

The decay kinetics of residual chlorine in cooling seawater simulation experiments

To find out the decay character of residual chlorine (RC) in the sea water, the concentration of RC was analyzed by N, N-diethyl-p-phenylenediamine (DPD) method under different simulation experimental conditions, in which salinity, temperature, and Chemical Oxygen Demand (COD) were selected. The water used in the experiment was the mixture of aging ocean water, coastal water and extracting solution of coastal sediment at appropriate level. Results are shown as follows:(1) Piecewise function can well reflect the decay dynamics of RC in the cooling seawater. Concretely, the decay dynamics of first 1 min is too rapid to ascertain using a specific kinetic function, and that of the time from 1 to 30 min is fit for the first-order kinetic model. (2) The results could be the foundation of the chemical behavior of RC in seawater, and be used as not only the guidance of the coastal power plants production and sea water desalting companies, but also the establishment of the correlative trade standard.     

地形对陆架拦截波性质及机制的影响

陆架波的性质如频散关系、形成机制等受地形影响。研究地形对陆架波的性质影响具有重要意义。基于陆架拦截波理论,数值计算了分段线性地形下不同宽度陆架上陆架拦截波的频散关系、长波假设下波动的相速度、阻尼情况下的波动耗散率以及强迫波的外力影响因子。分析了陆架宽度及坡度对自由及强迫陆架拦截波性质的影响。陆架宽度影响陆架拦截波的频散关系。陆架变宽,使得长波频散曲线的斜率增大。陆架宽度的增加使第一模态陆架拦截波有明显的性质变化:相速度增大,波动受辐散影响的程度变大,摩擦衰减距离增大,且风应力旋度在波动的生成机制中起到的作用渐强。在宽的陆架上,研究陆架拦截波的生成及强迫波的振幅时,应充分考虑风应力旋度的作用。第二、三模态波动的相速度受陆架坡度的影响较大,但摩擦衰减距离基本都在200km左右,几乎不随陆架宽度改变,属于局地波。     

Adriatic seiche decay and energy loss to the Mediterranean

A salient feature of sea level records from the Adriatic Sea is the frequent occurrence of energetic seiches of period about 21 h. Once excited by a sudden wind event, such seiches often persist for days. They lose energy either to friction within the Adriatic, or by radiation through Otranto Strait into the Mediterranean.The free decay time of the dominant (lowest mode) seiche was determined from envelopes of handpassed sea level residuals from three locations (Bakar, Split and Dubrovnik) along the Croatian coast during twelve seiche episodes between 1963 and 1986 by taking into consideration only time intervals when the envelopes decreased exponentially in time, when the modelled effects of along-basin winds were smaller than the error of estimation of decay time from the envelopes and when across-basin winds were small. The free decay time thus obtained was 3.2±0.5 d. This value is consonant with the observed width of the spectral peak.The decay caused by both bottom friction and radiation was included in a one dimensional variable cross section shallow water model of the Adriatic. Bottom friction is parameterized by the coefficient k appearing in the linearized bottom stress term _ρ0u (where u is the along-basin velocity and ρ₀ the fluid density). The coefficient k is constrained by values obtained from linearization of the quadratic bottom stress law using estimates of near bottom currents associated with the seiche, with wind driven currents, with tides and with wind waves. Radiation is parameterized by the coefficient f appearing in the open strait boundary condition ζ =auh/c (where ζ is sea level, h is depth and c is phase speed). This parameterization of radiation provides results comparable to allowing the Adriatic to radiate into an unbounded half plane ocean. Repeated runs of the model delineate the dependence of model free seiche decay time on k and a, and these plus the estimates of k allow estimation of a.The principle conclusions of this work are as follows.

1. (1) Exponential decay of seiche amplitude with time does not necessarily guarantee that the observed decay is free of wind influence.

2. (2) Winds blowing across the Adriatic may be of comparable importance to winds blowing along the Adriatic in influencing apparent decay of seiches; across-basin winds are probably coupled to the longitudinal seiche on account of the strong along-basin variability of across-basin winds forced by Croatian coastal orography.

3. (3) The free decay time of the 21.2 h Adriatic seiche is 3.2±0.5 d.

4. (4) A one dimensional shallow water model of the seiche damped by bottom stress represented by Godin's (1988) approximation to the quadratic bottom friction law ρ₀C_Du|u| using the commonly accepted drag coefficient C_D = 0.0015 and quantitative estimates of bottom currents associated with wind driven currents, tides and wind waves, as well as with the seiche itself with no radiation gives a damping time of 9.46 d; radiation sufficient to give the observed damping time must then account for 66% of the energy loss per period. But independent estimates of bottom friction for Adriatic wind driven currents and inertial oscillations, as well as comparisons between quadratic law bottom stress and directly measured bottom stress, all suggest that the quadratic law with C_D=0.0015 substantially underestimates the bottom stress. Based on these studies, a more appropriate value of the drag coefficient is at least C_D=0. In this case, bottom friction with no radiation leads to a damping time of 4.73 d, radiation sufficient to give the observed damping time then accounts for 32% of the energy loss per period.