Internal waves in a high-latitude region

Internal waves are studied in two high-latitude regions of the Kara Sea. The measurements were carried out with a towed CTD profiler and a distributed temperature sensor on a mooring. The lack of internal waves with an M2 tidal period and the presence of high-frequency waves are demonstrated on the basis of the measurements and numerical modeling.     

Internal wave signal processing: a model-based approach

A model-based approach is proposed to solve the oceanic internal wave signal processing problem that is based on state-space representations of the normal-mode vertical velocity and plane wave horizontal velocity propagation models. It is shown that these representations can be utilized to spatially propagate the modal (depth) vertical velocity functions given the basic parameters (wave numbers, Brunt-Vaisala frequency profile, etc.) developed from the solution of the associated boundary value problem as well as the horizontal velocity components. These models are then generalized to the stochastic case where an approximate Gauss-Markov theory applies. The resulting Gauss-Markov representation, in principle, allows the inclusion of stochastic phenomena such as noise and modeling errors in a consistent manner. Based on this framework, investigations are made of model-based solutions to the signal enhancement problem for internal waves. In particular, a processor is designed that allows in situ recursive estimation of the required velocity functions. Finally, it is shown that the associated residual or so-called innovation sequence that ensues from the recursive nature of this formulation can be employed to monitor the model's fit to the data     

Internal wave dispersions in density-stratified deep oceans with a thermocline

As to two typical Väisälä frequency profiles in deep oceans, one in the Arctic Ocean and one in the Atlantic, the approximate analytical method ofHyun (1976) is used to calculate internal wave dispersion relations. The method is shown to have good agreement with the matrix numerical method. By making calculations for an exemplary Väisälä frequency profile with a thermocline, an assessment is made of the inaccuracies in the dispersion curves obtained by the ordinary WKB method which does not take into account the turning point singularities.     

Internal inlet for wave generation and absorption treatment

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.     

A view on capsizing under direct and parametric wave excitation

The behavior of a ship that is simultaneously heaving, swaying and rolling in waves is examined by using an early developed model by Thompson et al. [Thompson, J. M. T., Rainey, R. C. T. and Soliman, M. S. (1992) Mechanics of ship capsize under direct and parametric wave excitation. Philosophical Transactions of the Royal Society London A 338, 471-490]. A second-order nonlinear differential equation has been used as a mathematical model which is analyzed by using numerical methods to obtain geometrical phase space techniques of nonlinear dynamics. Bifurcation diagrams and Poincaré maps are two of the geometrical techniques used in this study. The result of the calculation is given to allow the naval architect to make a self comparison.     

Internal wave generation in an improved two-dimensional Boussinesq model

A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model.     

Internal wave generation in an improved two-dimensional Boussinesq model

A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model.     

Validation of the Boccotti's generalized model for large nonlinear wave heights from laboratory mixed sea states

The presented work aims at validating the generalization of the asymptotic distribution model of Boccotti for large wave heights recently proposed by Tayfun [1] to laboratory generated mixed sea states with two-peak spectra. The input wave spectra are modelled as the sum of two JONSWAP spectra describing unidirectional wave systems with different or identical directions of propagation (crossing or following mixed seas). In order to account for the effect of the energetically dominant wave system on the largest observed waves, the Boccotti's parameters were calculated at the absolute minimum of the autocorrelation function which can differ from the first minimum for some cases of mixed seas, such as those dominated by the swell or seas with comparable contribution of the two spectral components. So far the proposed model has been validated elsewhere against samples of large wave heights exceeding the significant wave height in wind seas and in mechanically generated long-crested seas, both characterized by unimodal spectra and strong third-order nonlinearities. The present study demonstrates that it can predict equally well the tail of the distributions for mixed seas, irrespective of the type of the mixed sea, particularly when the third-order statistics is relatively large. Typically, the mixed seas from the considered offshore basin experiment display such conditions as the propagation distance from the wavemaker increases, though this effect is less pronounced for mixed following than for mixed crossing wave conditions. Moreover, the generalized model remains valid irrespective of the sign of the fourth-order sum Λ which is a key parameter of the distribution. Its good predictive ability is quantified here by the root-mean-square errors between observations and theory.     

近破波作用下沉箱式防波堤运动特性的模型实验研究

对近破波作用下沉箱式防波堤的运动特性进行了模型实验研究。实验中测量了沉箱模型与基床的摩擦系数、基床刚度和阻尼系数;不同水位情况下作用于沉箱模型上的近破波波压力时程;近破波作用下沉箱模型的位移和转角响应时程等,并与数学模型计算结果进行了比较分析。实验结果表明,若沉箱的滑移力大于沉箱与基床间的摩擦力,在连续波浪作用下,沉箱将连续出现间歇式滑移运动,数学模型可较好地模拟这一运动过程。     

Wave reflection from a vertical permeable wave absorber

A theoretical solution for the reflection of linear shallow-water waves from a vertical porous wave absorber on a horizontal bottom is presented. Periodic solutions are matched at the front face of the absorber by assuming continuity of pressure and mass. The friction term describing the energy loss inside the absorber is linearized and, by using Lorentz principle of equivalent work, the reflection coefficient is determined as a function of parameters describing the incoming waves and the absorber characteristics.     

CODAR wave measurements from a North Sea semisubmersible

CODAR, a high-frequency (HF) compact radar system, was operated continuously over several weeks aboard the semisubmersible oil platform Treasure Saga for the purpose of wave-height directional measurement and comparison. During North Sea winter storm conditions, the system operated at two different frequencies, depending on the sea state. Wave data are extracted from the second-order backscatter Doppler spectrum produced by nonlinearities in the hydrodynamic wave/wave and electromagnetic wave/scatter interactions. Because the floating oil rig itself moves in response to long waves, a technique has been developed and successfully demonstrated to eliminate to second order the resulting phase-modulation contamination of the echo, using separate accelerometer measurement of the platform's lateral motions. CODAR wave height, mean direction, and period are compared with data from a Norwegian directional wave buoy; in storm seas with wave heights that exceeded 9 m, the two height measurements agreed to within 20 cm RMS, and the mean direction to better than 15° RMS     

波浪作用下海洋石油井架模态参数识别与承载力评价

提出基于试验模态参数识别和优化算法修改动力有限元模型的海洋石油井架安全承载能力评价方法.推导基于波浪脉动的试验模态参数识别公式,介绍有限元模型动力修正的一阶优化方法.以海洋随机波浪脉动作为激励,对勘探三号海洋石油井架进行了现场模态试验,识别出前二阶固有频率.以此作为有限元模型修正的基础,应用一阶搜索优化算法,对动力有限元模型进行了修正,结果表明:该修正模型比较准确反映了井架目前的结构状态,能够用于进一步的静、动力分析和安全承载能力评价.     

波浪作用下斜坡上护面块体内部应力分布数值模拟

基于3D FEMDEM方法建立三维原型尺度数值模型,模拟波浪荷载作用下斜坡上护面块体内部的应力分布。波浪作用下结构物的水动力荷载采用微幅波理论模拟,护面块体之间的运动、碰撞接触以及块体内部的应力变化采用3D FEMDEM方法模拟。块体之间的接触力采用基于势函数的罚函数法计算,有限元的变形采用中心差分的显式方法求解。应用该数值模型与ANSYS软件程序对自重作用下混凝土扭王字块的内部应力分布特性进行了比较分析,验证了数值模型应力计算的可行性和计算精度。通过数值模拟计算给出了波浪作用下斜坡上护面块体之间的相对运动和块体内部的应力分布及应力历时曲线,探讨了块体内部应力变化特性。     

Correlation between successive wave heights and periods in mixed sea states

The degree of dependence between successive wave heights and periods is examined for sea states resulting from the combination of a remotely generated wave field and a locally generated wave system, based on simulated wave records. The sea states analysed represent situations that are swell dominated, wind–sea dominated or they have equivalent energy in the wind–sea and swell components. Results of the analysis of the simulated data have been compared with those expected from the theories for the joint distributions of consecutive wave heights and periods and with the results from a Pierson–Moskowitz target spectrum.     

Simulation of the ocean surface mixed layer under the wave breaking

A one-dimensional mixed-layer model, including a Mellor-Yamada level 2.5 turbulence closure scheme, was implemented to investigate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic energy released through wave breaking was incorporated into the model as a source of energy at the ocean surface, and the influence of the breaking waves on the mixed layer was studied. The numerical simulations show that the simulated SST is overestimated in summer without the breaking waves. However, the cooler SST is simulated when the effect of the breaking waves is considered, the corresponding discrepancy with the observed data decreases up to 20% and the MLD calculated averagely deepens 3.8 m. Owing to the wave-enhanced turbulence mixing in the summertime, the stratification at the bottom of the mixed layer was modified and the temperature gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.     

The long-term trend of the sea surface wind speed and the wave height (wind wave, swell, mixed wave)in global ocean during the last 44 a

Utilizing the 45 a European Centre for Medium-Range Weather Forecasts(ECMWF)reanalysis wave data(ERA-40),the long-term trend of the sea surface wind speed and(wind wave,swell,mixed wave)wave height in the global ocean at grid point 1.5×1.5 during the last 44 a is analyzed.It is discovered that a majority of global ocean swell wave height exhibits a significant linear increasing trend(2–8 cm/decade),the distribution of annual linear trend of the significant wave height(SWH)has good consistency with that of the swell wave height.The sea surface wind speed shows an annually linear increasing trend mainly concentrated in the most waters of Southern Hemisphere westerlies,high latitude of the North Pacific,Indian Ocean north of 30 S,the waters near the western equatorial Pacific and low latitudes of the Atlantic waters,and the annually linear decreasing mainly in central and eastern equator of the Pacific,Juan.Fernandez Archipelago,the waters near South Georgia Island in the Atlantic waters.The linear variational distribution characteristic of the wind wave height is similar to that of the sea surface wind speed.Another find is that the swell is dominant in the mixed wave,the swell index in the central ocean is generally greater than that in the offshore,and the swell index in the eastern ocean coast is greater than that in the western ocean inshore,and in year-round hemisphere westerlies the swell index is relatively low.     

Reflection of a long wave from an underwater slope

Reflection of long sea waves from an underwater slope described by a power law is studied within the shallow water theory. The slope is connected with the flat bottom. This model allows us to estimate the roles of a pointwise reflection from the inflection point of the bottom profile and distributed reflection at the underwater slope. The case of the underwater slope described by the so-called nonreflecting beach (h(x) ∼ x ^4/3, where h is the depth of the basin and x is the coordinate) when the wave is reflected only from the inflection point (pointwise reflection) is specially considered. The reflection and transmission coefficients over the bottom topography were calculated, and it was shown that the sum of the squared absolute values of these values differs from unity for all profiles except the nonreflecting one. This difference is related to the distributed re-reflections (resonances) over the underwater slope that lead to the deviations in the wave height from the known Green’s law.     

Note on wave parameters from moored wave buoys

For decades, the accelerometer wave buoy has been a preferred choice for offshore wave measurements. Although these measurements are accurate and robust, there are some issues of practical character that need to be inspected before using such measurements for detailed time-series investigations. Here three potential sources of inaccuracies are outlined which can appear due to improper mooring, limited high-frequency resolution or overly simple procedures for attaching measurement times (time stamps) to the measurements. The last two of these apply to all types of single-point wave-measuring devices.

An example of a wave-height series is given, in which part of the observed variation seems to be induced by the mooring. It is argued that unexpected semi-tidal modulations in measured wave-height can be an indication of a mooring that is too rigid. By truncating observed wave spectra from a deep-water location, it is demonstrated how the high-frequency cut-off limit of a wave measurement influences the most commonly used wave parameters. It is observed that the accuracy of common wave parameters remains acceptable up to a cut-off limit in the range of 0.30–0.35 Hz if the spectra above the cut-off frequency are replaced by a prognostic f⁻⁵ tail. Finally it is noted that the procedure of connecting time stamps to wave measurements can in some cases introduce an artificial time-lag compared to the real-time sea state.     

Internal wave band kinetic energy production: flat vs. sloping bottom

Velocity and temperature measurements obtained with acoustic Doppler current profilers and thermistor strings are used to evaluate the production of internal wave band kinetic energy mainly in the frequency band σ>15 cpd. Results from a flat 19 m deep, vigorous tidal environment in a shelf sea are compared with energy production in a bottom boundary layer above a continental slope. In the tidal environment, maximum production occurs in the near-bottom and near-surface layers. A distinct mid-depth maximum in KE production occurs during a period when wind speeds exceed 10 m s⁻¹ and significant wave height ∼2 m. At the same time, no significant changes in the along-shore current speed take place but the cross-shore current, generated by strong stratification, is weakened. This suggests a direct energy input from the wind via surface waves into the water column turbulence. Maximum kinetic energy production in the frequency band σ>1.9 cpd, thus including the semidiurnal tide, occurs at mid-depth when strong stratification is present. The overall magnitude of internal wave band kinetic energy production agrees well with independent dissipation estimates obtained from microstructure profilers. Above the sloping bottom, KE production is somewhat larger than observed in the shallow tidal environment, despite rms currents being ∼50% smaller and wind effects being small. Above the sloping bottom KE shear production was comparable to buoyancy production. The latter was negligible at the shelf sea site.     

Internal wave characteristics at the ASIAEX site in the east China Sea

The characteristics of internal waves (IWs) observed during the Asian Sea International Acoustics Experiment 2001 in the East China Sea are presented in this paper. Temperature data from a 17-element thermistor chain exhibit clear IW features in shallow water. Large-amplitude oscillations, up to 35 m, are noted due to the semi-diurnal internal tides. High-frequency (HF) and narrow-bandwidth IW trains around 6 c/h ride on semi-diurnal IWs. The spectrum of vertical displacement of the IWs, calculated from the thermistor chain data, falls as /spl omega//sup -1.6/ in the frequency band of 0.1-4 c/h. For higher frequencies (>6 c/h), the spectrum falls as /spl omega//sup -3.0/. Vertical coherence of the IWs for both semi-diurnal internal tides and HF IWs is analyzed. Comparisons of our observations with other data, obtained from SWARM95, the Barents Sea, and the Gulf of Mexico, display some common characteristics of shallow-water IWs.