Turbulent dispersion in the ocean

The mathematical framework for turbulent transport in the ocean is reasonably well established. It may be applied to large-scale fields of scalars in the ocean and to the instantaneous or continuous discharge from a point. The theory and its physical basis can also provide an interpretation of passive scalar spectra. Spatial variations in the rate of turbulent transfer can be related to the movement of the center of mass of a scalar and to a formulation in terms of entrainment. The relative dispersion of a scalar with respect to its center of mass and the streakiness of the concentration field within the relative dispersion domain need to be considered. In many of these problems it is valuable to think in terms of simple models for individual streaks, as well as overall statistical properties.     

On the Scale of Aggregation of Meio-benthic Copepods on a Tidal Mudflat

Abstract. The dispersion pattern of mciobenthic harpacticoid copepods was measured on a mudflat at different tidal conditions. Samples were collected using a 5 times 5 array of contiguous cores (8 mm ID), and analyzed by spatial autocorrelation (MOHAN'S I statistic). Four species were abundant, and all were judged to be patchy by autocorrelation. The apparent scale of patchincss did not differ with tidal stage. Three species were aggregated at very small spatial scales (0.5 to 1cm²), with patches probably distributed at random within a sampling array. The fourth species was also aggregated at the smallest spatial scale (neighboring cores), but may have been regularly spaced at distances longer than 5 cm. This study shows that processes on the order of several cm² must dictate the patch dynamics of small metazoans.     

Comments on the “shear effect” and diffusion in the Lagrangian framework

We indentify three different types of Lagrangian coordinate systems that are used in oceanography. These are: true Lagrangian coordinates (TLC), Lagrangian coordinates (LC), and averaged Lagrangian coordinates (ALC). The diffusion process is studied in each of these coordinate systems. At large scales the eddydiffusivity is proven to be independent of molecular diffusivity, providing the spectrum of turbulent kinetic energy varies as scale raised to a power less than 4 1/3. The shear effect is examined using solutions to the averaged Lagrangian diffusion equation obtained by Okuboet al. (1983). In Eulerian coordinates both advection and diffusion are necessary for the occurrence of the shear effect, while in ALC timedependent dispersion coefficients are necessary for the process. In TLC we use the method of Taylor (1921) to study the dispersion of material by a velocity field, that from the Eulerian perspective, consists of turbulent motion across a uniform shear. The transformation of the above Eulerian velocity field into TLC results in a uniform deformation field and turbulent motion both along and across the shear. This work shows how dispersion of material is related to the turbulent Eulerian velocity and uniform velocity gradients. The instantaneous rate of change of variance of a spreading patch of material is completely specified by the instantaneous divergence obtained over the area occupied by the patch (Kawai, 1976). This relationship is shown to depend upon the fact that at any particular instant it is possible to define TLC that are equivalent to the Eulerian coordinates. In order to describe patch spreading from divergence measured over longer periods it is also necessary to consider other dispersive processes.Contribution number of the Newfoundland Institute of Cold Ocean Science.     

Calibration/Validation of an Altimeter Wave Period Model and Application to TOPEX/Poseidon and Jason-1 Altimeters

The altimeter radar backscatter cross-section is known to be related to the ocean surface wave mean square slope statistics, linked to the mean surface acceleration variance according to the surface wave dispersion relationship. Since altimeter measurements also provide significant wave height estimates, the precedent reasoning was used to derive empirical altimeter wave period models by combining both significant wave height and radar backscatter cross-section measurements. This article follows such attempts to propose new algorithms to derive an altimeter mean wave period parameter using neural networks method. Two versions depending on the required inputs are presented. The first one makes use of Ku-band measurements only as done in previous studies, and the second one exploits the dual-frequency capability of modern altimeters to better account for local environmental conditions. Comparison with in situ measurements show high correlations which give confidence in the derived altimeter wave period parameter. It is further shown that improved mean wave characteristics can be obtained at global and local scales by using an objective interpolation scheme to handle relatively coarse altimeter sampling and that TOPEX/Poseidon and Jason-1 altimeters can be merged to provide altimeter mean wave period fields with a better resolution. Finally, altimeter mean wave period estimates are compared with the WaveWatch-III numerical wave model to illustrate their usefulness for wave models tuning and validation.     

Calibration/Validation of an Altimeter Wave Period Model and Application to TOPEX/Poseidon and Jason-1 Altimeters

The altimeter radar backscatter cross-section is known to be related to the ocean surface wave mean square slope statistics, linked to the mean surface acceleration variance according to the surface wave dispersion relationship. Since altimeter measurements also provide significant wave height estimates, the precedent reasoning was used to derive empirical altimeter wave period models by combining both significant wave height and radar backscatter cross-section measurements. This article follows such attempts to propose new algorithms to derive an altimeter mean wave period parameter using neural networks method. Two versions depending on the required inputs are presented. The first one makes use of Ku-band measurements only as done in previous studies, and the second one exploits the dual-frequency capability of modern altimeters to better account for local environmental conditions. Comparison with in situ measurements show high correlations which give confidence in the derived altimeter wave period parameter. It is further shown that improved mean wave characteristics can be obtained at global and local scales by using an objective interpolation scheme to handle relatively coarse altimeter sampling and that TOPEX/Poseidon and Jason-1 altimeters can be merged to provide altimeter mean wave period fields with a better resolution. Finally, altimeter mean wave period estimates are compared with the WaveWatch-III numerical wave model to illustrate their usefulness for wave models tuning and validation.     

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.     

Investigation and comparison of one-dimensional (1-D) analytical models prediction for salt intrusion condition in two selected estuaries

Abstract

In this paper, two analytical models used worldwide to assess salinity variation in alluvial estuaries are applied to the Ashtamudi estuary, a Ramsar site, southwest coast of India; and Bouregreg estuary, in northwest part of Morocco. The estuaries’ bathymetry is described by an exponential function. Both models are quite similar and use a predictive equation for the dispersion in the estuary mouth (D₀). The major difference between the two models is the use of the constant value of K?=?0.5 for the Van der Burgh coefficient (K) and the introduction of the correction factor ζ, which is a function of damping (δ) and shape (γ). The performance of these two models was evaluated by comparing their results with field measurements; this revealed that both analytical models apply well to both the estimation of salinity distribution and the prediction of salt intrusion in the Ashtamudi and Bouregreg estuaries (Ashtamudi: RMSE = 0.60–1.22 ppt; Bouregreg: RMSE = 0.92–2.71 ppt). One model agrees more with the field measurements of salinity distribution along the estuaries axis; the second underestimate and overestimate some values of salinity distribution along the estuaries. Possibly, the constant value of K?=?0.5 for the Van der Burgh coefficient (K) has applicability limits for the estuaries under tidal conditions. The specifying of the parameterization may be a field of research.     

Responses of DMS in the seawater and atmosphere to iron enrichment in the subarctic western North Pacific (SEEDS-II)

Simultaneous measurements of dimethylsulfide (DMS) in the seawater and atmosphere were conducted during SEEDS-II to investigate the responses of DMS to iron (Fe) fertilization in the subarctic North Pacific. No significant increases in the seawater DMS (DMSw) concentration were observed inside the fertilized patch compared to those outside the patch, while particulate dimethylsulfoniopropionate (DMSPp) concentration inside the patch increased 2-fold compared to those outside the patch in the phytoplankton bloom of major DMSP producers such as prasinophytes, cryptophytes, diatoms and prymnesiophytes. In the decline phase of the bloom, maximum DMSw was observed both inside the patch (ca. 6.2 nM) and outside the patch (ca. 9.3 nM). In this period, increases in mesozooplankton and decreases in the DMSP producers (prymnesiophytes and diatoms) were observed both sides of the patch, but larger inside the patch than outside the patch. Large decreases in the DMSPp inside the patch, which was probably related to the large increases in mesozooplankton inside the patch, did not result in increases in the DMSw concentration. Considering biological and nonbiological parameters, we discussed these results, although they could not be completely explained. Unfortunately, the impact of Fe fertilization on the atmospheric DMS (DMSa) concentration was not detected due to no significant changes in DMSw. However, it is noted that DMSa concentrations were dependent on the sea–air DMS flux in the air from higher latitudes and/or the Eurasian continent, though the DMS flux was a minor role to the budget of DMSw. Therefore if DMSw were significantly changed by Fe fertilization, DMSa might be affected through changes in the sea-air flux in this condition.     

波浪的非线性显式弥散关系

波浪的非线性弥散关系在应用于求解波浪的变形问题时很不方便，需要与含非线性效应的缓坡方程一起进行迭代运算，往往导致数值计算的计算量太大，计算过于复杂。采用显式形式表达非线性弥散关系，可以克服上述缺点，大为简化波浪变形数值计算的计算量。本文通过将现有的非线性弥散关系进行分析比较，给出了一个更为一般的非线性弥散关系及其显式表达式，经比较可知，该显式弥散关系与相对应非线性弥散关系吻合的很好。本文最后用该显式结合含弱非线性效应的缓坡方程，对复式浅滩地形上的波浪折射绕射进行了计算。结果表明，考虑弱非线性可以得出与实验数据更为相符的结果，而采用显式弥散关系可以有效提高计算效率,在波浪的非线性计算中不失为一种切实有效的方法。     

Lagrangian diffusion equation and its application to oceanic dispersion

The Lagrangian diffusion equation appropriate for the dispersion of current followers (e. g., floats, drogues, drifters) is proposed. The analytical solution to the equation is obtained for a uniform deformation field, characterized by Lagrangian deformations and anisotropic eddy diffusivities both varying with time. Expressions are derived for the patch area and its elongation and rotation. For small values of elapsed time after the initial release the patch area can be accounted for by the exponential of the cumulative value of the horizontal divergence; the relative rate of change of the patch area can be accounted for by the horizontal divergence.     

Dispersion relation of internal waves in the western equatorial Pacific Ocean

Based mainly on TOGA COARE data, that is, the CI''D data from R/V Xiangyanghong No.5 (Pu et al.,1993),the temperature and current data from the Woods Hole mooring and other deep current data, the layered numerical profiles of buoyancy frequency and mean current components are figured out.A numerical method calculating internal wave dispersion relation without background shear current, used by Fliegel and Hunkins (1975),is improved to be fit for the internal wave equation with mean currents and their second derivatives.The dispersion relations and wave functions of the long crested internal wave progressing in any direction can be calculated inveniently by using the improved method.A comparison between the calculated dispersion relation in the paper and the dispersion relation in GM spectral model of ocean internal waves (Garret and Munk, 1972) is performed.It shows that the mean currents are important to the dispersion relation of internal waves in the western equatorial Pacific Ocean and that the currents make the wave progressing co-directional with (against) the currents stretched (shrink).The influence of the mean currents on dispersion relation is much stronger than that of their second derivatives, but that on wave function is less than that of their second derivatives.The influences on wave functions result in the change of vertical wavenumber, that is, making the wave function stretch or shrink.There exists obvious turning depth but no significant critical layer absorption is found.     

The dispersion relations for surface plasmon in a nonlinear—metal—nonlinear dielectric structure

In the asymmetric and symmetric nonlinear--metal--nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.     

Analytical Study of Longitudinal Mass Flux Due to the Shear Effect in a Tidal Basin

The fundamental nature of the mass flux due to the shear effect is examined analytically in a basin with steady and oscillatory currents to promote a better understanding of the mass transport process in coastal waters. The currents are given from solutions of the simplified motion equation so as to be consistent with the diffusion equation. The matter concentration used is given by an analytical solution of the diffusion equation with the settling flux term contained. Mass flux, yielding the depth-averaged dispersion coefficient, is rather varied vertically in both steady and oscillatory currents. In the oscillatory current with a Stokes layer in particular, the vertical profile of flux is more complicated and even negative flux is induced near the basin floor. This negative flux does not necessarily yield a negative value of the vertically averaged dispersion coefficient. The exact dispersion coefficient given by the flux analysis is realized only in the steady state of the matter concentration distribution, though we can scarcely observe the steady state in the actual sea. The vertically uniform longitudinal dispersion coefficient at the stationary stage is shown to be caused from the vertical complexity of mass flux by the action of the vertical diffusing and the settling flux. This revised version was published online in July 2006 with corrections to the Cover Date.     

Studies of ballast water dispersal in Port Valdez, Alaska

All oily ballast water from tankers arriving at Valdez, Alaska, is treated prior to discharge into Port Valdez, a northeasterly fjord-like extension of Prince William Sound in south-central Alaska. In addition to specifying the quality and allowable quantity, the permits for this discharge also required field studies of the outfall diffuser system to determine its actual dispersion characteristics under the extremes of oceanographic conditions experienced in Port Valdez. Two dye studies of the diffuser effluent were performed by the University of Alaska Institute of Marine Science to meet this permit requirement. For this diffuser study, Rhodamine WT dye was the effluent tracer and a SeaMarTec Fluorometer/Nephelometer was the detection instrument. The latter is an optical device which, when coupled with conventional STD instrumentation, enabled the rapid acquisition of continuous vertical profiles of salinity, temperature, and dye concentration at many locations surrounding the diffuser where depths ranged from 20 to 150 m. The procedures described herein provided sufficient data to describe the three-dimensional development of the dye plume and to evaluate the diffuser's capability to satisfy the effluent dilution requirements stipulated by the ballast water discharge permits.     

Non-linear restoring forces of an offshore platform

The method of calculation of non-linear restoring forces presented in this paper is simple, concise and feasible to apply easily in the calculation of restoring forces of platforms in order to simulate motion responses of offshore platforms in the time-domain. In this method, hydrostatic restoring forces and moments are related to the translational and/or rotational displacements. Calculations of non-linear yaw, roll and pitch restoring moments are based on the catenary type of moorings. Although the method presented here is a simple one, it is capable of the calculation of restoring forces for use in the time-domain motion simulations of offshore platforms, with an acceptable degree of accuracy when the numerical simulation results were compared with the experimental measurements.     

An analysis of horizontal dispersion due to the drift current with an Ekman layer

An analytical method for describing horizontal matter dispersion in shear currents is presented using a tensor expression from the point of view that matter dispersion due to the shear effect should be one of the principal mixing dilution processes. Although the behavior of horizontal dispersion is considerably more complicated than common longitudinal dispersion, the present study elucidates the vertical structure of dispersion and the dispersing process from the initial to the stationary stage, besides the usual depth-averaged dispersion coefficient at the stationary stage. As one of the typical applications of horizontal dispersion, dispersion due to the pure drift current with an Ekman layer is examined theoretically using the present method. This examination reveals that the displacement of the centroid and the major axis of dispersion are twisted in the vertical direction more than the direction of the current vector forming the Ekman spiral; that the variance increases in proportion to the third power of the elapsed time; and that the dispersion coefficient at the stationary stage remains constant, independent of the depth normalized by an Ekman layer thickness. Such dependence of the dispersion coefficient in the steady current is shown to be different from that in the oscillatory current, which is inversely proportional to the depth normalized by a Stokes layer thickness. This is considered to be induced by the difference of the vertical profiles of the first order moment in both currents, that is, the shear region of the first order moment is restricted around the floor by the alternation of the current shear in the oscillatory current while it is diffused in the whole depth in the steady current.     

An experimental study of the spatial structures of the instabilities of longshore currents on plane beaches

A laboratory experiment on alongshore currents is conducted for two plane beaches with slopes 1:40 and 1:100 to investigate the instability of alongshore currents.The dye release experiment is also performed synchronously in surf zone.Complicated and strongly unstable motions of alongshore currents are observed in the experiment.To examine the spatial and temporal variations of the shear instabilities of longshore clearly,dye batches are released in surf zone.The deformation of the dye patch is observed efficiently and effectively with charge coupled device(CCD) system.Some essential characteristics of the shear instability are validated from the results of image analyses of the temporal variation of the dye patch.The influences of alongshore currents,Stokes drift,large-scale vorticity and the shear instabilities on the transport of dye are analyzed using the collected images.The spatial structure of the instabilities of longshore currents is studied by analyzing collected images of the dye patch.And the phase velocity of the meandering movements is obtained through measuring the movement distances of the oscillations of dye patch in alongshore direction with time.The results suggest that the propagation speed of the shear instability is approximately 50%-75% of maximum of mean alongshore currents for irregular and regular waves.The calculated propagation speed using a linear instability analysis theory is compared with the experimental results.The comparison shows agreements between them.     

三维海洋溢油预测模型的建立(英文)

提出一个海洋溢油三维物理归宿和输运的动力学综合模型。该模型包含了一系列的数学公式来描述对流、湍扩散、表面扩展、铅直扩散、乳化和蒸发过程。每一公式的建立是独立的并且与相关过程、环境和其它参数相联系。该模型需要输入流场作为输运的媒介 ,这可从感兴趣区域的三维潮和风驱动的流体动力学模型获得。模型用来预测和后报溢油在海洋环境中的归宿和输移 ,可为溢油应急反应和环境影响评价服务。     

南黄海辐射沙洲区悬沙潮扩散规律数值研究

在对南黄海辐射沙洲区的潮汐、潮流特征作进一步探讨的基础上,数值模拟了该区的悬沙潮扩散。根据计算结果,分析了计算海域悬沙含量在一个半日潮过程中随潮流场的瞬时变化规律,研究了不同地点悬沙含量与潮位、潮流的关系,总结了涨、落潮平均含沙量的平面分布规律。结果表明,该区的潮流场控制着悬沙的扩散、运移和分布,进而控制着海底地形的发育,尤其是辐射沙洲北大南小不对称格架的塑造与辐射沙洲根部的加积淤高。