Energetics of lateral eddy diffusion/advection：Part Ⅲ. Energetics of horizontal and isopycnal diffusion/advection

Gravitational Potential Energy （GPE） change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps： stirring and sub scale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stir ring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordi nates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eule rian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.     

Scattering of water wave by a submerged horizontal plate and a submerged permeable breakwater

Based on a two-dimensional linear water wave theory, this study develops the boundary element method (BEM) to examine normally incident wave scattering by a fixed, submerged, horizontal, impermeable plate and a submerged permeable breakwater in water of finite depth. Numerical results for the transmission coefficients are also presented. In addition, the numerical technique's accuracy is demonstrated by comparing the numerical results with previously published numerical and experimental ones. According to that comparison, the transmission coefficient relies not only on the submergence of the horizontal impermeable plate and the height of the permeable breakwater, but also on the distance between horizontal plate and permeable breakwater. Results presented herein confirm that the transmission coefficient is minimum for the distance approximately equal to four times the water depth.     

Scattering of water wave by a submerged horizontal plate and a submerged permeable breakwater

Based on a two-dimensional linear water wave theory, this study develops the boundary element method (BEM) to examine normally incident wave scattering by a fixed, submerged, horizontal, impermeable plate and a submerged permeable breakwater in water of finite depth. Numerical results for the transmission coefficients are also presented. In addition, the numerical technique's accuracy is demonstrated by comparing the numerical results with previously published numerical and experimental ones. According to that comparison, the transmission coefficient relies not only on the submergence of the horizontal impermeable plate and the height of the permeable breakwater, but also on the distance between horizontal plate and permeable breakwater. Results presented herein confirm that the transmission coefficient is minimum for the distance approximately equal to four times the water depth.     

Evaluation of perfluoromethyldecalin as a deliberate tracer for the study of water mixing processes

A deliberate tracer experiment has been carried out in an enclosed lagoon in a coastal area. The tracer used was a perfluorocarbon, perfluoro- -methyldecalin (PMD), analysed using liquid-liquid extraction and electron capture gas chromatography. The results show good recovery of the tracer, indicating that adsorption and volatilization did not occur to an appreciable extent over the short time period of the experiment. A mathematical model, PHOENICS, developed for simulation of flow systems, was used to simulate the experiment.     

Mass transport of a mesoscale eddy in the South China Sea identified by a simulated passive tracer

To quantitatively investigate the water mass transport of mesoscale eddies,the mass transport induced by a simulated anticyclonic eddy in the South China Sea wa...     

On the recovery of surface wave by pressure transfer function

Except the commonly selected pressure transfer function derived from the linear wave theory, a previous study on the pressure transfer function for recovering surface wave from underwater pressure transducer suggested that the pressure transfer function is a function of frequency parameter only. With careful analysis, this study showed that the pressure transfer function should include a transducer submergence parameter as that given by the linear theory. It was found that the previously suggested empirical formula should be restricted to measurements with the pressure transducer close to the surface; otherwise overestimation of wave height would result. Field measurements were carried out with an acoustic wave gauge and a synchronized pressure transducer located at various depths with submergence parameter close to 1 (near the sea floor). It was shown that the previous one-parameter empirical formula might overestimate the significant wave height by more than 30%. This study found that with deep-water wave bursts excluded, the transfer function based on the linear wave theory provided a fairly good estimation on the significant wave heights, with an average deviation of 3.6%.     

随机波对水平板冲击作用实验研究

波浪对透空式海上建筑物的冲击作用已经成为此类建筑物安全的重要影响因素。进行了单向随机波对水平板冲击作用水槽实验研究。总共进行了4个方向(0°、15°3、0°、45°),相对入射波波高H1/3/d=0.093 75~0.25,周期Tp=1.0~2.0 s,水平板距离静水面的高度s与入射波高H1/3的比值s/H1/3=0.0~0.5的实验研究。采用小波分析方法去除了由于测压传感器振荡引起的测量数据的振荡和漂移,在此基础上统计分析给出了不同方向水平板下的压力峰值分布情况。采用无因次方法,讨论了无因次冲击力与相对入射波高H1/3/d、相对板宽B/L、相对净空s/H1/3及波向角β的关系。     

渤海示踪物输移扩散季节性变化的研究

利用一个三维斜压模式ROMS,对夏季和冬季的渤海流场、示踪物输运及扩散进行了简要模拟。模拟结果表明渤海环流在夏季和冬季呈现多涡环流模态,垂向平均流场更为突出,渤海各大港口排放的保守污染物浓度在80天左右后显著降低,不过影响范围呈现季节性分布,污染物的输运扩散受与流场紧密相关,渤海湾是影响最为严重的海域。     

A new approximate analytic solution for water wave scattering by a submerged horizontal porous disk

This study gives a new approximate analytic solution for water wave scattering by a submerged horizontal porous disk in the context of the linear potential theory. The solution is based on the domain decomposition method. The velocity potentials are determined by two different approaches. One approach is to adopt decompositions for velocity potentials, and the other is to expand the vertical derivative of the velocity potential on the porous disk along the radial direction. Hence the velocity potentials are determined by the matched eigenfunction expansions. Differing from previous solutions with respect to the porous disk, the present solution needs no complex dispersion relations. Thus the new solution is easier for numerical implementation. According to numerical examples, the convergence of the present solution is satisfactory. In addition, the present predictions of the wave surface elevation and the vertical wave force on the disk agree very well with previous results by different approaches. The present solution can also be extended to other structures involving disks, such as a fish cage, a porous disk with finite thickness, and a submerged elastic disk.     

Second-order vertical and horizontal wave forces on a circular dock

A second-order potential solution is presented for the diffraction of a nonlinear progressive wave in finite-depth water, incident on a fixed circular dock. The usual perturbation analysis is used to produce first- and second-order subproblems. The mathematical method is based on the assumption that inner and outer solutions exist and these are matched by the requirements of continuity for mass flux and pressure between adjacent regions. It is shown that the solutions for the second-order problem can be derived in the same manner as in the first-order theory.     

Second-order wave loading on a horizontal rectangular cylinder of substantial draught

Approximate first- and second-order analytical solutions of wave diffraction of a semi-submerged horizontal cylinder of rectangular cross-section are presented. The solutions are based on the assumption that the pressure in the fluid domain underneath the cylinder is linearly dependent on the horizontal space coordinate. Basically, this approach is valid when the clearance between the bottom of the cylinder and the sea bottom is small in comparison with the wave length and is recommended for a cylinder of substantial draught where due to the small clearance other methods are difficult to apply. Boundary conditions are satisfied by a choice of a proper form of the potential functions and by making use of the properties of matching conditions. Theoretical results reveal that the magnitude of the vertical second-order time-dependent loads could be significant and even exceed the corresponding first-order quantities. This phenomenon, which occurs even at moderate steepnesses, as well as the assumption of a linear pressure distribution, are confirmed by experiments performed in a wave tank.     

Mesoscale eddy effects on temporal variability of surface chlorophyll a in the Kuroshio Extension

We investigated the relationship between chlorophyll a (Chl-a) concentrations estimated from satellite observations and the activity of eddies in the Kuroshio Extension region. High (low) area-averaged Chl-a concentrations were frequently observed in the core of cyclonic (anticyclonic) eddies. Such relationships between Chl-a concentrations and eddy cores were not frequently observed in the southern part of the recirculation gyre, and advection of background meridional gradient of Chl-a by eddy-edge currents accounted for Chl-a spatial variability. Decadal-scale changes of Chl-a concentrations around the Kuroshio Extension were strongly affected by eddy activity and transport but not by large-scale near-surface isopycnal heaving. We also found that decadal changes of nutrient concentrations near the main stream could affect Chl-a concentrations in the southern part of the recirculation gyre via southward transport of eddies and mean flow.     

Forces and moment on a horizontal plate due to wave scattering

Wave reflection and transmission from a fixed horizontal plate have been widely studied but theoretical solutions are only available for certain limiting conditions. A general solution for this wave scattering problem is presented using the finite-element method, covering the whole range of relative depth ratio from shallow to deep water limits and submergence depth ratio from the water surface to the bed. Existing long-wave solutions for the surface plate and the submerged plate have been extended to obtain the hydrodynamic forces and overturning moment exerted on the plate. Results from the finite-element program compare well with these solutions. Variations of the reflection coefficient, wave forces and moment, with the plate width to wave length ratio, relative depth ratio and submergence depth ratio are discussed.     

Three-dimensional wave patterns in long air cavities on a horizontal plane

Significant drag reduction of large displacement vessels can be achieved by applying multi-wave air cavities arranged on the hull bottom. Waves generated on the air–water interface of air cavities impose requirements on the dimensions of a hull recess that accommodates the air cavity. An approximate model for calculating wave patterns in the critical upstream part of long air cavities in a simplified, horizontal-plane geometry is presented in this paper. The influence of the recess planform boundaries and other factors on the wave patterns is studied parametrically. Some hydrodynamic aspects of multi-wave air cavities are discussed.     

Statistics of wave forces on large horizontal cylinders

To the first order in a Stokes expansion, the pressure force exerted by a sea state on a large horizontal cylinder represents a stationary random Gaussian process. A relationship is obtained between the spectrum of this process and the wave spectrum. As a consequence, the basic statistical properties of the height and period of the individual waves of the force-process are also obtained. It is proven that these statistical properties agree very well with the data from a small scale field experiment.     

应用镭-226解读南极普里兹湾表层水的来源与运移

中国第22次南极科学考察航次(2005年12月至2006年1月)期间,利用Mn-纤维富集大体积表层海水中的Ra同位素,并通过222Rn直接射气法测量226Ra的比活度,结果表明,普里兹湾表层水的226Ra比活度变化为0.92~2.09 Bq/m3,平均值为1.61 Bq/m3,在深海区域表现出226Ra含量高的特征。从空间分布看,表层水226Ra比活度呈现出由湾内向湾外增加的反常态势,反映出不同Ra含量水团的混合影响2。26Ra比活度与盐度的关系证实研究海域表层水的Ra含量主要受三种端元水体的混合所控制:其一为具有镭含量高、盐度高特征的南极夏季表层水;其二为低镭、低盐特征的冰融水;其三为高盐、中等镭含量的普里兹湾中深层水,该水体的226Ra纯粹由海底沉积物间隙水向上扩散所维持。结合S-226Ra示踪体系及上述三端元混合模型,计算出各组成水体的比例并描绘出它们的空间分布。南极夏季表层水的份额由湾外向湾内逐渐降低,并且在68°E断面向南影响范围较大;冰融水的比例由湾内向湾外降低,并且在湾内东部的高温水体中具有最大贡献;普里兹湾中深层水中受沉积物镭来源影响比较显著的区域出现在湾内西北部,其影响向湾外逐渐降低。冰融水与普里兹湾中深层水份额分别于普里兹湾湾顶东、西部出现高值的分布特征证实埃默里冰架前沿海流东进、西出的运移规律。     

About a limiting vortical wave on a fluid surface

A non-linear stabilized vortical wave on the surface of an infinitely-deep fluid is considered. The angle between the tangents at the apex of the limiting symmetric wave, similar to the Stokes limiting, is shown to equal 120°.Translated by V. Puchkin.     

Note on the propagation of a shallow water wave in water of variable depth

In this technical note, the phenomena of non-linear water-wave propagation above a seabed with variable depth is re-examined. The conventional Korteweg-de Vries (KdV) equation is re-derived for the general case of variable water depth. In the new form of KdV equation, the seabed bottom function is included. Two different bottom profiles are considered in this study; case 1: $b^{\prime }\left(x^{\prime }\right)=c\epsilon \sin \lambda x^{\prime }$ and case 2: $b^{\prime }\left(x^{\prime }\right)=c\epsilon {\mathrm{e}}^{-\lambda {\left(x^{\prime }-x_0^{\prime }\right)}^2}$. The effects of three bottom profile parameters, c, λ and ε on the wave profile are examined. Numerical results indicate that both ε and λ affect the wave profile significantly in case 1, while ε significantly affects the wave profile in case 2.