Shear Flow Dispersion Under Wave and Current

The longitudinal dispersion of solute in open channel flow with short period progressive waves is investigated. The waves induce second order drift velocity in the direction of propagation and enhance the mixing process in concurrent direction. The 1-D wave-period-averaged dispersion equation is derived and an expression for the wave-current induced longitudinal dispersion coefficient (WCLDC) is proposed based on Fischer's expression (1979) for dispersion in unidirectional flow. The result shows that the effect of waves on dispersion is mainly due to the cross-sectional variation of the drift velocity. Furthermore, to obtain a more practical expression of the WCLDC, the longitudinal dispersion coefficient due to Seo and Cheong (1998) is modified to incluee the effect of drift velocity. Laboratory experiments have been conducted to verify the proposed expression. The experimental results, together with dimensional analysis, show that the wave effect can be reflected by the ratio between the wave amplitude and wave period. A comparative study between the cases with and without waves demonstrates that the magnitude of the longitudinal dispersion coefficient is increased under the presence of waves.     

Applied hydrodynamic wave-resistance computation by Fourier transform

An applied Fourier transform computation for the hydrodynamic wave-resistance coefficient is shown, oriented to potential flows with a free surface and infinity depth. The presence of a ship-like body is simulated by its equivalent pressure disturbance imposed on the un-perturbed free surface, where a linearized free surface condition is used. The wave-resistance coefficient is obtained from the wave-height downstream. Two examples with closed solutions are considered: a submerged dipole, as a test-case, and a parabolic pressure distribution of compact support. In the three dimensional case, a dispersion relation is included which is a key resource for an inexpensive computation of the wave pattern far downstream like fifteen ship-lengths.     

Longitudinal dispersion due to the boundary layer in an oscillatory current: Theoretical analysis in the case of an instantaneous line source

The longitudinal dispersion effect due to the boundary layer formed by a tidal oscillatory current is examined theoretically. This analysis reveals the process whereby the dispersion coefficient becomes steady after the release of the diffusing substance. Though the dispersion due to an oscillatory current has so far been investigated mostly in the case of a linear velocity profile, the following result was found by taking account of the boundary layer in the oscillatory current. The depth-averaged dispersion coefficient for the case of a current having a boundary layer can be a few times larger than in the case of a linear velocity profile when the characteristic mixing time is long; the phase lead in the boundary layer induces nearly 20 percent of the longitudinal dispersion effect.     

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.     

Longitudinal dispersion in wave-current-vegetation flow

The flow, turbulence, and longitudinal dispersion in wave-current flow through submerged vegetation are experimentally examined. Laboratory experiments are carried out by superimposing progressive waves on a steady flow through simulated submerged vegetation. The resultant wave-current-vegetation interaction shows strong interface shear with increase in the velocity due to the wave-induced drift. The increase in turbulence in the region of vegetation is found to be about twice higher than in the no-wave case due to the additional mixing by wave motions. Solute experiments are conducted to quantify the wave-current-vegetation longitudinal dispersion coefficient (WCVLDC) by the routing method and by defining length and velocity scales for the wave-current-vegetation flow. An empirical expression for the WCVLDC is proposed. Although the increase in vertical diffusivity is observed as compared with bare-bed channels, the shear effect is stronger, which increases the value of the WCVLDC. The study can be a guideline to understand the combined hydrodynamics of waves, current, and vegetation and quantify the longitudinal dispersion therein. Published in Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 50–67, January–February, 2009.     

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.     

A numerical simulation of the distribution of water temperature and salinity in the Seto Inland Sea

Constant flows, as well as oscillatory tidal flow, play an important role in the long-term dispersion of water in the Seto Inland Sea. Two kinds of numerical model (1-line and 2-line models) of the Seto Inland Sea have been developed to determine the role of density-induced currents, one type of the constant flow, in water dispersion in the Inland Sea. The seasonal variations of temperature, salinity and density fields are simulated and the density-induced current field is predicted at the same time. It is found that the most appropriate value of the longitudinal eddy diffusion coefficient,K _x, is 5×10⁶–7×10⁶ cm²sec^–1. The value of the overall mean dispersion coefficient is of the order of 10⁷cm²sec^–1 (Hayami and Unoki, 1970). Consequently, it is suggested that 50–70% of the total dispersion in the Seto Inland Sea can be attributed to currents other than density-induced currents,i.e., tidal currents, tide-induced currents and wind-driven currents.In winter, both density and velocity fields, calculated using the 1-line model, satisfy the conditions for the existence of a coastal front in Kii Channel and in the eastern Iyo-nada.     

A dispersion equation and dispersion coefficient for material transport in Inland Seas

To analyse material transport in inland seas, a horizontal two-dimensional dispersion equation is derived, and the dispersion coefficient due to the combined effect of vertical turbulent mixing and vertical shear of both a steady current and a tidal current is studied. In the present study, the assumption that velocity is uniform in horizontal planes is not necessary, and velocity has a free vertical profile; thus the dispersion coefficient formulated is general, and is represented by a tensor of the second order. The properties of the dispersion coefficient in the horizontal two-dimensional dispersion model are also investigated, and it is shown that the time-averaged dispersion coefficient due to the tidal current over a tidal period is approximately half that due to the steady current, if the velocity amplitude and the vertical profile of the tidal current are the same as those of the steady current (a similar result was presented byBowden (1965) for horizontal one-dimensional models). Finally, the dispersion coefficient in Hiuchi-Nada (Hiuchi Sound) in the central part of the Seto Inland Sea is evaluated by using the model. The values of the dispersion coefficient in that region range from 10³ cm² s^–1 to 10⁵ cm² s^–1 when vertical turbulent diffusivity is taken to be 50 cm² s^–1.     

PIV measurements of hull wake behind a container ship model with varying loading condition

Flow characteristics of the hull wake behind a container ship model were investigated under different loading conditions (design and ballast loadings) by employing the particle image velocimetry (PIV) technique. Measurements were made at four transverse locations and two longitudinal planes for three Reynolds numbers (Re) (=U₀Lpp/ν, where U₀ is the freestream velocity, Lpp is the length between two perpendiculars of the ship model and ν is the kinematic viscosity) of 5.08×10⁵, 7.60×10⁵, and 1.01×10⁶. It was observed that symmetric, large-scale, longitudinal counter-rotating vortices (with respect to centerline) of nearly the same strength were formed in the near wake. For the ballast-loading condition, the vortices appear at propeller plane below the propeller-boss. The vortex center exhibits a significant upward shift near the propeller-boss as the Reynolds number increase, and as the flow moves downstream. Under the design-loading condition, the vortices first appear at a further downstream location than that for the ballast-loading condition above the propeller-boss. This difference in the flow structure can significantly change the inflow conditions to the propeller blades, such as the streamwise mean velocity profiles and turbulence intensity distributions at the propeller plane. In particular, under the ballast-loading condition, asymmetric inflow may weaken the propulsion and cavitation performance of the marine propeller.     

Numerical investigation on the gas entrainment of ventilated partial cavity based on a multiscale modelling approach

Ventilated cavitation which is acknowledged as an efficient drag reduction technology for underwater vehicle is characterised by the very disparate length and time scales, posing great difficulty in the application of this technology. A multiscale numerical approach which integrates a sub-grid air entrainment model into the two-fluid framework is proposed in this paper to resolve the complex flow field created by ventilated cavity. Simulations have been carried out for the partially ventilated cavity underneath flat plate, with special efforts putting on understanding the gas entrainment at the cavity tail and the bubble dispersion process downstream. The flow parameters including the void fraction, the bubble velocity and the bubble size distributions in and downstream of the ventilated cavity are fully investigated. Comparisons between the numerical results with the experimental data are in satisfactory agreement, demonstrating the potential of the proposed methodology. The ventilation rate effect on the cavity shape and bubbly flow parameters are further investigated, obtaining the law of bubble dispersion and the bubble size evolution. This research not only provide a useful method for the investigation on the multiscale multiphase flow, but also give insight on understanding the combined drag reduction mechanism resulted from large-scale cavity and microbubbles.     

含油多孔介质二维弥散特性初步研究

为了研究含油多孔介质的二维水动力弥散特性,控制砂土中柴油和机油含油率为0、1%、2%,作为供试的含油多孔介质,采用自己设计的二维水动力弥散试验装置测定示踪剂(氯化钙)的穿透曲线,并定量确定了含油砂土的有效孔隙度、纵向弥散度、横向弥散度以及砂土中孔隙水的流速。试验结果表明,有效孔隙度随石油含量的增加而减小,而且含柴油砂土的有效孔隙度减小比含机油砂土更加显著;在纵向上,示踪剂浓度峰值的到达时间和峰值浓度的大小主要取决于孔隙水流速的大小,孔隙水流速越大,示踪剂达到浓度峰值的时间越短,且峰值浓度越大;含机油砂土的纵向弥散度小于清洁砂土,而含柴油砂土的纵向弥散度大于清洁砂土;不同含油率砂土的纵向弥散度变化范围为0.133～0.370cm,横向弥散度变化范围为9.83×10-3～4.64×10-2 cm,纵向弥散度均大于其横向弥散度。     

随机波浪下泰勒离散系数的时域解

利用Wolk提出的粒子追踪方程,通过等分频率法划分不规则波谱,利用MATLAB做粒子运动模拟计算,得到无因次化泰勒离散系数K/D随时间t变化的曲线;通过与Huang等得到的P-M谱的泰勒离散系数K/D计算结果比较证明了本计算方法的可靠性。采用该方法研究了不规则波条件下,波序列(同一谱型不同波面序列)和谱型(谱峰周期、有效波高、谱峰升高因子)对波浪离散系数的影响;计算结果表明:同一谱型不同波序列对泰勒纵向离散系数稳定值和稳定时间无影响;不规则波谱峰周期越大,纵向离散系数K/D越小,稳定时间越短;有效波高越大,纵向离散系数K/D越大,稳定时间越长;谱峰升高因子越大,泰勒离散系数K/D越大,稳定时间越长;与规则波相比,不规则波的泰勒离散系数K/D的值略小10%~30%。     

Long-term dispersion in unsteady skewed free surface flow

An analysis of two-dimensional horizontal plane shear dispersion in steady, periodic, almost-periodic and randomly forced skewed free surface flow is presented. A two-time scale perturbation analysis of the advection-diffusion equation is used to derive the two-dimensional advection-dispersion equation and the horizontal dispersion coefficient tensor. For combinations of steady, periodic and almost-periodic flow, the time dependent dispersion coefficient tensor contains steady terms and periodic terms at frequencies associated with the forcing frequencies and their sums and differences. For combinations of steady, periodic, almost-periodic and stationary random forcings, the expected value dispersion coefficient tensor contains terms associated with the steady forcings and terms associated with the unsteady forcings represented by the spectral density functions of the unsteady forcings. Estimates of the magnitude of the expected value dispersion coefficient tensor are presented for representative estuarine and continental shelf conditions.     

Oblique and Multi-Directional Random Wave Loads on Vertical Breakwaters

1 .IntroductionTraditionally ,thedesignofcoastalstructuresisbasedontheformulaedevelopedforhead onuni directionalwaves .However,wavesusuallyattackabreakwaterobliquely ,formingshort crestedwavesinfrontofthebreakwater.Ontheotherhand ,asthehumanactivityareaisspreading ,thewaterdepthattheconstructionsiteforbreakwatershasatendencytobecomelarge ,andsomebreakwatershavebeenconstructedinwaterareasdeeperthan 6 0minJapan (Tanimotoetal.,1 988) .Theseawaveismulti directionalandrandom ,especiallyindeepwater…     

Chiral composites as underwater acoustic attenuators

A plane-wave propagation in an elastic matrix containing the structural chiral microstructures is employed to model the dynamic response of a particles-mixture composite. Two nondispersive longitudinal wavenumbers and four dispersive circularly polarized transverse wavenumbers result from the dispersion equation of the so-called effective chiral (isotropic, noncentrosymmetric) composite. Our previous research indicated both that two transition frequencies divide the frequency spectrum of the transverse wavenumbers into three varying groups and that the four transverse modes can be distinguished only in a specified frequency range. This study illustrates the reflected and transmitted characteristics at a fluid-chiral interface at certain frequencies. The reflected and transmitted fields at the fluid-isotropic interface are solved to depict the effects of the chirality. The chiral material should instigate a reducible reflected plane wave and may be used as an anechoic coating to “absorb” sound underwater, due to the mode conversion of the chirality in the chiral medium     

Longitudinal dispersion of matter due to the stokes layer: Its time-dependence in the case of an instantaneous point-source

Longitudinal dispersion from an instantaneous point-source in an oscillatory current with a Stoke layer is investigated theoretically using a simplified two-dimensional model. This study introduces a new definition of the variance expressing the degree of mixing at the initial stage in the point-source case, and reveals that the Stokes layer can induce a large dispersion coefficient during the initial stage in the case where the released point is at the solid boundary (bottom) producing the Stokes layer. Furthermore, this study shows that the dispersion coefficient is independent of the depth during the initial first period but is inversely proportional to the depth at the stationary stage.     

Flow-induced transverse motions of a flexible cable aligned with the flow direction

Experimental studies of the transverse motions induced in a long flexible cable by axial flows have been conducted in a large blowdown water channel. A cable with a diameter of 1.59 cm and a length of 9 m was employed. Experiments were conducted over a fluid velocity range of 4.6-9.1 m/s. Both free and fixed downstream terminations of the cable were utilized, the former simulating a towed cable and the latter a mooring cable. Measurements of the drag coefficient of the cable with the free end were also made. These results were compared with those obtained previously for a flexible cylinder with a smooth exterior surface, and the following conclusions were drawn. 1) The amplitudes of the flow-induced transverse motions in a flexible cable or cylinder with a free downstream end in general decrease with increasing distance from this end, but they exhibit weak dependence on flow velocity and surface roughness near this end. 2) The amplitudes of the flow-induced motions are in general smaller when the cable is fixed at both ends than when the downstream end is free. 3) The drag coefficient of the flexible cylinder or cable increases with increasing surface roughness.     

Seawater Intrusion in Semi-Closed Convergent Estuaries (Case Study of Moroccan Atlantic Estuaries): Application of Salinity Analytical Models

Salinity is an important parameter influencing the water quality of estuaries, and can constitute a serious problem to society due to the need for freshwater for industry and agriculture. Therefore, the determination of salt intrusion length in estuaries is a challenge for managers as well as scientists in this field. The managers tend to use simple and reliable tools for salinity variation. Although 2-D and 3-D numerical models are common tools for the prediction of salinity intrusion now, analytical models of salinity variation are much more efficient, and also require minimal sets of river data. In this paper, two analytical solutions, Brockway and Savenije used worldwide to assess longitudinal salinity variation in alluvial estuaries, are applied to the Moroccan Atlantic semi-closed estuaries, i.e., Sebou and Loukkos. The solutions are derived from salt convection-dispersion equations, with different assumptions for the dispersion coefficient. The estuaries' bathymetry is described by an exponential function. The performance of these two solutions was evaluated by comparing their results with field-measured salinity data. The Brockway model's salinity predictions performs well to observations especially in downstream reaches of the two estuaries (Sebou: R² = 0.95, root mean square error [RMSE] = 1.50‰, normalized root mean square error [NRMSE] = 3.45‰; Loukkos: R² = 0.95, RMSE = 1.13‰, NRMSE = 3.01‰), while the Savenije model outperformed the Brockway's model and is better to predict salt intrusion length and salinity variation along the two estuaries (Sebou: R² = 0.97, RMSE = 1.15‰, NRMSE = 2.85‰; Loukkos: R² = 0.98, RMSE = 0.95‰, NRMSE = 1.94‰). This revealed that both analytical solutions apply well to the estimation of salinity variation and the prediction of salt intrusion in these two estuaries.     

Longitudinal and depth variation of bacterioplankton productivity and related factors in a temperate estuary

Bacterioplankton productivity (BP) spatial variation was investigated in relation to potential resources, including primary productivity and dissolved organic matter, in the micro-tidal Neuse River–Pamlico Sound estuarine system, North Carolina, USA. Estuarine BP was predicted to correlate with the trophic gradient, decreasing along the salinity gradient in parallel with the decrease in organic matter and primary productivity. This prediction was tested over four years at spatial scales ranging from kilometers to meters along the riverine axis and with depth. The general pattern of BP across the salinity gradient was unimodal and matched the phytoplankton patterns in peak location and variability. Peak locations varied with discharge, especially in 2003 when above average discharge moved peaks downstream. Spatial coherence of BP with other variables was much less at short time scales. The effect of temperature, nutrients, and phytoplankton on BP varied by location, especially fresh versus brackish stations, although only temperature explained more than 20% of the BP variation. Depth variation of BP was as great as longitudinal variation and bottom samples were often higher than surface. BP was strongly correlated with particulate organic carbon at the pycnocline and bottom, highlighting the importance of particulate matter as a resource. Station-averaged BP and phytoplankton data corresponded well with two published meta-analyses, although the offset of the freshwater station suggested longitudinal differences in community composition or resource availability.     

Analytical study of the effect of the geometrical parameters during the interaction of regular wave-horizontal plate-current

The present work is an analytical study of the influence of geometrical parameters, such as length, thickness and immersion of the plate, on the reflection coefficient of a regular wave for an immersed horizontal plate in the presence of a uniform current with the same direction as the propagation of the incident regular wave. This study was performed using the linearized potential theory with the evanescent modes while searching for complex roots to the dispersion equation that are neither pure real nor pure imaginary. The results show that the effects of the immersion and the relative length on the reflection coefficient of the plate are accentuated by the presence of the current, whereas the plate thickness practically does not have an effect if it is relatively small.