Experimental study of the instabilities of alongshore currents on plane beaches

A laboratory experiment on alongshore currents was conducted for two plane beaches, with gradients 1:40 and 1:100, to investigate the instability of alongshore currents. Complicated and strongly unstable alongshore current motions were observed. In order to clearly examine the spatial and temporal variations of the shear instability of the currents, digital images from a charge-coupled device (CCD) recorded the deformations of dye batches released in the surf zone. Some essential characteristics of the shear instability were obtained from analyses of images showing the temporal variation of the dye patches.A high-resolution spectral analysis technique (the maximum entropy method, or MEM) was used to analyze the dominant frequency of the observed oscillation, along with the trigonometric regression method for determining the variations of the oscillation strength in the cross-shore direction. The propagation speed of the dye patch was obtained by tracking the movement over time of fixed locations in the dye patch, such as its peak, in the longshore direction. This data was then fitted linearly.Alongshore and cross-shore velocity time series acquired from sensors showed clearly that large-amplitude, long-period (about 50 s or 100 s) oscillations were present for all sensors deployed in the cross-shore direction under regular and irregular wave conditions. The analysis found that the maximum shear wave amplitude was approximately one-sixth of the maximum for the mean alongshore current, and occurred approximately at the position of the maximum of the mean alongshore current for irregular waves. The spatial structure of the shear waves was studied by analyzing collected images of the dye patches. The phase velocity of the meandering movements was obtained by measuring the magnitude of the oscillations of the dye patches in the alongshore direction with respect to time. The results suggest that the propagation speed of the shear instability was approximately one-half to three-quarters of the maximum mean longshore current for both regular and irregular waves.Linear instability analysis theory was applied to the characteristics of alongshore current instability, which suggested that there are two instability modes related to the observed oscillations: the frontshear mode observed for the 1:100 slope, and the backshear mode observed for the 1:40 slope. Theoretical analyses agreed with the experimental results in both cases. The velocity profile of the mean longshore current was found to affect the instability mode significantly, leading to further investigations on the influence of the velocity profiles and to provide support for the above conclusions.     

沿岸流非线性不稳定特征数值研究

当不稳定剪切波的波幅达到有限幅值之后,需要用非线性不稳定模型来分析沿岸流不稳定运动特征。本文通过建立并验证沿岸流非线性不稳定数学模型,在讨论该模型参数对沿岸流不稳定影响的基础上,率定实验中的模型参数并利用该数学模型模拟了实验中沿岸流不稳定的发展过程及其特征,主要结论有:（1）底摩擦系数越小,侧混系数越小,不稳定发生的时间越早,不稳定的波动幅值越大;（2）沿岸流非线性不稳定演化可能出现的5个阶段（线性阶段、倍周期阶段、大周期阶段、波群阶段以及不规则阶段）,实验中出现的沿岸流通常处于线性阶段或非线性倍周期阶段,倍周期阶段的涡旋是由线性阶段的涡旋发生追赶、配对直至合并产生的。涡旋配对以碰撞的形式发生,大部分能量转移至追踪波,然后以较慢的涡旋速度沿岸传播。     

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.     

波生流对海岸污染物输移的影响

通过物理模型实验对海岸波浪作用下污染物运动特性进行了分析,重点分析了质量输移流、沿岸流、沿岸流不稳定运动及破波带内旋涡运动等海岸水动力因素的影响.实验中坡度分别取为1:100和1:40,实验中采用CCD摄像机记录墨水的运动轨迹,同步测量流体质点速度以及波面升高.实验表明,在破碎带外污染物主要受波浪非线性引起的质量输移流的影响;在破碎带内主要受沿岸流的影响,同时还受沿岸流不稳定运动及大尺度旋涡运动的影响.     

Longshore currents of regular waves on different beaches

The experiment and numerical computations of longshore currents produced by regularwaves on the two beaches with the slopes of 1:100 and 1:40 are made. The cross-shore distributions of longshore current velocities and wave heights are given and the influences of wave heights, wave periods and beach slopes on the longshore currents are discussed. The discussion is also made for the influences of different eddy viscosity coefficients on the numerical results of longshore current velocities.     

Longshore Currents over Barred Beach with Mild Slope

The laboratory experiment and numerical simulations of wave-driven longshore currents by random waves on barred beaches with slopes of 1:100 and 1:40 were conducted to investigate the bimodal feature of mean longshore currents, with emphasis on the location and ratio of two peaks of longshore currents. The location and ratio of two peaks are controlled by the sand bar. The influences of wave heights and beach slopes on the longshore currents are discussed. Numerical simulations were also performed to compute the measured velocity profile, with the emphasis on the effect of lateral mixing, bottom friction and surface rollers on numerical results.     

Longshore Currents of Random Waves on Different Plane Beaches

1 .IntroductionWhenwavespropagateobliquelytotheshorelineandbreak ,ameancurrentisgeneratedflowingparalleltothecoast.Thegenerationoflongshorecurrentscanbeexplainedasfollows .Withbreakingwaveheightdecreasing ,themomentumofwavemotionwillchangecorrespondingly .Accordingtothemomentumconservationtheory ,thechangesofthemomentumwillbeaccompaniedwithadditionalforcesactingonfluid .Longuet Higgins ( 1 970 )usedtheconceptofradiationstresstodescribetheaboveadditionalforceactingonfluidduetothechangeofwavemo…     

A morphological stability analysis for a long straight barred coast

A morphological stability analysis is carried out for a long straight coast with a longshore bar. The situation with oblique wave incidence and a wave-driven longshore current is considered. The flow and sediment transport are described by a numerical modelling system. The models comprise: (i) a wave model with depth refraction, shoaling and wave breaking, (ii) a depth integrated model for wave driven currents and (iii) a sediment transport model for the bed load transport and the suspended load transport in combined waves and current. The direction of the sediment transport is taken to be parallel to the depth integrated mean current velocity, neglecting the effects of a bed slope and secondary currents. An instability is found to develop around the bar crest. The instability is periodic in the alongshore direction, and tends to form rip channels and to steepen the offshore face of the bar between the rip channels. The alongshore wave length of the most unstable perturbation is determined for different combinations of the wave conditions and the geometry of the profile.     

Numerical simulation of nearshore circulation on field topography under random wave environment

In order to investigate surf zone hydrodynamics through two-dimensional numerical simulations of nearshore circulation under random wave environment, a nearshore circulation model, SHORECIRC, and a random wave model, SWAN, were combined and utilized. Using this combined model, a numerical simulation of the October 2, 1997 SandyDuck field experiment was performed. For this simulation, field topography and an input offshore spectrum were constructed using observed data sets synchronized with the experiment. The wave-breaking model in SWAN was modified by using breaker parameters varied according to bottom slope. The simulation results were compared with the experimental data, which revealed a well-developed longshore current, as well as with results using other combinations which were SHORECIRC and its original monochromatic wave-driver, and SHORECIRC and the default of SWAN. The results from the novel combined model agreed well with the experimental data. The results of the present simulation also indicate that alongshore field topography influences shear fluctuation of longshore currents.     

The nearshore current along a high-rainfall,trade-wind coast-Nicaragua

Runoff from abundant rainfall on the watersheds along the east coast of Nicaragua results in a well-defined nearshore current, extending 20–40 km out from the coast. Important terms in the controlling dynamical balance are the Coriolis forces, and eddy frictional forces. Calculations of the diabathic surface slope 0(10^?5) show a smooth setup of 4–5 cm from the outer edge of the current to the shoreline. A longshore surface slope of 0(10^?8) appears to be set up by the longshore wind stress, and further computations allow an estimate of ～ 6 gr cm^?1 s^?1 for the dynamic eddy viscosity. An analytical expression including diabathic surface slope and density gradient, parabathic surface slope, wind stress, and quadratic bottom friction reproduces the salient observed features of the nearshore current. These include the pronounced maximum in the parabathic (along-shelf) current about 10 km off the coast, a complex diabathic velocity structure, and a shelf countercurrent just seaward of the outer edge. Further calculations suggest that the dominant driving arises from the freshwater-induced density gradients, accounting for upward of 80% of the flow velocity. As suggested by Royer (1982), the prevailing trade wind exerts an onshore wind stress that serves the important role of maintaining the integrity of the density gradients via the convergence of a surface Ekman layer toward the coast.     

地形斜坡对东海黑潮陆架坡折锋稳定性影响研究

为了研究地形斜坡对东海黑潮陆架坡折锋稳定性的影响,利用简化的线性原始方程,在一定背景流的情况下,主要从增长率、相速度、空间结构和能量方面分析海底地形斜坡变化对坡折锋稳定性的影响。模式结果表明,平底地形时,扰动的强度大且扰动区域广,但有地形斜坡时,扰动区域变窄,强度变弱,地形对坡折锋起稳定性作用。通过能量分析得出东海黑潮陆架坡折锋是正压和斜压的混合不稳定,其中斜压不稳定占主导地位。实验分析得出,地形对东海黑潮陆架坡折锋起稳定作用,斜坡增大,斜压不稳定和正压不稳定均减弱,斜压不稳定减弱更明显。     

沙坝海岸沿岸流速度剖面特征研究

通过对两个坡度沙坝地形沿岸流实验测量和基于能量方程的沿岸流数值模拟,研究了沙坝海岸平均沿岸流速度剖面的双峰剖面特征,重点分析了第二个峰值的特征和两峰值的比值。综合考虑入射波高、入射波类型和坡度对波生沿岸流垂直岸线速度剖面的影响。结果表明,平均沿岸流速度剖面出现双峰剖面特征:第一峰值发生在沙坝向岸侧面的中部,第二个峰值发生在靠近岸线处;同一坡度情况两个峰值的位置和比值,不受入射波类型、入射波高的影响。数值模型中包括了侧混、底摩擦和水滚等因素,其数值模拟结果和实验值拟合较好,并讨论了有无侧混和水滚对速度剖面的影响。     

Establishing uniform longshore currents in a large-scale sediment transport facility

A large-scale laboratory facility for conducting research on surf-zone sediment transport processes has been constructed at the U.S. Army Engineer Research and Development Center. Successful execution of sediment transport experiments, which attempt to replicate some of the important coastal processes found on long straight beaches, requires a method for establishing the proper longshore current. An active pumping and recirculation system comprised of 20 independent pumps and pipelines is used to control the cross-shore distribution of the mean longshore current. Pumping rates are adjusted in an iterative manner to converge toward the proper settings, based on measurements along the beach. Two recirculation criteria proposed by Visser [Coastal Eng. 15 (1991) 563] were also used, and they provided additional evidence that the proper total longshore flow rate in the surf zone was obtained. The success of the external recirculation system and its operational procedure, and the degree of longshore uniformity achieved along the beach, are the subjects of this paper. To evaluate the performance of the recirculation system, and as a precursor to sediment transport experiments, two comprehensive test series were conducted on a concrete beach with straight and parallel contours (1:30 slope), one using regular waves and the other using irregular waves. In the regular wave case, the wave period was 2.5 s and the average wave height at breaking was approximately 0.25 m. In the irregular wave case, the peak wave period was 2.5 s and the significant breaking wave height was approximately 0.21 m. The longshore current recirculation system proved to be very effective in establishing uniform mean longshore currents along the beach in both cases. This facility and the data presented here are unique for the following reasons: (1) the high cross-shore resolution of the recirculation system and the ease with which changes can be made to the longshore current distribution, (2) the degree of longshore uniformity achieved as a percentage of the length of the basin (even near the downdrift boundary), (3) the scale of the wave conditions generated, and (4) the relatively gentle beach slope used in the experiments (compared to previous laboratory studies of the longshore current). Measured data are provided in an appendix for use in theoretical studies and numerical model development and validation.     

On the stability of the Soya Warm Current

The stability of the Soya Warm Current is examined, in an attempt to explain the mechanism of the formation of the wave-like pattern seen in satellite infrared imagery in summer. A linear stability theory is applied to barotropic shear flows over a realistic bottom topography. Effects of bottom friction are also taken into consideration. For this current in summer, when volume transport is greatest, the possibility of barotropic instability is suggested. The most unstable waves obtained in this study have wavelengths of 60–80 km, periods of about 1. 5 days, and phase velocities of 45–55 cm sec^–1, which is in good agreement with observations.     

近岸沿岸流及污染物运动的数值模拟

基于双曲型缓坡方程和近岸浅水方程对近岸波浪斜向入射破碎所生成的沿岸流及污染物在沿岸波流作用下的运动进行了数值模拟,并对数值模拟结果进行了验证分析。数值模拟结果表明,在相近工况参数下,随着入射波高的增大,沿岸流流速和平均水面升高值均明显增大;随着岸坡坡度的增加,沿岸流流速和平均水面升高值明显增大;随着入射波浪周期的增大,平均水面升高值明显增大。在沿岸缓坡区域,由斜向入射波浪破碎所产生的沿岸流对污染物的运动起着不可忽略的影响。     

Numerical study of wave and longshore current interaction

Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induced longshore currents were modeled by shallow water equation.Water wave provided the radiation stress gradients to drive current.Wave and longshore current interactions were considered by cycling the wave and longshore current models to a steady state.The experiments for regular and irregular breaking wave induced longshore currents by Hamilton and Ebersole（2001） and Reniers and Battjes（1997） were simulated.The numerical results indicate that the present models are effective for simulating the interaction of wave and breaking wave induced longshore currents,and the numerically simulated longshore current at wave breaking point considering wave and longshore current interaction show some disagreement with those neglecting the wave-current interaction,and the breaking wave induced longshore current effect on wave transformation is not obvious.     

沿岸流不稳定性的实验研究及理论分析

在坡度为1:40的平面斜坡上进行了单向不规则波的沿岸流不稳定运动实验,观测到了沿岸流的周期性波动(波动周期约为100 s)。利用最大熵方法和三角函数回归法求得这种波动的主频率以及幅值,分析了波动幅值在垂直岸线方向的变化,结果表明该变化与沿岸流变化类似,即在沿岸流最大值附近这种波动强度最大。为了分析波动的机理,利用线性沿岸流不稳定模型对模型实验结果进行了分析,求得了不稳定运动增长模式和波动周期,并与对应实测结果进行了比较,结果表明,计算结果与实测值符合,从而说明实验中观测到的这种周期性波动为沿岸流不稳定引起的剪切波。     

The mesoscale variability in the Caribbean Sea. Part II: Energy sources

The processes which drive the production and the growth of the strong mesoscale eddy field in the Caribbean Sea are examined using a general circulation model. Diagnostics of the simulations suggest that:(1) The mean currents in the Caribbean Sea are intrinsically unstable. The nature of the instability and its strength vary spatially due to strong differences of current structure among basins.(2) The greatest and most energetic eddies of the Caribbean Sea originate in the Venezuela Basin by mixed barotropic-baroclinic instability of an intense jet, formed with waters mostly from the surface return flow of the Meridional Overturning Circulation and the North Equatorial Current which converge and accelerate through the Grenada Passage. The vertical shear of this inflow is enhanced by an eastward undercurrent, which flows along the south American Coast between 100 and 250 m depth. The shallow eddies (less than 200 m depth) formed in the vicinity of the Grenada Passage get rapidly deeper (down to 1000 m depth) and stronger by their interaction with the deep interior flow of the Subtropical Gyre, which enters through passages north of St. Lucia. These main eastern Caribbean inflows merge and form the southern Caribbean Current, whose baroclinic instability is responsible for the westward growth and strengthening of these eddies from the Venezuela to the Colombia Basin.(3) Eddies of lesser strength are produced in other regions of the Caribbean Sea. Their generation and growth is also linked with instability of the local currents. First, cyclones are formed in the cyclonic shear of the northern Caribbean Current, but appear to be rapidly dissipated or absorbed by the large anticyclones coming from the southern Caribbean. Second, eddies in the Cayman Sea, which impact the Yucatan region, are locally produced and enhanced by barotropic instability of the deep Cayman Current.(4) The role of the North Brazil Current (NBC) rings is mostly to act as a finite perturbation for the instability of the mean flow. Their presence near the Lesser Antilles is ubiquitous and they appear to be linked with most of the Caribbean eddies. There are some evidences that the frequency at which they form near the Grenada Passage is influenced by the frequency at which the NBC rings impinge the Lesser Antilles. But large Caribbean eddies also form without a close influence of any ring, and comparison between simulations shows that mean eddy kinetic energy and eddy population in the Caribbean Sea are not substantially different in absence or presence of NBC rings: their presence is not a necessary condition for the generation and growth of the Caribbean eddies.     

Double-celled circulation in coastal upwelling

Simple numerical experiments on two-dimensional coastal upwelling are made with emphasis on the role of non-geostrophic solenoidal field of density in the formation of double-celled circulation and multi-celled density front. Geometry of shelf and slope is not taken into account. Existence of poleward undercurrent presumably caused by the longshore variation of the large scale pressure field is also suppressed for the sake of simplicity.The results are, (1) double-celled circulation revealed in the present experiment is closely related with the internal frictional layer, where the horizontal density gradient balances with the vertical gradient of the longshore velocity and the vertical diffusion of the vorticity. (2) density front formed by the emergence of the pycnocline to the sea surface is successively advected offshoreward by the Ekman transport. (3) the pycnocline intersecting the sea surface forms the density front which is nearly vertical on account of the small scale convection. The surface currents converge at the front and construct an anti-clockwise circulation (viewed from the lee side). (4) small coefficient of eddy viscosity and strong wind stress lead the Ekman transport unstable and form a multi-celled structure in the frontal region.     

Instability of the Kuroshio in Luzon Strait: Effects of ridge topography and stratification

The spectral analyses of moored current velocities in the central Luzon Strait reveal northward (i.e., downstream of the Kuroshio) propagation of a frontal wave with a five-day period, with wave amplitude increasing northward. Estimated from both curve fitting and frequency domain Empirical Orthogonal Function methods, the characteristics of five-day variations have wave speeds ranging from 32 to 40 cm s⁻¹, wavelengths ranging from 130 to 150 km, and e-folding time scales for growth ranging from 0.8 to 3 days. An analytical two-layer model used to explore linear stability characteristics indicates that bottom topography (two meridional ridges) is important for the Kuroshio stability characteristics in the Luzon Strait. In the two-layer model with the two ridges, the flow is stabilized for the long-wave mode but destabilized for the short-wave mode (due to increasing vertical shear in the horizontal velocity). The analytical model produces wavelengths and phase speeds for the most unstable mode which is similar to the observation, but the growth rate is underestimated. However, a spectral numerical model applied with a more realistic stratification and velocity structure does obtain faster growth rates comparable to the observations. Parameter sensitivity tests were conducted using the analytical model. The characteristics of the most unstable mode are most sensitive to the surface front location relative to the bottom topography but not sensitive to varying the density difference and thickness of the upper layer.