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1.
Multiple intertidal bars and troughs, often referred to as ‘ridges and runnels’, are significant features on many macrotidal sandy beaches. Along the coastline of England and Wales, they are particularly prevalent in the vicinity of estuaries, where the nearshore gradient is gentle and a large surplus of sediment is generally present. This paper examines the dynamics of such bar systems along the north Lincolnshire coast. A digital elevation model of the intertidal morphology obtained using LIDAR demonstrates that three to five intertidal bars are consistently present with a spacing of approximately 100 m. The largest and most pronounced bars (height = 0·5–0·8 m) are found around mean sea level, whereas the least developed bars (height = 0·2–0·5 m) occur in the lower intertidal zone. Annual aerial photographs of the intertidal bar morphology were inspected to try to track individual bars from year to year to derive bar migration rates; however, there is little resemblance between concurrent photographs, and ‘resetting’ of the intertidal profile occurs on an annual basis. Three‐dimensional beach surveys were conducted monthly at three locations along the north Lincolnshire coast over a one‐year period. The intertidal bar morphology responds strongly to the seasonal variation in the forcing conditions, and bars are least numerous and flattest during the more energetic winter months. Morphological changes over the monthly time scale are strongly affected by longshore sediment transport processes and the intertidal bar morphology can migrate along the beach at rates of up to 30 m per month. The behaviour of intertidal bars is complex and varies over a range of spatial and temporal scales in response to a combination of forcing factors (e.g. incident wave energy, different types of wave processes, longshore and cross‐shore sediment transport), relaxation time and morphodynamic feedback. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

2.

Saw-tooth bars are shore-oblique sand bars that are found along most ebb-tidal deltas of the Frisian Wadden Islands. Although they might significantly affect sediment transport pathways and volumes on the deltas, their general characteristics and dynamics are largely unknown. The main aim of this paper is to determine the typical saw-tooth bar heights, wave lengths, widths, orientations, migration rates and depths of occurrence. To this end, we analysed bathymetries from the Dutch and German Frisian Wadden Islands between 1970 and 2015. Bar heights range between 0.5 and 2 m, and wave lengths range between 300 and 900 m, with an average of 670 m, and the bar crests have a down contour orientation of approximately 25°. The bars are between 800 and 2200 m wide. Saw-tooth bars are located at depths from 3 to 12 m, depending on the slope of the area. Migration speeds of up to 112 m/year were found, using a spatial correlation method. Bar height and migration speed are positively linearly correlated, as well as bar wave length and bar width, bar height and the orientation of the depth contours and migration speed and the orientation of the area. The derived characteristics are compared to those of other bar types to evaluate hypotheses regarding the formation mechanism of the bars.

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3.
Nearshore bars play a pivotal role in coastal behaviour, helping to protect and restore beach systems particularly in post‐storm conditions. Examination of bar behaviour under various forcing conditions is important to help understand the short‐ to medium‐term evolution of sandy beach systems. This study carried out over a nine‐week period examines, the behaviour of three intertidal bars along a high energy sandy beach system in northwest Ireland using high‐frequency topographic surveys and detailed nearshore hydrodynamic modelling. Results show that, in general, there was onshore migration for all the bars during the study period, despite the variability observed between bars, which was driven mostly by wave dominated processes. Under the prevailing conditions migration rates of up to 1.83 m day?1 and as low as 0.07 m day?1 were observed. During higher wave energy events the migration rates of the bars decelerated in their onshore route, however, under lower wave energy conditions, they quickly accelerated maintaining their shoreward migration direction. Tidal influence appears to be subordinate in these conditions, being restricted to moderating the localized wave energy at low tides and in maintaining runnel configurations providing accommodation space for advancing slip faces. The study highlights the intricate behavioural patterns of intertidal bar behaviour along a high energy sandy coastline and provides new insights into the relative importance of wave and tidal forcing on bar behaviour over a relatively short time period. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

4.
Berm formation and morphological development of the beach face have been observed during a neap–neap tidal cycle on the gently sloping and accreting beach at Vejers, Denmark. During the field campaign, an intertidal bar migrated onshore and stabilized as a berm on the foreshore. A new intertidal bar occurred on the lower beach face, migrated onshore on the rising tide and finally merged with the pre‐existing berm. As the tide continued to rise, the new berm translated further onshore as an intertidal bar to the uppermost part of the foreshore. The sediment transport during the berm transition was onshore directed in the upper swash and offshore directed in the lower swash. This berm development can be described through both the neap‐berm, ridge‐and‐runnel and berm‐ridge development concepts proposed by Hine (Sedimentology 1979; 26: 333–351), and all three stages were observed during only three tidal cycles. The main factors controlling this fast transformation were the gentle slope of the cross‐shore profile, rapid water level translation rates, substantial swash overtopping of the berm, and low infiltration rates. Despite the onshore migration of intertidal bars and berm formation, no net foreshore accretion took place during the field campaign. This was largely due to the formation of rip channels with strong rip currents cutting through the intertidal bars and the berm, which acted as a sediment drain in the profile. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

5.
The intertidal drainage channels on a macrotidal bar–trough (ridge‐and‐runnel) beach were monitored during a 17‐day survey. Type 1 channels were persistent, dominantly longshore systems essentially limited to the wide intertidal zone between mean high and low water neap tidal levels. The cumulative length of this channel type fluctuated as a function of topographically controlled through‐flow or flow impedance in troughs, and showed no correlation with the semi‐lunar tidal cycle. Smaller, ephemeral type 2 channels appeared as dominantly cross‐shore systems incising bars on the narrower upper and lower beach zones during spring tides. They disappeared during neap tides through infill by waves and aeolian activity. The only significant phase of type 1 channel mobility occurred during a brief moderate‐energy storm at the start of the survey. The effect of this mobility on beach morphology was inextricably linked to that of waves and currents. Meander bend migration, forced by wave‐ and longshore‐current‐induced migration of a bar during the storm, resulted in important but highly localized morphological change that was only a minor part of an irregular saw‐tooth pattern of change that affected the entire beach profile, and that was largely controlled by wave processes and longshore currents. The flow velocities in channels on this beach are too weak to generate the formation and longshore migration of high‐energy bedforms. Channel mobility and impact on beach morphology are expected to increase under storm conditions. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

6.
Multiple intertidal bars are common features of wave‐dominated sandy beaches, yet their short‐term (<1 month) and small‐scale (<1 km) morphology and dynamics remain poorly understood. This study describes the morphodynamics of multiple intertidal bars in North Lincolnshire, England, during single and lunar tidal cycles under two contrasting conditions – first when significant wave height was <0·5 m and second when significant wave height frequently exceeded 1 m. The relative importance of swash, surf and shoaling processes in determining morphological change was examined using detailed field observations and a numerical model. The beach featured four intertidal bars and both cross‐shore and longshore bar morphology evolved during the field investigation, particularly under medium to high wave‐energy conditions. Numerical modelling suggests shoaling processes are most common on the seaward two bars under calm wave conditions (Hs < 0·5 m) and that surf zone processes become more common during neap tides and under more energetic (Hs < 0·5 m) conditions. Surf processes dominate the inner two bars, though swash influence increases in a landward direction. The numerical modelling results combined with low tide survey data and high‐resolution morphological measurements strongly suggest changes in the intertidal bar morphology are accomplished by surf zone processes rather than by shoaling wave or swash processes. This is because shoaling waves do not induce significant sediment transport to have any morphological effect, whereas swash action generally does not have enough scope to act as the swash zone is much narrower than the surf zone. It was found, however, that the absolute rate of morphological change under swash action and surfzone processes are of similar magnitudes and that swash action may induce a significant amount of local morphological change when the high tide mark is located on the upper bar, making this process important for bar morphodynamics. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

7.
This paper outlines a general framework for analysis of the problem of beach gradients which divides the system into: (1) the independent controls, (2) the hydrodynamics, (3) the sediment dynamics, and (4) the morphodynamics. A model is derived from the combination of these stages which shows close agreement with field data for wave steepnesses of less than about 0.06, but predicts lower beach gradients than arc observed for steeper waves. The use of ‘analytical feedback’ in the present model rather than the ‘iterative feedback’ which is used in computer simulations demonstrates that differential sediment transport may be responsible for stabilizing the beach gradient.  相似文献   

8.
Many estuaries contain sandy beaches that provide habitats and offer protective buffers for wetlands and infrastructure, alongside cultural and recreational resources. Research underpinning coastal management tends to focus on tide- and swell-dominated sandy beaches, but little attention is given to beaches in estuaries and bays (BEBs) that exist along a continuum of wind/swell wave, tide and riverine influence. BEBs are subject to less wave energy than open coast locations because of the generally narrow window of directions for which ocean waves can propagate through the entrance. However, when storm wave direction coincides with the orientation of the estuary or bay entrance, waves can penetrate several kilometres inside. Here we focus on eight BEBs in two major bays/estuaries in Sydney, Australia and present observations from before and after a major extratropical storm with waves from an atypical direction in June 2016. We quantify magnitudes of beach erosion and recovery rates for 3 years post-storm. We show that when high-energy storm waves penetrate bays and estuaries, BEBs can undergo up to 100% of subaerial beach erosion. Three years after the storm, only 5 of the 29 (17%) eroded subaerial beach profiles had recovered to their pre-storm volume. This is likely due to the lack of low-frequency, beach-building waves at BEBs under modal weather conditions in between storms, in contrast to open coast beaches. We also show that the recovery of BEBs may be limited by the absence of adjacent sediment reservoirs due to the dominance of tidal processes mid-channel. Our study highlights the unique behaviour of BEBs relative to beaches on the open coast, and that shifting wave direction needs to be considered in long-term beach resilience under climate change. © 2020 John Wiley & Sons, Ltd.  相似文献   

9.
The role of wave forcing on the main hydro-morphological dynamics evolving in the shallow waters of the nearshore and at river mouths is analyzed. Focus is mainly on the cross-shore dynamics that evolve over mildly sloping barred, dissipative sandy beaches from the storm up to the yearly timescale, at most. Local and non-local mechanisms as well as connections across three main inter-related subsystems of the nearshore – the region of generation and evolution of nearshore bars, river mouths and the swash zone – are analyzed. The beach slope is a major controlling parameter for all nearshore dynamics. A local mechanism that must be properly described for a suitable representation of wave-forced dynamics of all such three subsystems is the proper correlation between orbital velocity and sediment concentration in the bottom boundary layer; while specific dynamics are the wave–current interaction and bar generation at river mouths and the sediment presuspension at the swash zone. Fundamental non-local mechanisms are both infragravity (IG) waves and large-scale horizontal vortices (i.e. with vertical axes), both influencing the hydrodynamics, the sediment transport and the seabed morphology across the whole nearshore. Major connections across the three subsystems are the upriver propagation of IG waves generated by breaking sea waves and swash–swash interactions, the interplay between the swash zone and along-river-flank sediment transport and the evolution of nearshore sandbars. © 2019 John Wiley & Sons, Ltd.  相似文献   

10.
The reflection of incident gravity waves over an irregular swash zone morphology and the resulting influence on surf zone dynamics remains mostly unexplored. The wave-phase resolving SWASH model is applied to investigate this feedback using realistic low-tide terraced beach morphology with well-developed beach cusps. The rhythmic reflection generates a standing wave that mimics a subharmonic edge wave, from the superimposition of incident and two-dimensional reflected waves. This mechanism is enhanced by shore-normal, narrow-banded waves in both direction and frequency. Our study suggests that wave reflection over steep beaches could be a mechanism for the development of rhythmic morphological features such as beach cusps and rip currents.  相似文献   

11.
Crescentic sandbars and rip channels along wave‐dominated sandy beaches are relevant to understand localized beach and dune erosion during storms. In recent years, a paradigm shift from hydrodynamic template models to self‐organization mechanisms occurred to explain the formation of these rhythmic features. In double sandbar systems, both the inner‐ and outer‐bar rip channels and crescentic planshapes are now believed to be free instabilities of the nearshore system arising through self‐organization mechanisms alone. However, the occasional occurrence of one or two inner‐bar rip channels within one outer‐bar crescent suggests a forced, morphologically coupled origin. Here we use a nonlinear morphodynamic model to show that alongshore variability in outer‐bar depth, and the relative importance of wave breaking versus wave focussing by refraction across the outer bar, is crucial to the inner‐bar rip channel development. The coupling patterns simulated by our model are similar to those observed in the field. Morphological coupling requires a template in the morphology (outer‐bar geometry) which, through the positive feedback between flow, sediment transport and the evolving morphology (that is, self‐organization) enforces the development of coupling patterns. We therefore introduce a novel mechanism that blurs the distinction between self‐organization and template mechanisms. This mechanism may also be extended to explain the dynamics of other nearshore patterns, such as beach cusps. The impact of this novel mechanism on the alongshore variability of inner‐bar rip channels is investigated in the companion paper. Copyright © 2010 John Wiley and Sons, Ltd.  相似文献   

12.
Digital elevation models and topographic pro?les of a beach with intertidal bar and trough (ridge‐and‐runnel) morphology in Merlimont, northern France, were analysed in order to assess patterns of cross‐shore and longshore intertidal bar mobility. The beach exhibited a pronounced dual bar–trough system that showed cross‐shore stationarity. The bars and troughs were, however, characterized by signi?cant longshore advection of sand under the in?uence of suspension by waves and transport by strong tide‐ and wind‐driven longshore currents. Pro?le changes were due in part to the longshore migration of medium‐sized bedforms. The potential for cross‐shore bar migration appears to be mitigated by the large size of the two bars relative to incident wave energy, which is modulated by high vertical tidal excursion rates on this beach due to the large tidal range (mean spring tidal range = 8·3 m). Cross‐shore bar migration is also probably hindered by the well‐entrenched troughs which are maintained by channelled high‐energy intertidal ?ows generated by swash bores and by tidal discharge and drainage. The longshore migration of intertidal bars affecting Merlimont beach is embedded in a regional coastal sand transport pathway involving tidal and wind‐forced northward residual ?ows affecting the rectilinear northern French coast in the eastern English Channel. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

13.
Intertidal bars are common in mesotidal/macrotidal low-to-moderate energy coastal environments and an understanding of their morphodynamics is important from the perspective of both coastal scientists and managers. However, previous studies have typically been limited by considering bar systems two-dimensionally, or with very limited alongshore resolution. This article presents the first multi-annual study of intertidal alongshore bars and troughs in a macrotidal environment using airborne LiDAR (light detection and ranging) data to extract three-dimensional (3D) bar morphology at high resolution. Bar and trough positions are mapped along a 17.5 km stretch of coastline in the northwest of England on the eastern Irish Sea, using eight complete, and one partial, LiDAR surveys spanning 17 years. Typically, 3–4 bars are present, with significant obliquity identified in their orientation. This orientation mirrors the alignment of waves from the dominant south-westerly direction of wave approach, undergoing refraction as they approach the shoreline. Bars also become narrower and steeper as they migrate onshore, in a pattern reminiscent of wave shoaling. This suggests that the configuration of the bars is being influenced by overlying wave activity. Net onshore migration is present for the entire coastline, though rates vary alongshore, and periods of offshore migration may occur locally, with greatest variability between northern and southern regions of the coastline. This work highlights the need to consider intertidal bar systems as 3D, particularly on coastlines with complex configurations and bathymetry, as localized studies of bar migration can overlook 3D behaviour. Furthermore, the wider potential of LiDAR data in enabling high-resolution morphodynamic studies is clear, both within the coastal domain and beyond. © 2019 John Wiley & Sons, Ltd.  相似文献   

14.
The formation of an inner nearshore bar was observed during a high‐energy event at the sandy beach of Vejers, Denmark. The bar accreted in situ during surf zone conditions and the growth of the bar was associated with the development of a trough landward of the bar. Measurements of hydrodynamics and sediment fluxes were obtained from electromagnetic current meters and optical backscatter sensors. These process measurements showed that a divergence in sediment transport occurred at the location of the developing trough, and observed gradients in cross‐shore net sediment flux were consistent with the morphological development. The main cause for the flux gradients were cross‐shore gradients in offshore‐directed mean current (undertow) speed which depended upon local relative wave height and local bed slope. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

15.
Sandy beaches typically have one or more shore-parallel bars with superimposed smaller-scale three-dimensional (3D) bars. Knowledge of their morphodynamic behaviour under more realistic wave conditions is limited. This study investigates the response of beaches with two shore-parallel bars to sinusoidally time-varying angles of incidence, using a non-linear morphodynamic model. Different periods and amplitudes of this sinusoidal variation are considered, as well as different time-mean wave angles. For time-invariant and normally incident waves, results show that alongshore rhythmic 3D bars form in the domains of inner and outer shore-parallel bars. The 3D bars in the inner domain are coupled at half the outer-bars wavelength. This phase coupling breaks up when the wave angle varies in time. Initially, regular 3D bars form in the inner domain (free behaviour), which become irregular when 3D bars develop in the outer domain (forced behaviour). The heights of the 3D bars oscillate with time, reaching maximum values when the forcing period is comparable to the system adjustment time scale (∼ 10–20 days). For a time-varying wave angle around an oblique mean, alongshore migrating 3D bars emerge in both inner and outer domains. In contrast, for an oblique (constant) wave angle, 3D bars only form in the inner domain and they hardly migrate alongshore. For any forcing period, the dominant response period of the oscillating bar heights is at half the forcing period when waves are (on average) normally incident, and it equals the forcing period when waves are on average obliquely incident. Compared with time-invariant angles, heights of inner and outer 3D bars are (on average) smaller and larger, respectively, when the angle varies with time, particularly for forcing periods in the order of the system adjustment time scale. Increasing the amplitude of the time-varying wave angle weakens bar growth. Explanations of these results are also provided.  相似文献   

16.
Long-term, net offshore bar migration is a common occurrence on many multiple-barred beaches. The first stage of the process involves the generation of a longshore bar close to the shoreline that oscillates about a mean position for some time, followed by a stage of net offshore migration across the upper shoreface, and finally a stage of decaying bar form through loss of sediment volume at the outer boundary of the upper shoreface. The phenomenon has been previously documented in the Netherlands, the USA, the Canadian Great Lakes, and in New Zealand, but our present understanding of the morphodynamic processes and sediment transport pathways involved in bar decay is limited. In this paper, long-term, net offshore bar migration is investigated at Vejers Beach, located on the North Sea coast of Denmark where offshore bar migration rates are of the order of 45–55 m a−1. A wave height transformation model confirmed that the decay of the outer bar results in increased wave heights and undertow speeds at the more landward bar potentially causing this bar to speed up its offshore migration. The causes for outer bar decay were investigated through field measurements of sediment transport at the decaying bar and at a position further seaward on the lower shoreface. The measurements showed that a cross-shore transport convergence exists between the bar and the lower shoreface and that the loss of sediment involved in bar decay is associated with a longshore directed transport by non-surf zone processes. At Vejers, and possibly elsewhere, the net offshore migration of bars and the subsequent loss of sand during bar decay is an important part of the beach and shoreface sediment budget.  相似文献   

17.
Alpine gravel-bed rivers are dynamic systems that have been subjected to many anthropic alterations in the past centuries. Riparian vegetation development on previously bare sediment bedforms has been a common adjustment, raising important management issues in terms of flood risks and biodiversity. Many of these rivers are also channelized, and as a result present a pattern of alternate bars. Considering recent advances in numerical biomorphodynamic modeling, this study aims at exploring numerically the morphodynamics of alternate bars in the presence of riparian vegetation. To this end, a dynamic vegetation module has been implemented on top of an existing morphodynamic model, accounting for ecological processes of seed dispersal, seedling recruitment, growth, and mortality. Numerical simulations have been performed on a simplified reach of a gravel-bed river with free migrating alternate bars at initial state. In this work 96 scenarios have been simulated, each representing 50 years of channel evolution, with different flood regimes characterized by various peak discharges and flood durations. Yearly peak discharge variability is explicitly modeled in 48 scenarios. Model outcomes present two possible equilibrium biomorphodynamic behaviors: stationary vegetated bars, or free migrating bars in the case of frequent vegetation removal during floods. This binary behavior holds true when the stochasticity of annual peak discharges is represented, and for a wide range of parameter values included in vegetation dynamic modeling. Transient mobility of vegetated bars is observed in specific configurations where large sediment deposits deflect the flow field, eroding bar heads. Modeled bar wavelengths are in the range of values predicted for free bars by linear bar theory, and remain far from the theoretical values of hybrid, steady bars. The shift from unvegetated migrating bars to steady vegetated bars seems to show that in these simulations vegetation constitutes a hydraulic forcing, leading to a shift from free bars to forced bars, with a final configuration largely inherited from the initial state. © 2019 John Wiley & Sons, Ltd.  相似文献   

18.
Formation and development of alternate bars in an engineered mountainous reach of the Arc River, France, is studied using photo analysis, 1D modelling and by applying theoretical and empirical models for alternate bar systems. Alternate bars already existed in the 80s in the form of a stable confined wandering system. In 1994, the river bed was flattened after engineering works. However, aerial photographs and cross-sectional profiles show that bars rapidly recovered within a few years. The alternate bar system evolved rapidly with a reduction of the number of bars and so an increasing bar length. The width-to-depth ratio, the slope change, the bend upstream of the reach, and the sediment supplies are the main controls of bar formation and evolution. The system appears to lead to force bars due to the bend but also due to a bridge in the downstream part of the reach. Nevertheless some free mobile bars are still observed in the middle of the reach. A discussion on the alternate bar formation is provided using empirical and analytical models. Finally, impacts of low flows and vegetation seem to be significant in the stabilization of the system toward a confined wandering system as observed before the engineering works.  相似文献   

19.
The Aquitanian Coast (France) is a high-energy meso-macrotidal environment exhibiting a highly variable double sandbar system. The inner and the outer bar generally exhibit a bar and rip morphology and persistent crescentic patterns, respectively. In June 2007, an intense five-day field experiment was carried out at Biscarrosse Beach. A large array of sensors was deployed on a well-developed southward-oriented bar and rip morphology. Daily topographic surveys were carried out together with video imaging to investigate beach morphodynamic evolution. During the experiment, offshore significant wave height ranged from 0.5 to 3 m, with a persistent shore-normal angle. This paper identifies two types of behavior of an observed rip current: (1) for low-energy waves, the rip current is active only between low and mid tide with maximum mean rip current velocity reaching 0.8 m/s for an offshore significant wave height (Hs) lower than 1 m; (2) for high-energy waves (Hs≈ 2.5–3 m), the rip current was active over the whole tide cycle with the presence of persistent intense offshore-directed flows between mid and high tide. For both low and high-energy waves, very low-frequency pulsations (15–30 min) of the mean currents are observed on both feeder and rip channels.A persistent slow shoreward migration of the sandbar was observed during the experiment while no significant alongshore migration of the system was measured. Onshore migration during the high-energy waves can be explained by different sediment transport processes such as flow velocity skewness, wave asymmetry or bed ventilation. High-frequency local measurements of the bed evolution show the presence of significant (in the order of 10 cm) fluctuations (in the order of 1 h). These fluctuations, observed for both low- and high-energy waves, are thought to be ripples and megaripples, respectively and may play an important but still poorly understood role in the larger scale morphodynamics. The present dataset improves the knowledge of rip dynamics as well as the morphological response of strongly alongshore non-uniform meso-macrotidal beaches.  相似文献   

20.
A two‐dimensional shallow water hydro‐sediment‐morphodynamic model is applied to investigate alternate bar formation, development and sediment sorting in straight channels. The model is coupled, explicitly incorporating the flow–sediment–bed interactions by using the full mass and momentum conservation equations, which are numerically solved by a well‐balanced version of the finite volume Slope Limiter Centred (SLIC) scheme. The model is first tested against a flume experiment on alternate bars formed over a uniform sediment bed, which clearly exhibits processes of bar formation, migrating and finally approaching an equilibrium state. Then it is applied to another flume experiment on alternate bars due to non‐uniform sediment transport. The computational results are evaluated, with a focus on the longitudinal and vertical sediment sorting. It is argued for the first time that the inconsistent sediment sorting patterns observed in previous studies are determined by different sediment transport conditions, i.e. full versus partial transport. When a condition of full transport is achieved, under which all size fractions are fully mobilized and transported, the longitudinal surface sediment shows a sorting pattern of coarse‐on‐head and fine‐in‐pool, and the vertical substrate sediment exhibits an immobile‐fine‐coarse structure upwards. In contrast, for a partial transport condition, under which only finer fraction participates in the transport process, an opposite longitudinal pattern (i.e. fine‐on‐head and coarse‐in‐pool) and a different vertical structure (i.e. immobile‐coarse‐fine) are observed. Concurrently, numerical experiments with specified conditions show that the critical aspect ratio for the formation of migrating alternate bars is approximately equal to 12. With the increase of the aspect ratio, the bar length grows gradually, while the bar height increases rapidly for moderate values of the aspect ratio and then keeps nearly stable. The bar celerity, however, is weakly sensitive to the variation of this ratio. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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