A mathematical model of spit growth and barrier elongation: Application to Fire Island Inlet (USA) and Badreveln Spit (Sweden)

A mathematical model of spit growth and barrier elongation adjacent to an inlet (of arbitrary width), supplied by sediment coming from longshore sediment transport, was developed based on the spit growth model proposed by Kraus (1999). The fundamental governing equation is the conservation equation for sand, where the width of the spit is assumed constant during growth. The portion of the longshore sediment transport feeding the spit has been estimated based on the ratio between the depth of the inlet channel and the depth of active longshore transport. Sediment transport from the channel due to the inlet flow, as well as other sinks of sand (e.g., dredging), are taken into account. Measured data on spit elongation at Fire Island Inlet, United States, and at Badreveln Spit, Sweden, were used to validate the model. The simulated results agree well with the measured data at both study sites, where spit growth at Fire Island was restricted by the inlet flow and the growth at Badreveln Spit was unrestricted. The model calculation for Fire Island Inlet indicates that the dredging to maintain channel navigation is the major reason for the stable period observed from 1954 to 1994 at the Fire Island barrier. The average annual net longshore transport rate at the eastern side of the Fire Island inlet obtained in this study was about 220,000 m³/yr, of which approximately 165,000 m³/yr (75% of the net longshore transport) is deposited in the inlet feeding the spit growth, whereas the remaining portion (25%) is bypassed downdrift through the ebb shoal complex.     

Shoreline accretion and sand transport at groynes inside the Port of Richards Bay

The south-western shoreline along the entrance channel inside the Port of Richards Bay has experienced continued erosion. Four groynes were constructed to stabilise the shoreline. Monitoring of shoreline evolution provided valuable data on the accretion adjacent to two of the groynes and on the sediment transport rates at these groynes. Tides, beach slopes, winds, wave climate, current regime, and sand grain sizes were documented. The one site is “moderately protected” from wave action while the other is “protected” according to the Wiegel [Wiegel, R. L. (1964). Oceanographical engineering. Prentice Hall, Inc., Englewood Cliffs, NJ.] classification. The shoreline accreted progressively at the two groynes at 0.065 m/day and 0.021 m/day respectively. The shorelines accreted right up to the most seaward extremity of the groynes. Equilibrium shorelines were reached within about 3.5 years to 4 years, which compare well with other sites around the world. The mean wave incidence angle is large and was found to be about 22°. The median sand grain sizes were 0.33 mm and 0.37 mm. The groynes acted as total traps, the beach surveys were extended to an adequate depth, and cross-shore sediment transport did not cause appreciable net sand losses into the entrance channel. The net longshore transport rate along the study area, which is north-westbound, is only slightly lower than the gross longshore transport. The actual net longshore transport rates are 18 000 m³/year and 4 600 m³/year respectively at the two groynes. A rocky area limits the availability of sand at one groyne. There is fair agreement between the predicted and measured longshore transport rates at the other groyne.     

The past, present and future evolution of Hurst Castle spit, Hampshire

Previous models of the evolution of Hurst Castle Spit over-emphasised longshore growth at the expense of other processes, particularly rise in sea-level. Initially, a Pleistocene valley system was submerged creating a tidal strait, the West Solent, between Christchurch Bay and the East Solent. This almost certainly caused a major hydrodynamic change, transforming much of Christchurch Bay and the West Solent from a low to a high tidal energy environment. Hurst Castle Spit and the Shingles Bank then began to form due to a combination of an easterly littoral drift, offshore gravel movement due to the high tidal energy, a rising sea-level, the transgression of Hurst Beach due to overwashing and the formation of recurves due to waves in the West Solent. The growth of the Shingles Bank due to offshore sediment movement from Hurst Castle Spit was of particular importance because of its influence on the wave energy along Hurst Beach. Significant local supplies of shingle in the vicinity of Hurst Castle Spit, reworked from Quatenary deposits, were also of importance. Thus, it is not a classic multi-recurved spit and the transgressive segment, Hurst Beach, has much in common with barrier coastlines.The same processes are continuing to shape Hurst Castle Spit at present, with the additional effects of human interference in the coastal sediment system. The construction of sea defences at Milford-on-Sea in the period 1936 to 1968 has modified the sediment budget and Hurst Castle Spit is experiencing a phase of rapid evolution: maximum recession rates have increased from 1.5m a⁻¹ (1867–1968) to 3.5m a⁻¹ (1968–1982). It is difficult to quantify the exact role of sea-level rise in the present evolution of Hurst Castle Spit.The future evolution of Hurst Castle Spit will depend largely on man. If there is no further interference, which is highly unlikely, the beach volume will continue to decline, resulting in a further increase in the rate of recession. Ultimately, a true tidal breach will probably form, marking a new phase in the evolution of Hurst Castle Spit and its environs. However, shingle renourishment, or another coastal engineering solution will probably be undertaken. The future rate of sea-level rise will have important long-term influences on all these options.     

Effects of shoreline and bedrock irregularities on the morphodynamics of the Alexandria coast littoral cell,Egypt

Beach-nearshore profiles combined with beach and surficial sediment samples were analyzed in conjunction with wave, current, littoral drift and sea-level data to determine the effect of bedrock on morphodynamic processes within the littoral zone of Alexandria on the Mediterranean coast of Egypt. This 14.5-km-long littoral cell is bounded by pronounced embayments and pocket beaches separated by headlands which prevent bypassing of beach sands, in effect making this cell a large, semi-closed basin. The compartmented nature of this cell acts together with the rough irregularity of the rocky seafloor to trap a thin veneer of sediment (<3 m thick), showing proportional mixing between two sedimentary provinces. A modern fine-grained sediment facies consisting of mixed carbonate/siliciclastic sand flanks most of the nearshore zone down to a depth of 8–10 m. Beyond this depth, considered to be the depth of closure, a relict late Pleistocene to mid-Holocene coarse-grained facies composed of biogenic carbonate sand is found. Along a short section of the coastline (km 3–6), the coarser sediment also occupies the nearshore zone. Over most of the study area the two sediment types are mixed in various proportions, largest mixing coinciding with poorest sorting. Profile analyses revealed seasonal changes in sediment volume along the coast which closely follow the cyclicity of seasonal changes in wave climate. The present shoreline orientation, headlands and rough, irregular rocky seabed are reflected in the erosion/accretion pattern, sediment characteristics, and the reversibility of longshore currents and littoral drift. Although there is a marked deficiency in the sediment balance, the sand budget for this cell, including artificial material (2.339*10⁶ m³) has increased slightly by 0.041*10⁶ m³ year^–1 as a result of engineering works carried out to widen the coastal road (Corniche). In addition to the physical properties of the bedrock (degree of induration), the accelerating sea-level rise during the Holocene and human influences, the modern morphology of the coast, the erosional seabed features in the nearshore zone, and the texture of seabed sediments are all controlled by the original geometry of the coast which consisted of an elevated subaerial ridge.     

A numerical shoreline model for shorelines with large curvature

This paper presents a new numerical model for shoreline change which can be used to model the evolution of shorelines with large curvature. The model is based on a one-line formulation in terms of coordinates which follow the shape of the shoreline, instead of the more common approach where the two orthogonal horizontal directions are used. The volume error in the sediment continuity equation which is thereby introduced is removed through an iterative procedure. The model treats the shoreline changes by computing the sediment transport in a 2D coastal area model, and then integrating the sediment transport field across the coastal profile to obtain the longshore sediment transport variation along the shoreline. The model is used to compute the evolution of a shoreline with a 90° change in shoreline orientation; due to this drastic change in orientation a migrating shoreline spit develops in the model. The dimensions of the spits evolving in the model compare favorably to previous model results and to field observation of the Skaw Spit in the north of Denmark.     

Modeling beach profile evolution at centennial to millennial scales

The proposed model allows the satisfactory reproduction of the changes in the profile geometry in each time step depending on the sediment budgets in a given morphodynamic system. The applied modification to the general Bruun rule governing the conservation of mass must account for the effect of the sediment transport, which is described in terms of the erosion and accretion rates (Er and and Ac, respectively). The scale of the erosion is a function of the total annual wave energy flux reaching the beach. The accretion is governed by the Er, on the one hand, and by the sediment budget in the morphodynamic system, on the other hand. The equilibrium profile obtained for the case of a balanced sediment budget (Er = Ac) shows good agreement with the observed profiles. A deficit or surplus in the sediment budget results in the shoreline??s retreat or advance accompanied by either a decrease or increase in the slope of the bottom profile. The model accounts for different types of shoreline responses to changes in the sea level (the Bruun rule, the development of a coastal barrier, and abrasion). Sediment budget imbalances can be a factor in the profile??s evolution due to changes in the sea level, while the combination of both factors will produce a variety of behaviors of the shoreline, as was shown by our calculations. The model was verified using historical data on the behavior of the Central Holland coast and the Abkhazian coast during the Late Holocene. It was shown that the model satisfactory reproduces the progradation of coastal barriers. An example of a relatively short-term forecast (over a 100-year period) is given.     

Delta lobe degradation and hurricane impacts governing large-scale coastal behavior,South-central Louisiana,USA

A large deficit in the coastal sediment budget, high rates of relative sea-level rise (~0.9 cm/year), and storm-induced current and wave erosion are forcing barrier shoreface retreat along the periphery of the Mississippi River delta plain. Additionally, conversion of interior wetlands to open water has increased the bay tidal prism, resulting in degradation of barrier islands due to inlet widening, formation of new inlets, and sediment sequestration at ebb-tidal deltas. Single-beam bathymetric surveys along a 165-km stretch of south-central Louisiana barrier coast, from Raccoon Point in Terrebonne Parish to Sandy Point in Plaquemines Parish, were conducted in 2006. These data, combined with historical bathymetry from three time periods (dating to the 1880s), provide a series of digital elevation models that were used to calculate sediment volumetric changes and determine long-term erosional-depositional trends. Dominant patterns during the 125-year period include (1) erosion of ~1.6 × 10⁹ m³ from the shoreface, forcing up to 3 km of shoreface retreat, (2) sediment deposition in coastal bights and at ebb-tidal deltas, and (3) a combined increase in tidal inlet cross-sectional area from ~41,400 m² to ~139,500 m². Bathymetric and shoreline change datasets separated by shorter time periods (sub-annual) demonstrate that these long-term trends are driven by processes associated with major hurricane impacts, and that rates of shoreface erosion are an order of magnitude greater during active hurricane seasons compared to long-term trends.     

Short-term shoreline changes due to cross-shore structures: a one-line numerical model

The proposed numerical model simulates the short-term temporal changes in shoreline position due to a structure interrupting the longshore sediment flux. The impacts of both the groin-type construction and underwater trench of arbitrary orientation relative to the shore are discussed. In order to estimate the sediment mass trapped by the structure, a submodel of the longshore sediment transport induced by a random wave field is developed. The contribution of the surface roller in momentum balance as well as in sediment suspension is included. The shoreline changes are computed from the equation deduced from the mass conservation. The perturbations in the longshore sediment discharge caused by a structure are assumed to concentrate within some boundary area of which the spatial scale is proportional to the structure's length until the latter is exceeded by the width of the sediment flux. It is shown in particular that the total effect of a long trench (channel) and a pier in its nearshore part results in general shoreline recession except for the vicinity of a pier. The model is tested against the laboratory data of Baidei et al. (1994) and applied to the Baidara Bay coast (Kara Sea) where a pipeline would be designed.     

Alongshore Sediment Transport Near Tidal Inlets of Chilika Lagoon; East Coast of India

ABSTRACT

Chilika, a lagoon along the east coast of India, is undergoing transformation due to frequent shoreline change near inlet(s). Shoreline change near inlet includes change in position and shape of inlet, inlet channel length, and spit growth/erosion. These variable features of lagoon inlet(s) critically depend on alongshore sediment transport (LST) and discharge (water and sediment) from the lagoon to the sea. The LST and the processes responsible for sand spit growth/erosion, considered as important attributes of inlet stability, are the subject matter of the present investigation and hence the study assumes importance. The study includes integration of observational and modeling framework. Observations include nearshore wave, bathymetry, beach profile, shoreline and sediment grain size of spits while numerical modeling includes simulation of the wave using MIKE 21 Spectral Wave model and LST simulation using LITtoral DRIFT. The results indicate that the predominant wave directions as S and SSE, which induces round the year south to north alongshore transport with significant seasonal variation in magnitude. The estimated LST closely matches with previous studies near Chilika inlet and for other locations along the Odisha coast. Besides temporal variability, the study reveals spatial variability in alongshore transport near Chilika inlet and considers it as one of the important attributes along with northward spit growth for inlet migration/closure/opening.     

Morphodynamics of a high discharge tropical delta, San Juan River, Pacific coast of Colombia

The San Juan River has one of the most extensive and best developed deltas on the Pacific coast of South America, measuring 800 km². The river drainage basin measures 16?465 km² and is located in one of the areas with the highest precipitation in the western hemisphere. The annual rainfall varies from 7000 to 11?000 mm, and as a result the San Juan River has the highest water discharge (2550 m³ s⁻¹), sediment load (16×10⁶ t yr⁻¹), and basin-wide sediment yield (1150 t km⁻² yr⁻¹) on the west coast of South America. The San Juan delta growth began approximately 5000 years BP. The structure of the delta is determined by the interactions between fluvial deposition and the effect of 1.7-m significant swells, mostly from the SW, and strong tidal currents. Analysis of delta progradation indicates that during 1848-1992 the morphology of the delta was characterized by beach ridge accretion, spit growth, narrowing of inlets, and a general advance of the delta shoreline. During the past decade processes such as rapid erosion of the delta shore, narrowing of barrier islands, and breaching of a new inlet, are the result of a long-term relative sea-level rise of 2.6 mm yr⁻¹ due to tectonically induced subsidence coupled with a eustatic rise of sea-level. The delta also experiences strong oceanographic manifestations associated with the El Niño-La Niña cycle, causing regional sea-level elevation of 20-30 cm during El Niño years. Recent coastal subsidence in the delta is evidenced by: (1) increased occurrence of non-storm washover events; (2) increased erosion of barrier islands with average loss of 11 m yr⁻¹ during 1993-1997; and (3) a relative sea-level rise of 3.4 mm yr⁻¹ during 1991-1999. The morphology and recent evolution of the San Juan delta are unique when compared to other deltas of South America because of the singular combination of extreme climatic, geologic, and oceanographic conditions under which the delta has formed and the absence of human-induced impact in the drainage basin.     

Long-term variation of longshore sediment transport

For planning and designing a new harbour located on the sand coast of Nouakchott, Mauretania, the Bijker formula was adopted to compute the longshore sediment transport. The shoreline is nearly straight at this site. The beach is composed of fine sand with a median grain diameter of D₅₀ = 200 μm. The beach slope is about 1:20. Wave observation data from 1976 to 1982 were used for the formula. Computed results show a clear variation of annual transport. The ratio maximum:mean value is 1.31, and the ratio maximum: minimum is 1.89 in seven years.Probability analysis indicates that the long-term variation of the longshore transport follows the Gumbel distribution. Accordingly, the formulae which can predict the probable and most disadvantageous total sediment transport values for multiple years blocked by a littoral barrier are derived.     

Sea-level, sediment supply and coastal changes: Examples from the coast of Ireland

Sediment supply and pre-existing shoreline morphology are crucial factors in controlling coastal changes due to sea-level rise. Using examples from both southeast and northeast Ireland, it can be shown that sea-level change may trigger a sequence of events which leads to both static and dynamic shoreline equilibrium. Cliff erosion and longshore sediment movement in east Co. Wexford has led to injection of sediment onto the shelf, and the growth, under both wave and tide regimes, of linear offshore shoals. These shoals now control the pattern of shoreline erosion and provide a template for possible stepwise evolution of the coast under any future sea-level rise. In contrast, the nearby coast of south Co. Wexford comprises a series of coarse clastic barriers moving monotonously onshore, via overwash processes. Here the behavior of the barrier is conditioned by the antecedent morphology of both the beach face and stream outlet bedforms. Finally, the rock platform coast of Co. Antrim presents a far more resistant shoreline to incident marine processes, yet even here there is strong evidence of present process control over so-called ‘raised’ platforms and embayments. It is concluded that coastal sediment supply and dynamics, together with coastal morphology and its interaction with waves, present a far more complex variety of sea-level indicators than is normally acknowledged.     

杭州湾北岸岸滩变化对海平面上升的响应——以龙泉—南竹港岸段为例

相对海平面上升引发的海岸潜在侵蚀是海岸带资源利用与规划的重点关注内容.基于杭州湾北岸龙泉—南竹港岸段实测断面资料,利用历史岸线后退和淹没法则计算法分析了该地区的海岸变化对海平面上升的响应.结果表明:近10 a来岸滩呈侵蚀后退趋势,年侵蚀速率为3.7～5.7 m/a,相对海平面上升对岸滩迁移后退的贡献为2％～6％;未来1...     

The coastal profile in the eastern Gulf of Finland: The results of a survey and the reconstruction of the evolution in the Late Holocene

The studies carried out by the Karpinskii All-Russia Research Institute of Geology using side-scan profiling, echo sounding, and surface sediment sampling allowed revealing the detailed structure of the underwater coastal slope in the eastern Gulf of Finland. In particular, a submarine sand terrace was found at depths of 4–5 m. An attempt at the reconstruction of the coastal evolution over the period of the Late Holocene was made using mathematical modeling in order to explain the observed morphology of the submarine coastal slope. The key assumption of the concept suggested is that, at the earlier stage, the tectonic processes played the main role, while, at the later stage, the sea-level changes were of greater importance. The tectonic block comprising the investigated area of the Gulf of Finland at first rapidly increased and then it stabilized and was influenced by the sea level’s rise. These processes resulted in the formation of a series of terraces. The earlier of those are now located on dry land, while the later terraces are observed on the submarine slope. Within the concept proposed, the coastal evolution in the Late Holocene appears as a process of the gradual erosion of the above-water terraces and the formation of new underwater terraces. During the transgressive phases, the rate of the coast’s recession reached 0.5 m year⁻¹, while decreasing by a factor of two during the intermediate stages. The submarine terrace developed over the period of 3.2–1.2 thousand years ago, and it extended in equal measure due to the coast’s recession and the material’s accumulation near its external edge. During that period, the coast retreated by approximately 500 m, while the average accumulation rate could have been as high as 0.7 m³ m⁻¹ year⁻¹.     

Sediment transport and morphology at the surf zone of Presque Isle, Lake Erie, Pennsylvania

A four-year investigation of surf zone sedimentation at Presque Isle, Pennsylvania, was undertaken in preparation for the design of a segmented breakwater system. Sediment transport calculations were based on hind-cast annual wave power statistics and “calibrated” by known accretion rates at the downdrift spit terminus. 30,000 m³ of sediment reaches the peninsula annually from updrift beaches. The transport volume increases downdrift due to shoreface erosion and retreat of the peninsular neck. At the most exposed point on Presque Isle (the lighthouse) the annual transport is 209,000 m³. East of the lighthouse is a zone of net shoreface accretion as the longshore transport rate progressively decreases.

The downdrift variation in sediment supply, combined with increasing refraction and attenuation of the dominant westerly storm waves produce a systematic change in prevailing surf zone morphology. Storms produce a major longshore bar and trough along the exposed peninsular neck. The wave energy during non-storm periods is too low to significantly alter the bar which consequently becomes a permanent feature. The broad shoreface and reduced wave energy level east of the lighthouse produce a morphology characterized by large crescentic outer bars, transverse bars, and megacusps along the beach. At the sheltered and rapidly prograding eastern spit terminus the prevalent beach morphology is that of a ridge and runnel system in front of a megacuspate shore.

The morphodynamic surf zone model developed for oceanic beaches in Australia is used as a basis for interpretation of shoreface morphologic variability at Presque Isle. In spite of interference by major shoreline stabilization structures, and differences between oceanic and lake wave spectra, the nearshore bar field at Presque Isle does closely correspond to the Australian model.     

Even–odd analysis on a complex shoreline

An even–odd signal decomposition is performed on a complex shoreline having a longshore sediment transport gradient. The expected impact of erosion due to a navigation channel and structures is discussed and implications of the transport gradient on the decomposed shoreline signal are noted.     

Directional wave measurement at Haifa,Israel, and sediment transport along the Nile littoral cell

Results of three years of directional wave measurement at the Eastern Mediterranean coast of Haifa, Israel are presented. The wave-height and energy-flux distributions reveal a moderately high-energy coast with a bimodal annual cycle.The rate of wave-induced longshore sediment transport is estimated from the directional energy flux distributions. It describes an annual cycle with a maximum northward transport of 75 ± 14 × 10³ m³/month in midwinter and a southward transport of 26 ± 5 × 10³ m³/month in summer. The net annual transport is northward and computed at 110 ± 100 × 10³ m³/yr.We show that a wave-induced transport is sufficient in explaining the apparent transport of sediments in the Nile Littoral Cell, from the Nile Delta source to the Haifa Bay sink.     

堆积海岸平衡岸线轮廓的解析

对堆积海岸平衡岸线轮廓的三个表达式进行了分析和对比,其中平衡岸线轮廓表达式在一定程度上包含了潮流作用对岸线塑造的影响,适用于对凹岸和沙质海岸岸线轮廓的分析,同时也适用于对凸岸和淤泥质海岸岸线轮廓的分析,因而较基本平衡岸线形态方程和B.A.保保夫堆积岸弧方程适用范围更广。利用平衡岸线轮廓表达式,对舟山群岛金塘山和册子山附近水道的两段岸线轮廓进行了分析,结果表明:两岸段均为堆积岸弧,且理论弧长与实测弧长、理论半径与实测半径的值接近,说明理论岸线与实际岸线形态吻合得较好,同时,金塘山西部岸段较册子山西部岸段岸线形态更趋稳定,但两岸线均未达到稳定状态,目前仍处于演变过程中。     

Long-term morphological modeling of a tidal inlet: the Arcachon Basin,France

The Arcachon Lagoon on the French Atlantic coast is a triangular shaped lagoon of 20 km on a side connected to the ocean by a 3-km wide inlet between the mainland and an elongated sand spit. This tidal inlet exhibits a particularly active morphology due to locally strong tidal currents and rough wave conditions. During the past 300 years, minimum and maximum spatial extents of the Cap Ferret sand spit have varied by 8 km while one or two channels have alternately allowed circulation between the lagoon and the ocean. These impressive morphological changes have never prevented regular flushing of the lagoon, eventhough the spit came as close as 300 m from the coast during the 18th century. According to Bruun's concept of tidal inlet stability [Theory and Engineering (1978), 510 pp.], the balance between longshore littoral transport and the tidal prism ensures the perpetuity of the inlet.Process modeling was believed to give better insight into the respective roles of tides and waves in driving the long-term morphological changes of the inlet. A two-dimensional horizontal morphodynamic model was therefore developed, combining modules for hydrodynamics, waves, sediment transport and bathymetry updates. The use of process models at a scale of decades requires a schematization of the input conditions. We defined representative mean annual wave and tide conditions with respect to sediment transport, i.e. conditions that induce the same annual transport as measured in the field. Driven by these representative conditions, simulations run from the 1993 bathymetry show that the tide is responsible for the opening of a new channel at the extremity of the sand spit (where tidal currents are the strongest), while waves induce a littoral transport responsible for the longshore drift of sand bodies across the inlet. One particular simulation consisted in running the model from a hypothetical initial topography where the channels are filled with sand and the entire inlet is set to a constant depth (3 m). The results show the reproduction of a channel and bar system comparable to historical observations, which supports the idea that the lagoon is unlikely to be disconnected from the ocean, provided tide and wave conditions remain fairly constant in the following decades.