The influence of seaward boundary conditions on swash zone hydrodynamics

The influence of the seaward boundary condition on the internal swash hydrodynamics is investigated. New numerical solutions of the characteristics form of the nonlinear shallow-water equations are presented and applied to describe the swash hydrodynamics forced by breaking wave run-up on a plane beach. The solutions depend on the specification of characteristic variables on the seaward boundary of the swash zone, equivalent to prescribing the flow depth or the flow velocity. It is shown that the analytical solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. J. Fluid Mech. 16, 113–125] is a special case of the many possible solutions that can describe the swash flow, but one that does not appear appropriate for practical application for real waves. The physical significance of the boundary conditions is shown by writing the volume and momentum fluxes in terms of the characteristic variables. Results are presented that illustrate the dependence of internal flow depth and velocity on the boundary condition. This implies that the internal swash hydrodynamics depend on the shape and wavelength of the incident bore, which differs from the hydrodynamic similarity inherent in the analytical solution. A solution appropriate for long bores is compared to laboratory data to illustrate the difference from the analytical solution. The results are important in terms of determining overwash flows, flow forces and sediment dynamics in the run-up zone.     

Morphodynamic zone variability on a microtidal barred beach

This paper builds on the work of Masselink [Masselink, G., 1993. Simulating the effects of tides on beach morphodynamics. J. Coast. Res. SI 15, 180–197.] on the use of the residence times of shoaling waves, breaking waves and swash/backwash motions across a cross-shore profile to qualitatively understand temporal beach behaviour. We use a data set of in-situ measurements of wave parameters (height and period) and water depth, and time-exposure video images overlooking our single-barred intertidal measurement array at Egmond aan Zee (Netherlands) to derive boundaries between the shoaling zone, the surf zone and the swash zone. We find that the boundaries are functional dependencies of the local relative wave height on the local wave steepness. This contrasts with the use of constant relative wave heights or water levels in earlier work. We use the obtained boundaries and a standard cross-shore wave transformation model coupled to an inner surf zone bore model to show that large (> 5) relative tide ranges (RTR, defined as the ratio tide range–wave height) indicate shoaling wave processes across almost the entire intertidal profile, with surf processes dominating on the beach face. When the RTR is between 2 and 5, surf processes dominate over the intertidal bar and the lower part of the beach face, while swash has the largest residence times on the upper beach face. Such conditions, associated with surf zone bores propagating across the bar around low tide, were observed to cause the intertidal bar to migrate onshore slowly and the upper beach face to steepen. For RTR values less than about 2, surf zone processes dominate across the intertidal bar, while the dominance of swash processes now extends across most of the beach face. The surf zone processes were now observed to lead to offshore bar migration, while the swash eroded the upper beach face.     

Measurements and modelling of the advection of suspended sediment in the swash zone by solitary waves

Novel laboratory experiments and numerical modelling have been performed to study the advection scales of suspended sediment in the swash zone. An experiment was designed specifically to measure only the sediment picked up seaward of the swash zone and during bore collapse. The advection scales and settling of this sediment were measured during the uprush along a rigid sediment-free beach face by a sediment trap located at varying cross-shore positions. Measurements were made using a number of repeated solitary broken waves or bores. Approximately 25% of the pre-suspended sediment picked up by the bores reaches the mid-swash zone (50% of the horizontal run-up distance), indicating the importance of the sediment advection in the lower swash zone. The pre-suspended sediment is sourced from a region seaward of the shoreline (still water line) which has a width of about 20% of the run-up distance. An Eulerian–Lagrangian numerical model is used to model the advection scales of the suspended sediment. The model resolves the hydrodynamics by solving the non-linear shallow water equations in an Eulerian framework and then solves the advection–diffusion equation for turbulence and suspended sediment in a Lagrangian framework. The model provides good estimates of the measured mass and distribution of sediment advected up the beach face. The results suggest that the correct modelling of turbulence generation prior to and during bore collapse and the advection of the turbulent kinetic energy into the lower swash is important in resolving the contribution of pre-suspended sediment to the net sediment transport in the swash zone.     

On low-frequency waves in the surf and swash

Low-frequency waves in the surf and swash zones on various beach slopes are discussed using numerical simulations. Simulated surface elevations of both primary waves and low-frequency waves across the surf zone were first compared with experimental data and good agreement found. Low-frequency wave characteristics are then discussed in terms of their physical nature and their relationship to the primary wave field on a series of sea bottom slopes. Unlike primary waves, low-frequency wave energy increases towards the shoreline. Low-frequency waves in the surf and swash are a function of incident waves and the sea bottom slope and hence the saturation level of the surf zone. Wave energy on a gently sloping beach is dominated by low-frequency waves while primary waves play a significant role on a steep beach. Low-frequency wave radiation from the surf zone on a given beach depends on primary wave frequency and beach slope. However, a very poor correlation was found between surf similarity parameter and low-frequency wave radiation.     

粤东后江湾冲流带滩面高频振动及动力作用分析

利用涌浪影响下短时段内的冲流带滩面高频高程数据和碎波带波流资料,在奇异谱分析(SSA)的基础上,对比研究了不同形态滩面的冲淤变化趋势、趋势分布形状、冲淤变化周期和冲淤变化强度,以及同一条剖面不同桩点间各因素间的变化关系;用交叉谱方法探索了每分钟滩面高频冲淤变化与碎波带长重力波间的作用关系。分析结果表明,滩角韵律地形引起的冲流分流作用促进了滩脊向滩谷的泥沙转运,冲流带滩面存在明显的长重力波频段的周期性冲淤振动,滩面冲淤振动强度由滩面下部向上部递减,碎波带长重力波对滩面高频冲淤变化起重要作用。     

粤东后江湾冲流带滩面高频振动及动力作用分析

利用涌浪影响下短时段内的冲流带滩面高频高程数据和碎波带波流资料,在奇异谱分析(SSA)的基础上,以比研究了不同形态滩面的冲淤变化趋势、趋势分布形状、冲淤变化周期和冲淤变化强度,以及同一条剖面不同桩点间各因素间的变化关系;用交叉谱方法探索了每分钟滩面高频冲淤变化与碎波带长重力波间的作用关系.分析结果表明,滩角韵律地形引起的冲流分流作用促进了滩脊向滩谷的泥沙转运,冲流带滩面存在明显的长重力波频段的周期性冲淤振动,滩面冲淤振动强度由滩面下部向上部递减,碎波带长重力波对滩面高频冲淤变化起重要作用.     

Numerical experiments of swash oscillations on steep and gentle beaches

A weakly non-linear Boussinesq model with a slot-type shoreline boundary is used to simulate swash oscillations on beaches. Numerical simulations of swash were compared with laboratory measurements and in general good agreement found (less than 15% root-mean-square error of surface elevation except in regular waves). A series of numerical experiments on shoreline movement were then performed for a range of beach slopes and incident wave conditions. The resulting swash characteristics are then discussed in terms of their physical nature and spectral properties. On steep slopes, both individual bores and infragravity waves are equally significant in driving the swash while infragravity waves alone drive them on mild slopes. Swash excursions on any given slope are found to be highest when individual bores from a partially saturated surf zone ride on top of low-frequency waves. This is confirmed by the relationship found between swash excursion and wave groupiness in the surf zone. Swash excursions increase with increasing incident wave energy, even in fully saturated surf zones. However, a poor correlation is found between swash excursion and the surf similarity parameter due to the involvement of infragravity wave energy in the swash.     

冲流带海滩高频振动探讨

在粤东汕尾寮嘴口岬间海滩冲流带设置两条剖面,利用2003年10月13日一个潮周期实测高频剖面数据(采样间隔为1min和6min),分析了海滩的高频振动特征。并结合同期实测碎波带水位波动,探讨了海滩高频振动的动力原因。分析表明,此海滩过程主要以堆积为主,并表现有显著周期的振动：其日内变化受潮汐控制,表现为涨潮堆积、落潮侵蚀;波能对海滩高频振动过程有着重要的影响。     

Wave-induced water table fluctuations,sediment transport and beach profile change: Modeling and comparison with large-scale laboratory experiments

Coastal groundwater systems can have a considerable impact on sediment transport and foreshore evolution in the surf and swash zones. Process-based modeling of wave motion on a permeable beach taking into account wave-aquifer interactions was conducted to investigate the effects of the unconfined coastal aquifer on beach profile evolution, and wave shoaling on the water table. The simulation first dealt with wave breaking and wave runup/rundown in the surf and swash zones. Nearshore hydrodynamics and wave propagation in the cross-shore direction were simulated by solving numerically the two-dimensional Navier–Stokes equations with a k–ε turbulence closure model and the Volume-Of-Fluid technique. The hydrodynamic model was coupled to a groundwater flow model based on SEAWAT-2000, the latter describing groundwater flow in the unconfined coastal aquifer. The combined model enables the simulation of wave-induced water table fluctuations and the effects of infiltration/exfiltration on nearshore sediment transport. Numerical results of the coupled ocean/aquifer simulations were found to compare well with experimental measurements. Wave breaking and infiltration/exfiltration increase the hydraulic gradient across the beachface and enhance groundwater circulation inside the porous medium. The large hydraulic head gradient in the surf zone leads to infiltration across the beachface before the breaking point, with exfiltration taking place below the breaking point. In the swash zone, infiltration occurs at the upper part of the beach and exfiltration at the lower part. The simulations confirm that beaches with a low water table tend to be accreted while those with a high water table tend to be eroded.     

Sedimentology and morphodynamics of a macrotidal beach, Pendine Sands, SW Wales

The foreshore of Pendine Sands forms the seaward part of an extensive, sandy coastal barrier in a shallow Carmarthen Bay, SW Wales. The sedimentological features of the macrotidal foreshore reflect a tide-induced modification of nearshore wave characteristics. As the tide ebbs, the breaker height may decrease, the surf zone widens and becomes increasingly dissipative, and swash/backwash velocities diminish. A concomitant change from plunging to spilling breakers and increasingly symmetrical swash zone flows are associated with a decreasing beach gradient.

A zero net transport model demonstrates that the beach profile is self-stabilising in the short-term, and periodic levelling has shown that the beach is in long-term equilibrium with prevailing conditions, though this does not preclude a significant dynamic response to changing tides and waves.

The flow regimes of wave-generated currents decline as the tide ebbs, and normal beach processes do not usually affect the lower foreshore. Accordingly, there is an overall seaward-fining of the primary framework component of the sands. In more detail, this framework component displays a slight seaward-coarsening across an upper foreshore dominated by high water swash and surf; a rapid seaward-fining across the mid-foreshore in response to the ebb-attenuating swash zone flow velocities; and a slight seaward-fining across the lower foreshore under the action of nearshore shoaling waves. Bedforms vary from a swash/backwash emplaced flat bed across the upper foreshore to the small ripples of nearshore asymmetric oscillatory flows across the lower foreshore.

The surface sediment veneer is not representative of the subsurface sediments which form in response partly to fairweather conditions, partly to storms. The upper foreshore is characterised by swash/backwash emplaced plane bedding in fine sands frequently disrupted by bubble cavities. The mid-foreshore is composed of coarser-grained shelly traction clogs arranged as landward- and seaward-dipping large-scale cross bedding and/or plane bedding; these are probably storm breaker/surf deposits. The lower foreshore, though partially and sometimes totally bioturbated, shows landward-dipping small-scale cross bedding in very fine sands sorted by nearshore shoaling waves.

Tide- and storm-induced modification of the nearshore flow regimes therefore produces a distinctive shore-normal array of sedimentary facies. Each facies is characterised by diagnostic textural and structural signatures. A prograding sequence of such macrotidal deposits would be similar to, but more extensive than, a comparable microtidal sequence.     

Simulation and prediction of swash oscillations on a steep beach

This paper presents numerical simulations and analytical predictions of key aspects of swash oscillations on a steep beach. Simulations of the shoreline displacement based on bore run-up theory are found to give excellent agreement with recent experimental data for regular waves, wave groups and random waves. The theory is used to derive parameters that predict the onset of swash saturation and the spectral characteristics of the saturated shoreline motion. These parameters are again in good agreement with the measured laboratory data and are also consistent with previous experimental data. Simulation of irregular wave run-up using a series of overlapping monochromatic swash events is found to reproduce typical features of swash oscillations and can accurately describe both the low and high frequency spectral characteristics of the swash zone. In particular, the low frequency components of the run-up can be modelled directly using a sequence of incident short wave bores, with no direct long wave input to the numerical simulations. This suggests that wave groupiness must be accounted for when modelling shoreline oscillations.     

Surf zone dynamics simulated by a Boussinesq type model. Part II: surf beat and swash oscillations for wave groups and irregular waves

This is the second of three papers on the modelling of various types of surf zone phenomena. In the first paper the general model was described and it was applied to study cross-shore motion of regular waves in the surf zone. In this paper, part II, we consider the cross-shore motion of wave groups and irregular waves with emphasis on shoaling, breaking and runup as well as the generation of surf beats. These phenomena are investigated numerically by using a time-domain Boussinesq type model, which resolves the primary wave motion as well as the long waves. As compared with the classical Boussinesq equations, the equations adopted here allow for improved linear dispersion characteristics and wave breaking is modelled by using a roller concept for spilling breakers. The swash zone is included by incorporating a moving shoreline boundary condition and radiation of short and long period waves from the offshore boundary is allowed by the use of absorbing sponge layers. Mutual interaction between short waves and long waves is inherent in the model. This allows, for example, for a general exchange of energy between triads rather than a simple one-way forcing of bound waves and for a substantial modification of bore celerities in the swash zone due to the presence of long waves. The model study is based mainly on incident bichromatic wave groups considering a range of mean frequencies, group frequencies, modulation rates, sea bed slopes and surf similarity parameters. Additionally, two cases of incident irregular waves are studied. The model results presented include transformation of surface elevations during shoaling, breaking and runup and the resulting shoreline oscillations. The low frequency motion induced by the primary-wave groups is determined at the shoreline and outside the surf zone by low-pass filtering and subsequent division into incident bound and free components and reflected free components. The model results are compared with laboratory experiments from the literature and the agreement is generally found to be very good. Finally the paper includes special details from the breaker model: time and space trajectories of surface rollers revealing the breakpoint oscillation and the speed of bores; envelopes of low-pass filtered radiation stress and surface elevation; sensitivity of surf beat to group frequency, modulation rate and bottom slope is investigated. Part III of this work (Sørensen et al., 1998) presents nearshore circulations induced by the breaking of unidirectional and multi-directional waves.     

The role of bore collapse and local shear stresses on the spatial distribution of sediment load in the uprush of an intermediate-state beach

Spatial variations in sediment load in the swash uprush and textural properties of sediment in transport were evaluated to investigate the mechanisms responsible for sediment transport during wave uprush. Four streamer traps were deployed at 2.0-m intervals across the swash zone of a sheltered, microtidal sandy beach at Port Beach, Western Australia, over a 4-day period. During these trapping experiments, offshore significant wave heights were 0.3–0.5 m and wave periods were about 10 s. The average width of the uprush zone was 6.9 m and the average uprush duration was 5.9 s. Cross-shore distributions of sediment load for 70 uprush events reveal a maximum in sediment load landward of the base of the swash (at about 20% of swash width) during single events and a maximum closer to mid-swash (at about 40% of swash width) during multiple events characterized by swash interactions. Settling velocity distributions of trap samples during individual uprush events are similar to distributions found on the beach surface, with the lowest settling velocities (finest sediments) near the base of the swash zone and maximum settling velocities (coarsest sediments) around the mid-swash position. It was found that sediment transport during wave uprush occurs through two distinct mechanisms: (1) sediment entrainment during bore collapse seaward of the base of the swash zone and subsequent advection of this bore-entrained sediment up the beach by wave uprush; and (2) in situ sediment entrainment and transport induced by local shear stresses during wave uprush. Both mechanisms are considered important, but the first mechanism is considered most significant during the early stages of wave uprush when sediment is transported mainly in suspension, while the second mechanism is likely to dominate the mid- to later stages of wave uprush when sediment is transported mainly by sheet flow. The relative importance of the two mechanisms will vary between different beaches with the morphodynamic state of the beach (reflective versus dissipative) expected to play a major role.     

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool.     

Swash zone sediment fluxes: Field observations

This paper describes newly obtained, high-frequency observations of beach face morphological change over numerous tidal cycles on a macrotidal sandy beach made using a large array of ultrasonic altimeters. These measurements enable the net cross-shore sediment fluxes associated with many thousands of individual swash events to be quantified. It is revealed that regardless of the direction of net morphological change on a tidal time scale, measured net fluxes per event are essentially normally distributed, with nearly equal numbers of onshore and offshore-directed events. The majority of swash events cause net cross-shore sediment fluxes smaller than ± 50 kg m^− 1 and the mean sediment flux per swash event is only O(± 1 kg m^− 1) leading to limited overall morphological change. However, much larger events which deposit or remove hundreds of kilograms of sand per meter width of beach occur at irregular intervals throughout the course of a tide. It was found that swash–swash interactions tend to increase the transport potential of a swash event and the majority of the swash events that cause these larger values of sediment flux include one or more interactions. The majority of the larger sediment fluxes were therefore measured in the lower swash zone, close to the surf/swash boundary where swash–swash interactions are most common. Despite the existence of individual swash events that can cause fluxes of sediment that are comparable to those observed on a tidal time scale, frequent reversals in transport direction act to limit net transport such that the beach face volume remains in a state of dynamic equilibrium and does not rapidly erode or accrete.     

Alongshore fluid motions in the swash zone of a sandy and gravel beach

Field experiments were conducted on a low-gradient, high-energy sandy beach (Truc Vert, France) and a steep, low-energy gravel beach (Slapton, UK) to examine alongshore-directed currents within the swash zone. At Truc Vert, data were collected over 33 tidal cycles with offshore significant wave heights of 1–4 m and periods of 5–12 s. At Slapton data were collected during 12 tides with wave heights of 0.3–1 m and periods of 4–9 s. The swash motion was predominantly at infragravity frequencies at Truc Vert and incident frequencies at Slapton.     

Suspended sediment transport in the swash zone of a dissipative beach

Simultaneous high frequency field measurements of water depth, flow velocity and suspended sediment concentration were made at three fixed locations across the high tide swash and inner surf zones of a dissipative beach. The dominant period of the swash motion was 30–50 s and the results are representative of infragravity swash motion. Suspended sediment concentrations, loads and transport rates in the swash zone were almost one order of magnitude greater than in the inner surf zone. The vertical velocity gradient near the bed and the resulting bed shear stress at the start of the uprush was significantly larger than that at the end of the backwash, despite similar flow velocities. This suggests that the bed friction during the uprush was approximately twice that during the backwash.The suspended sediment profile in the swash zone can be described reasonably well by an exponential shape with a mixing length scale of 0.02–0.03 m. The suspended sediment transport flux measured in the swash zone was related to the bed shear stress through the Shields parameter. If the bed shear stress is derived from the vertical velocity gradient, the proportionality coefficient between shear stress and sediment transport rate is similar for the uprush and the backwash. If the bed shear stress is estimated using the free-stream flow velocity and a constant friction factor, the proportionality factor for the uprush is approximately twice that of the backwash. It is suggested that the uprush is a more efficient transporter of sediment than the backwash, because the larger friction factor during the uprush causes larger bed shear stresses for a given free-stream velocity. This increased transport competency of the uprush is necessary for maintaining the beach, otherwise the comparable strength and greater duration of the backwash would progressively remove sediment from the beach.     

On the transport of suspended sediment by a swash event on a plane beach

We develop solutions for the transport of suspended sediment by a single swash event following the collapse of a bore on a plane beach, and we investigate the morphodynamical role that such transport may play. Although the intrinsic asymmetry between uprush and backwash velocities tends to encourage the export of sediment, we find that swash events may be effective in distributing across the swash zone much or all of the sediment mobilised by bore collapse; additionally, settling lag effects may promote a weak onshore movement of sediment. We quantify both effects in terms of the properties of the sediment and of the swash event, and comment on the relationship between our findings and recent field studies of swash zone sediment transport.     

Reconstruction of paleo-wave conditions during the Late Pleistocene from marine terrace deposits, Monterey Bay, California

The Santa Cruz coastal terrace fringes much of the northern Monterey Bay region, California. It consists mainly of a regressive sequence of high-energy, barred nearshore marine sediments deposited during the last (Sangamonian) highstand of sea level. This sequence can be sub-divided into several depth-dependent facies on the basis of paleo-current data and vertical sequence of sedimentary structures. These include a lower shoreface facies deposited in 10–16 m water depth, an upper shoreface facies (including both a storm-dominated assemblage and a surf zone assemblage) deposited in 0–10 m water depth, and a foreshore facies deposited in the swash zone, up to 3.5 m above high tide.

The magnitudes of the storm events responsible for depositing these sediments were estimated by calculating paleo-wave heights using a variety of criteria (e.g., critical threshold equations, breaker depths, berm heights). In addition, the climate and paleogeography during the deposition of these sediments were essentially the same as today, allowing the use of present-day wave statistics to estimate the frequency of these storm events. The largest storms formed offshore-flowing currents (e.g., rip, wind-forced, and possibly storm-surge ebb currents) that resulted in the deposition of approximately 30% of the sediments seaward of the surf zone; however, the magnitude and frequency of these events are unknown. The remaining 70% of the sediment beyond the surf zone was deposited in response to smaller storm waves which were, on the average, at least 1.6 m high; such waves presently occur no more than 15% of the time. Sediments deposited during “fairweather” conditions (i.e., the remaining 85% of the time) have a low preservation potential, and are generally not preserved in this facies. In contrast, surf zone sediments were deposited by a variety of processes associated with waves whose maximum offshore heights were probably ≤ 2.2 m; such waves presently occur up to 92% of the time. Sediments within the swash zone were deposited by waves up to 3 m high, the largest of which presently occur approximately 2% of the time.

Most of the sediments were deposited by storms of intermediate magnitude and frequency; different facies, however, appear to preferentially record events of different recurrence intervals. In particular, surf zone sediments were deposited under relatively small storm and post-storm conditions, whereas sediments deposited farther offshore record increasingly larger, less frequent storm events. Relatively rare events (e.g., the 100 or 1000 yr events) do not appear to have significantly affected sedimentation in these nearshore environments.