Migrating sand waves

A simple mathematical model is described, which reproduces the major features of sand waves' appearance and growth and in particular predicts their migration speed. The model is based on the linear stability analysis of the flat configuration of the sea bottom subject to tidal currents. Attention is focused on the prediction of the complex growth rate that bottom perturbations undergo because of both oscillatory fluid motions and residual currents. While the real part _r of controls the amplification or decay of the amplitude of the bedforms, the imaginary part _i is related to their migration speed. Previous works on the migration of the sand waves (Németh etal. 2002) consider a forcing tide made up by the M2 constituent (oscillatory period equal to 12 h) plus the residual current Z0 and predict always a downcurrent migration of the bedforms. However, field cases exist of upcurrent-migrating sand waves (downcurrent/upcurrent-migrating sand waves mean bedforms moving in the direction of the steady residual tidal current or in the opposite direction, respectively). The inclusion of a tide constituent characterized by a period of 6 h (M4) is the main novelty of the present work, which allows for the prediction of the migration of sand waves against the residual current Z0. Indeed, the M4 tide constituent, as does also the residual current Z0, breaks the symmetry of the problem forced only by the M2 tide constituent, and induces sand-wave migration. The model proposed by Besio etal. (2003a) forms the basis for the present analysis. Previous works on the subject (Gerkema 2000; Hulscher 1996a,b; Komarova and Hulscher 2000) are thus improved by using a new solution procedure (Besio etal. 2003a) which allows for a more accurate evaluation of the growth rate for arbitrary values of the parameter r, which is the ratio between the horizontal tidal excursion and the perturbation wavelength. Responsible Editor: Jens Kappenberg     

Grain size dependency in the occurrence of sand waves

Sandy shallow seas, like the North Sea, are very dynamic. Several morphological features are present on the bed, from small ripples to sand waves and large tidal sandbanks. The larger patterns induce significant depth variations that have an impact on human activities taking place in this area. Therefore, it is important to know where these large-scale features occur, what their natural behaviour is and how they interact with human activities. Here, we extend earlier research that compares the results of an idealized model of large-scale seabed patterns with data of seabed patterns in the North Sea. The idealized model is extended with a grain size dependency. The adaptations lead to more accurate predictions of the occurrence of large-scale bed forms in the North Sea. Therefore, grain size dependency and, in particular, critical shear stress are important to explain the occurrence of sand waves and sandbanks in the North Sea. Responsible Editor: Alejandro Souza     

Modelling sand–mud morphodynamics in the Friesche Zeegat

The objective of the study presented in this paper is to investigate the predictive capabilities of a process-based sand–mud model in a quantitative way. This recently developed sand–mud model bridges the gap between noncohesive sand models and cohesive mud models. It explicitly takes into account the interaction between these two sediment fractions and temporal and spatial bed composition changes in the sediment bed [Van Ledden (2002) 5:577–594, Van Ledden et al. (2004a) 24:1–11, Van Ledden et al. (2004b) 54:385–391]. The application of this model to idealized situations has demonstrated a good qualitative agreement between observed and computed bed levels and bed composition developments. However, in real-life situations, a realistic quantitative prediction of the magnitude and timescale of this response is important to assess the short-term and long-term impacts of human interventions and/or natural changes. For this purpose, the Friesche Zeegat in the Wadden Sea (the Netherlands) is used as a reference to hindcast the morphological response in the period 1970–1994. Due to the closure of the Lauwerszee in 1969, the tidal prism of this tidal basin was reduced by about 30%. Significant changes in the bed level and bed composition have occurred in the decades following the closure to adjust to the new hydrodynamic conditions. We modeled the long-term bed level and bed composition development in the Friesche Zeegat in the period 1970–1994 starting with the geometry of 1970 by using a research version of Delft3D, which incorporates the sand–mud formulations proposed by [Van Ledden (2002) 5:577–594].The computed total net deposition in the tidal basin in the period 1970–1994 agrees well with the observations, but the observed decrease of the import rate with time is not predicted. The model predicts net deposition in the deeper parts and at the intertidal area in the basin and net erosion in between, which resembles the observations qualitatively. Furthermore, the computed distribution of sand and mud in the basin of the Friesche Zeegat appears to be realistic. Analysis of the results shows that the absence of the decreasing import rate in the basin is caused by a poor quantitative prediction of the changes in the hypsometry of the basin. Because of this, the computed velocity asymmetry in the main channel tends toward flood dominance, whereas the observations indicate that the system is ebb-dominant in 1992. Although the sand–mud model needs to be further improved and verified, the results presented in this paper indicate that the model can be applied as a first step to estimate the effects of human interventions on the large-scale bed level and bed composition changes in tidal systems with sand and mud.     

Non-linear response of shoreface-connected sand ridges to interventions

A non-linear morphodynamic model of a microtidal coastal shelf is used to study the response of shoreface-connected sand ridges and the net sand balance of the shelf to large-scale interventions. The model describes the interaction between storm-driven currents and the erodible bottom. The transport of sediment comprises both bedload and suspended load contributions and is due to the joint action of waves (stirring of sediment from the bed) and net currents (causing transport). Three basic types of interventions are studied: extracting sand from ridges, nourishing sand at the shelf and constructing navigation channels. The model results indicate that for all interventions studied a relatively fast local recovery (time scale of decades to centuries) of the disturbed bathymetry to its original pattern takes place. Readjustment of the global system to its original equilibrium state (the saturation process) occurs on a longer time scale (several centuries). During the adjustment stage, significant net sand exchanges between inner shelf and adjacent outer shelf and near-shore zone occur. The results further suggest that extraction of sand from the shelf and dredging of navigation channels have negative implications for the stability of the beach (its sand volume decreases).Responsible Editor: Iris Grabemann     

Internal nonlinear tidal waves generated at the Strait of Messina

Large amplitude internal waves were observed north and south of the Strait of Messina during two different periods. A comparison between the two sets of data is made. The behaviour of the shape of the waves is analysed from the physical parameters and two possible interpretations of these waves are given. The mechanism of formation related to the tide in the Strait is also discussed.     

Modelling offshore sand wave evolution

We present a two-dimensional vertical (2DV) flow and morphological numerical model describing the behaviour of offshore sand waves. The model contains the 2DV shallow water equations, with a free water surface and a general bed load formula. The water movement is coupled to the sediment transport equation by a seabed evolution equation. Using this model, we investigate the evolution of sand waves in a marine environment. As a result, we find sand wave saturation for heights of 10–30% of the average water depth on a timescale of decades. The stabilization mechanism, causing sand waves to saturate, is found to be based on the balance between the shear stress at the seabed and the principle that sediment is transported more easily downhill than uphill. The migration rate of the sand waves decreases slightly during their evolution. For a unidirectional steady flow the sand waves become asymmetrical in the horizontal direction and for a unidirectional block current asymmetrical in the vertical. A sensitivity analysis showed the slope effect of the sediment transport plays an important role herein. Furthermore, the magnitude of the resistance at the seabed and the eddy viscosity influence both the timescale and height of sand waves. The order of magnitudes found of the time and spatial scales coincide with observations made in the southern bight of the North Sea, Japan and Spain.     

The formation of tidal sand waves: Fully three-dimensional versus shallow water approaches

Tidal sand waves, also named tidal dunes, are large scale bedforms generated by the growth of perturbations of the sea bottom driven by tidal currents. Indeed, the interaction of an oscillatory tidal current with a bottom waviness gives rise to steady recirculating cells which tend to drag the sediment from the troughs towards the crests of the bottom perturbation. The net motion of the sediment towards the crests is opposed by gravity force and the growth of the perturbation is controlled by a balance between these two effects. In the literature, to determine the conditions which lead to the formation of sand waves and to determine the characteristics of the bedforms generated by this instability mechanism, both fully three-dimensional and shallow water approaches are employed. The shallow water approach is computationally less expensive than the fully three-dimensional one but, in many cases, it might be less accurate. This paper compares the quantitative predictions obtained by means of the two approaches and quantifies the range of the parameters such that the shallow water approximation provides reliable predictions.     

Sensitivity of tidal sand wavelength to environmental parameters: A combined data analysis and modelling approach

An integrated field data-modelling approach is employed to investigate relationships between the wavelength of tidal sand waves and four environmental parameters: tidal current amplitude, water depth, tidal ellipticity and median grain size. From echo sounder data at 23 locations on the Dutch continental shelf, the average wavelengths of observed sand waves are determined and compared with the wavelengths obtained with a process-based model. The latter describes the initial formation of these bedforms due to feedbacks between the tidal current and the erodible bed and uses environmental parameters for the 23 locations as input. Good agreement between observed and modelled wavelengths is found if the bottom stress experienced by tidal currents is adequately quantified. Model results show that the wavelength of sand waves increases with increasing water depth, tidal ellipticity and grain size (coarse sand), whilst it decreases with increasing tidal current amplitude and grain size (fine sand). Due to the limited number of stations and the fact that all four parameters change from location to location, the modelled relationships are only partly supported by the field observations.     

Modelling sand wave migration in shallow shelf seas

Sand waves form a prominent regular pattern in the offshore seabed of sandy shallow seas. The positions of sand-wave crests and troughs slowly change in time. Sand waves are usually assumed to migrate in the direction of the residual current. This paper considers the physical mechanisms that may cause sand waves to migrate and methods to quantify the associated migration rates. We carried out a theoretical study based on the assumption that sand waves evolve as free instabilities of the system. A linear stability analysis was then performed on a 2DV morphological model describing the interaction between the vertically varying water motion and an erodible bed in a shallow sea. Here, we disrupted the basic tidal symmetry by choosing a combination of a steady current (M₀) and a sinusoidal tidal motion (M₂) as the basic flow. We allowed for two different physical mechanisms to generate the steady current: a sea surface wind stress and a pressure gradient. The results show that similar sand waves develop for both flow conditions and that these sand waves migrate slowly in the direction of the residual flow. The rates of migration and wavelengths found in this work agree with theoretical and empirical values reported in the literature.     

Long-term evolution of sand waves in the Marsdiep inlet. II: Relation to hydrodynamics

A discussion is presented about the mechanisms that govern the spatial and seasonal variability in sand-wave height and migration speed in the 4 km wide Marsdiep tidal inlet, the Netherlands. Since 1998, current velocities and water depths have been recorded with an ADCP that is mounted under the ferry ‘Schulpengat’. In this paper, the current measurements were used to explain the sand-wave observations presented in Buijsman and Ridderinkhof [this issue. Long-term evolution of sand waves in the Marsdiep inlet. I: high-resolution observations. Continental Shelf Research, doi:10.1016/j.csr.2007.10.011]. Across nearly the entire inlet, the sand waves migrate in the flood direction. In the flood-dominated southern part of the inlet, the ‘measured’ (i.e. based on sand-wave shape and migration speed) and predicted bedload transport agree in direction, magnitude, and trends, whereas in the ebb-dominated northern part the predicted bedload and suspended load transport is opposite to the sand-wave migration. In the southern part, 55% of the bedload transport is due to tidal asymmetries and 45% due to residual currents. In addition to the well-known tidal asymmetries, asymmetries that arise from the interaction of _M2${\mathrm{M}}_2$ and its overtides with _S2${\mathrm{S}}_2$ and its compound tides are also important. It is hypothesised that in the northern part of the inlet the advection of suspended sand and lag effects govern the sand-wave migration. The relative importance of suspended load transport also explains why the sand waves have smaller lee-slope angles, are smaller, more rounded, and more three-dimensional in the northern half of the inlet. The sand waves in this part of the inlet feature the largest seasonal variability in height and migration speed. This seasonal variability may be attributed to the tides or a seasonal fluctuation in fall velocity. In both cases sediment transport is enhanced in winter, increasing sand-wave migration and decreasing sand-wave height. The influence of storms and estuarine circulation on the sand-wave variability is negligible.     

Rapid uplift,stepped marine terraces and raised shorelines on the Calabrian coast of Messina Strait,Italy

A series of 26 Quaternary shorelines, stepped between present sea level and 556 m, are studied. They are part of the flight of marine terraces of the Aspromonte region. The shorelines were determined using three geomorphological models: wave-cut platforms and gravel-built terraces associated with their sea-cliff foot, and observations of lateral changes between marine terraces and fluvial terraces. The elevation of the sea-cliff foot is either measured directly, by exposure in cross-section, or by estimation from geomorphological patterns. With caution, we connect the different landmarks of the shorelines which are discontinuous because of destruction between interfluves or because they are overlain by torrential deposits. The results of mapping show that there are few differential movements from one transect to another and mean uplift rate is 98 cm ka^?1. This rate is calculated on the basis of a correlation of the area studied with the Ravagnese Tyrrhenian site, 125 m high, whose date is isotopic substage 5e. Middle and Late Quaternary tectonic activity leads to faulting, slight folding and warping but some scarps associated with faults are actually ancient sea cliffs.     

Spatial differences in sand wave dynamics between the Amsterdam and the Rotterdam region in the Southern North Sea

The optimization of the bathymetric resurvey policy of the Netherlands Hydrographic Service requires insight into sea floor dynamics in the Southern North Sea. To study the spatial variations in sea floor dynamics, the bathymetric archives of the Netherlands Hydrographic Service are analyzed using deformation analysis, a statistical and innovative approach for bathymetric data. Based on the uncertainty of the data, our implementation of deformation analysis selects the significant spatial and temporal parameters, and provides estimates and their uncertainties for those parameters. We focus on sand wave areas in the regions of Rotterdam and of Amsterdam. In those areas, dredging takes place to guarantee a minimum depth. The results reveal a difference in sand wave migration between the two regions, over the past two decades. The dominant wavelengths of the sand waves vary within the regions, but we find a similar wavelength distribution for the two regions. We compare our results to earlier studies of the same sand wave areas in the Rotterdam region, showing similar migration rates, but different wavelengths. It is concluded, based on sand wave dynamics alone, that the Amsterdam region should be assigned a higher resurvey frequency than the Rotterdam region.     

The potential impact of bedform migration on seagrass communities in Torres Strait,northern Australia

Seagrass communities in the northwest of Torres Strait are known to disappear episodically over broad areas. Sediment mobility surveys were undertaken within two study areas during the monsoon and trade wind seasons, in the vicinity of Turnagain Island, to find out if the migration of bedforms could explain this disappearance. The two study areas covered sand bank and sand dune environments to compare and contrast their migration characteristics. Repeat multibeam sonar surveys were used to measure dune-crest migration during each season.     

Generation and evolution of internal solitary waves in the southern Taiwan Strait

ABSTRACT

The generation processes and potential energy sources of internal solitary waves (ISWs) in the southern Taiwan Strait are investigated by driving a high resolution non-hydrostatic numerical model with realistic background conditions. Two main types of ISWs are clarified according to their different energy sources. One is generated by the nonlinear disintegration of remote internal tides emanating from Luzon Strait, and the other type is generated by local tide-topography interaction at the continental slope. The basic properties and evolution processes differ between these two kinds of ISWs. The waves originated from the remote internal tides at Luzon Strait have amplitudes comparable to previous field observations. In contrast, the ISWs generated locally are much weaker than observed waves, even in the presence of a steady offshore background current, which intensifies the generation of onshore ISWs. The ISWs induced by remotely generated M₂ internal tides are stronger than those induced by K₁ internal tides, and the fraction of internal wave energy transmitted onto the shelf is not significantly influenced by the intensity of remotely generated internal tides.     

Attenuation of body waves in Southeastern Sicily (Italy)

The attenuation of P- and S-waves in Southeastern Sicily was estimated by applying two different methods in time and frequency domains. We analyzed waveforms from about 290 local events (0.6≤M_L≤4.6) recorded at a three-component digital network.By applying the pulse broadening method to the first P-wave pulse, we found an average Q_p value of ca. 140. The application of the frequency decay method provided a Q_p value of ca. 120, in the low-frequency band (3-9 Hz). Conversely, in the high frequency range (16-27 Hz) the average Q_p is significantly larger (ca. 640). The frequency decay method was also applied to S-waves spectra. In the low frequency range (2-5 Hz) the estimated average Q_s is ca. 190. As for Q_p, also Q_s, in the high frequency range (16-27 Hz), is larger (ca. 700). These results evidenced a frequency dependence of both the quality factors Q_p and Q_s, as commonly observed in tectonically active zones characterized by high degree of heterogeneity.     

Frequency dependence of site amplification factor in the Messina Strait area

The spectral ratio method is used here for evaluating the frequency dependence of a site amplification factor in the Messina Strait area. All stations exhibit the same features of spectral ratios evidencing two peaks at about 10 Hz and 16 Hz. We relate this observation to the same geological structures. In fact, all the stations (except the referenced one) are situated over pleistocenic sediments with a similar grain size. This causes the disappearing of any site effect when the average spectrum is used as a reference. MES station, situated in the city of Messina, presents a clear site effect at a different frequency (6 Hz) which cannot be related to any geological structure because no substantial difference is observed between the sediments on which this station is situated and the sediments on which the other stations are situated. MT1 station exhibits a spectral peak at about 2 Hz which can be explained with oscillations of a little sedimentary basin.     

Coastal morphological modeling to assess the dynamics of Arklow Bank, Ireland

A numerical modeling and simulation experiment is carried out to assess the sediment dynamics of Arklow Bank, Ireland. To meet a requirement for favorable site selection to establish windmills on the bank, the long-term morphological changes of the coast are studied using the CAMS （Coastal Area Morphological Shell） model of the Mike-21 suite of programs. The morphological modeling of the bank was accomplished by pursuing a probabilistic approach for the observed tide and wave characteristics that contribute significantly to the sediment transport processes over the bank. A series of simulations are performed using Mike-21 NSW （Nearshore Spectral Wind-Wave）, HD （Hydrodynamic）, and ST （Sand Transport） models to establish the coastal hydraulics parameters. The results of the morphological modeling showed that generally the bank is dynamically stable with most areas of the bank having average bed level changes on the order of ±8 cm/day.     

On the effect of subinertial phenomena on the internal lee waves generation in the Strait of Gibraltar

The generation of internal lee waves (ILW) in the Strait of Gibraltar takes place in the main sill where the tidal flow interacts with a submarine obstacle. The tidal flow is perturbed by subinertial phenomena of different nature summarized in the subinertial currents that can inhibit the ILW generation. The authors present an attempt to randomize the problem by the introduction of a Gaussian noise in the Taylor–Goldstein equation. The random number sets are generated from the statistical distribution of the previously isolated random part of the subinertial currents from experimental data taken in the area during the Gibraltar Experiment 94–96. The effect of the noise is translated into a continuous spreading of the spectrum around the solution of the noise-free problem. A stability analysis is carried out in order to determine the single neutral modes of oscillations and the phase space is divided onto regions of stability and instability as a function of the inflowing subinertial current. The methodology and results could be useful for the design and timing of oceanographic surveys in straits where the ILWs occur.     

The influence of tides, wind and waves on the net sand transport in the North Sea

Large-scale redistribution of sand by hydrodynamical processes in shelf seas is important for basin and coastal evolution on time scales of a thousand to tens of thousands of years. The influence of tides on the large-scale net sand-transport patterns in the North Sea has received much attention, but the influence of wind-driven flow and wind waves has hardly been investigated. Here, to establish the present-day situation and to develop a method that can also be used for palaeo-situations and forecasts for different sea levels, this influence is assessed for the present southern North Sea using a numerical flow model, a parametric wave model and a wave-averaged sand-transport formulation. Various forcing combinations are used to identify the dominant transport mechanisms: tides only, tides and wind, tides and waves, and combined tides, wind and waves. Wind forcing is applied in two ways to find an efficient, but still representative, method of incorporating this stochastic process: a statistical wind climatology and an observed time series. The results show that (i) the wind climatology yields a good approximation of the sand transport computed using the time series; (ii) wind-driven flow and waves only contribute significantly to the net sand transport by tides when acting together where tidal currents are small; and (iii) various combinations of forcings dominate the net sand transport in different regions of the southern North Sea: (a) tides dominate in the southern, middle and northwestern parts of the Southern Bight and in the region of The Wash; (b) tides, wind-driven flow and waves all are important in the northeastern part of the Southern Bight; and (c) wind-driven flow and waves dominate north of the Friesian Islands, in the German Bight and on the Dogger Bank. Qualitative comparison with observations shows good agreement.