Shallow Tidal Sea Research Articles

Turbulence characteristics inferred from time-lagged satellite imagery of surface algae in a shallow tidal sea

A pair of time-lagged satellite images of surface algae in the Great Barrier Reef lagoon is used to investigate characteristics of the horizontal velocity field at a spatial resolution as small as 4m. A distinctive feature is the occurrence of surface patches that are relatively clear of algae and which grow in size. These patches are interpreted as resulting from the horizontally diverging motion associated with boils. The surface divergence in such boils can be as large as ~ 0.01s−1, as deduced directly from the imagery. Overall, root-mean-squared values of divergence, vorticity, and strain rate are 45, 58, and 170, respectively, when normalized by the Coriolis parameter. By observing the algae and its fluid environment simultaneously, the analysis thus provides a glimpse of how underlying hydrodynamic processes help shape the distribution of surface algae — under the calm winds that favor the formation of dense surface aggregations.

A model to predict the migration of sand waves in shallow tidal seas

A model is presented to determine the wavelength, the height and, more importantly, the migration speed of sand waves (also named tidal dunes) in shallow tidal seas. The model is based on a linear stability analysis and predicts the growth and migration of the fastest growing mode of a random perturbation of the flat sea bed forced by tidal current and wind waves. The growth of the fastest growing mode is assumed to generate the sand waves and to have the same geometrical and kinematical characteristics of these bottom forms. The characteristics of the sand waves predicted by the stability analysis are found to be in fair agreement with field observations, even though the number of accurate quantitative and simultaneous measurements of sand waves and forcing tidal currents is small and does not allow an exhaustive comparison between theoretical results and field data.

Long bed waves in tidal seas: an idealized model

An idealized model is proposed to explain the appearance of the long bed waves that have been recently observed in shallow tidal seas. The model assumes that these bedforms grow due to tide–topography interaction. The water motion is described by means of the depth-averaged shallow water equations and the bottom evolution is governed by conservation of sediment mass. The sediment transport formulation includes a critical bottom stress below which no sediment moves. Also, anisotropic sediment transport, due to local bottom slopes in the longitudinal and transverse directions, is taken into account. A linear stability analysis of the flat bottom configuration reveals that different bottom patterns can emerge. In accordance with previous analyses, for strong tidal currents, the fastest growing modes are sand banks. However, if the tidal currents are elliptical and the maximum bottom stress is just above its threshold value for the initiation of sediment motion, the model shows the presence of further growing modes which resemble the long bed waves observed in the field.

Tidal sand wave formation: Influence of graded suspended sediment transport

The influence of graded suspended sediment transport on the formation of tidal sand waves is investigated. Hereto, in the framework of a linear stability analysis, we examine the time development of small‐amplitude perturbations superimposed to a flat heterogeneous seabed in a shallow tidal sea dominated by one tidal constituent. The heterogeneous bottom material is modeled by a bimodal sediment mixture and the transport of sediment close to the bottom, as well as in suspension, is considered. The active layer concept is employed and hiding/exposure effects are taken into account. The mechanisms giving rise to the sediment‐sorting process along the bed forms are found to be unaffected by the fractional transport of sediment in suspension. On the other hand, the formation of sand waves is quantitatively, substantially affected by the graded suspended sediment transport and the wavelength of the most amplified mode is found to depend strongly on the characteristics of the sediment mixture. In particular, the graded suspended sediment transport largely affects the contribution to the amplification rate related to the sorting process. This leads to the growth of bed forms characterized by a smaller wavelength compared with that predicted for a uniform sediment, when the mean grain size of the sediment mixture is relatively coarse. On the other hand, longer bed forms appear when the sediment mixture is characterized by a relatively fine mean grain size. Moreover, a destabilizing effect is identified in the former case while the flat bed configuration is stabilized in the latter case. A comparison of the theoretical predictions with field observations seems to support the model, even though it cannot be considered conclusive.

Grain sorting effects on the formation of tidal sand waves

A model is developed to investigate the process which leads to the formation of sand waves in shallow tidal seas characterized by a heterogeneous sea bed composition. The main goal of the analysis is the evaluation of the effects that a graded sediment has on the formation of the bottom forms and the investigation of the sorting process induced by the growth of the bottom forms. The analysis is based on the study of the stability of the flat bed configuration, i.e. small amplitude perturbations are added to the flat bottom and a linear analysis of their time development is made. For an oscillatory tidal current dominated by one tidal constituent, the results show that the graded sediment can stabilize or destabilize the flat bottom configuration with respect to the uniform sediment case, depending on the standard deviation σ* of the grain size distribution and on the ratio between the horizontal tidal excursion and the water depth. For moderate values of , i.e. values just larger than the critical value for which the sediment is moved and sand waves appear, the presence of a sand mixture stabilizes the flat bed. On the other hand, for large values of , the mixture has a destabilizing effect. In both cases the effect that a sand mixture has on the stability of the flat bed configuration is relatively small. Moreover, for moderate values of , the fine fraction of the mixture tends to pile up at the crests of the bottom forms while the coarse fraction moves towards the troughs. For large values of , the grain size distribution depends on the value of σ*. The results are physically interpreted and provide a possible explanation of the apparently conflicting field observations of the grain size distribution along the sand wave profile, carried out in the North Sea.

Impacts of blending on dilution of negatively buoyant brine discharge in a shallow tidal sea

A fine-resolution three-dimensional hydrodynamic model is applied to study the dilution of desalination brine discharged into a tidal sea. Based on given inflow rate and salinity excess of discharge brine, this study explores variations in mid-field dilutions when other low-salinity wastewater is added to the discharge. Findings reveal that this blending leads to a decrease in dilution in the mixing zone and therefore to higher levels of pollutants in this zone, while, on the other hand, the mixing zone occupies a smaller area. The reason is that the discharge of brine creates a density-driven flow that operates to partially remove effluent from the discharge location. This removal is less efficient for the decrease in density excess of the discharge. Hence, in an ambient sea of moderate mixing, blending can be expected to increase the risk of marine pollution in the mixing zone.

Wind-wave variability in a shallow tidal sea—Spectral modelling combined with neural network methods

In this paper the wind-wave variability in the tidal basins of the German Wadden Sea is modelled with combined numerical and neural-network (NN) methods. First, the wave propagation and transformation in the study area are modelled with the state-of-the-art third-generation spectral wave model SWAN. The ability of SWAN to accurately reproduce the phenomena of interest in nonstationary conditions governed by highly variable winds, water levels and currents is shown by comparisons of the modelled and measured mean wave parameters at four stations. The principal component analysis of the SWAN results is then used to reveal the dominating spatial patterns in the data and to reduce their dimensionality, thus enabling an efficient and relatively straightforward NN modelling of mean wave parameters in the whole study area. It is shown that the data produced with the approach developed in this work have statistical properties (discrete probability distributions of the mean wave parameters etc.) very close to the properties of the data obtained with SWAN, thus proving that this approach can be used as a reliable tool for wind wave simulation in coastal areas, complementary to (often computationally demanding) spectral wave models.

Three-dimensional tidal sand waves

The process which leads to the formation of three-dimensional sand waves is investigated by means of a stability analysis which considers the time development of a small-amplitude bottom perturbation of a shallow tidal sea. The weakly nonlinear interaction of a triad of resonant harmonic components of the bottom perturbation is considered. The results show that the investigated resonance mechanism can trigger the formation of a three-dimensional bottom pattern similar to that observed in the field.

Boils and Turbulence in a Weakly Stratified Shallow Tidal Sea

Abstract Measurements of turbulence are made in a weakly but variably stratified region of tidal straining in the eastern Irish Sea using turbulence sensors profiling vertically through the water column on the Fast Light Yo-yo (FLY) profiler and horizontally on the Autonomous Underwater Vehicle (AUV) Autosub. The tidal currents exceed 1 m s−1 at the location of the measurements in water of a depth of about 43.5 m, and result in turbulence extending from the seabed to the surface with a cycle period that is half that of the tides, as previously observed. The time of onset of enhanced turbulence that is measured by the sensors on FLY and Autosub as the speed of tidal currents increases are in good agreement, as are their mean levels. Boils on the sea surface are identified using the Autonomously Recording Inverted Echo Sounder, version 2 (ARIES II), a two-beam upward-pointing side-scan sonar mounted on a rig resting on the seabed. The boils have mean horizontal dimensions of about 25 m. They are continually present when turbulence within the water column near the surface is large, typically when the rate of dissipation of turbulent kinetic energy per unit mass ɛ exceeds about 3 × 10−6 W kg−1, compared to the rate of about 1 × 10−7 W kg−1 near times of slack tide when no boils are observed. The top of a region with a relatively high ɛ gradually extends upward from the seabed as the tidal flow increases and, in stably stratified conditions resulting from tidal straining during ebb tides, can be detected in the ARIES II sonographs as it approaches the sea surface, although only after sound reflection from the sea surface. Upward-moving bursts of enhanced turbulence below the surface with horizontal dimensions of about 5–9 m in the direction of the tidal flow are identified in the AUV record in periods of high tidal flow using conditional sampling. The bursts result in slight upward displacements of the AUV from its set operational depth. Boils first appear at times before the region of generally enhanced turbulence reaches the surface: large localized upward-moving bursts appear to precede the main advancing region of small-scale turbulence.

Boils and turbulence in a weakly stratified shallow tidal sea

Measurements of turbulence are made in a weakly but variably stratified region of tidal straining in the eastern Irish Sea using turbulence sensors profiling vertically through the water column on the Fast Light Yo-yo (FLY) profiler and horizontally on the Autonomous Underwater Vehicle (AUV) Autosub. The tidal currents exceed 1 m s−1 at the location of the measurements in water of a depth of about 43.5 m, and result in turbulence extending from the seabed to the surface with a cycle period that is half that of the tides, as previously observed. The time of onset of enhanced turbulence that is measured by the sensors on FLY and Autosub as the speed of tidal currents increases are in good agreement, as are their mean levels. Boils on the sea surface are identified using the Autonomously Recording Inverted Echo Sounder, version 2 (ARIES II), a two-beam upward-pointing side-scan sonar mounted on a rig resting on the seabed. The boils have mean horizontal dimensions of about 25 m. They are continually present when turbulence within the water column near the surface is large, typically when the rate of dissipation of turbulent kinetic energy per unit mass ε exceeds about 3 × 10−6 W kg−1, compared to the rate of about 1 × 10−7 W kg−1 near times of slack tide when no boils are observed. The top of a region with a relatively high ε gradually extends upward from the seabed as the tidal flow increases and, in stably stratified conditions resulting from tidal straining during ebb tides, can be detected in the ARIES II sonographs as it approaches the sea surface, although only after sound reflection from the sea surface. Upward-moving bursts of enhanced turbulence below the surface with horizontal dimensions of about 5–9 m in the direction of the tidal flow are identified in the AUV record in periods of high tidal flow using conditional sampling. The bursts result in slight upward displacements of the AUV from its set operational depth. Boils first appear at times before the region of generally enhanced turbulence reaches the surface: large localized upward-moving bursts appear to precede the main advancing region of small-scale turbulence.

Modelling of a medium-term dynamics in a shallow tidal sea, based on combined physical and neural network methods

The paper presents an approach towards a medium-term (∼decades) modelling of water levels and currents in a shallow tidal sea by means of combined hydrodynamic and neural network models. The two-dimensional version of the hydrodynamic model Delft3D, forced with realistic water level and wind fields, is used to produce a two-year-database of water levels and currents in the study area. The linear principal component analysis (PCA) of the results is performed to reveal dominating spatial patterns in the analyzed dataset and to significantly reduce the dimensionality of the data. It is shown that only a few principal components (PCs) are necessary to reconstruct the data with high accuracy (over 95% of the original variance). Feed-forward neural networks are set up and trained to effectively simulate the leading PCs based on water level and wind speed and direction time series in a single, arbitrarily chosen point in the study area. Assuming that the spatial modes resulting from the PCA are ‘universally’ applicable to the data from time periods not modelled with Delft3D, the trained neural networks can be used to very effectively and reliably simulate temporal and spatial variability of water levels and currents in the study area. The approach is shown to be able to accurately reproduce statistical distribution of water levels and currents in various locations inside the study area and thus can be viewed as a reliable complementary tool e.g., for computationally expensive hydrodynamic modelling. Finally, a detailed analysis of the leading PCs is performed to estimate the role of tidal forcing and wind (including its seasonal and annual variability) in shaping the water level and current climate in the study area.

Nonlinear principal component analysis of the tidal dynamics in a shallow sea

A nonlinear, neural‐network‐based extension of the principal component analysis (PCA) is applied to the water level and current fields in a shallow tidal sea at the German North Sea coast. Contrary to the linear PCA, which tends to split patterns in the data among several modes difficult to interpret, the nonlinear PCA enables to identify the nonlinear spatial patterns in the data with only a single mode. The first nonlinear principal component (PC) corresponds well with the joint probability distribution of the linear PCs and can be argued to represent a ‘typical’ tidal cycle in the study area.

Is phytoplankton growth in the Wadden Sea light or nitrogen limited?

The growth of phytoplankton in the Wadden Sea, a shallow tidal sea bordering the North Sea, is strongly regulated by nutrients and irradiance. The similarity and unity of this sea is documented on the basis of the annual phytoplankton biomass cycles at different sites. Due to the large inputs of nutrients in this area by several rivers (Rhine, Ems, Weser, Elbe) the Wadden Sea shows signs of eutrophication. The strong preference for eutrophication-related studies in this area can only be explained by the impact of policy-makers through funding of eutrophication-related studies and their will to manage the inputs of nutrients to the Wadden Sea. This strong preference has caused the relatively little interest for studies on the regulatory mechanisms of underwater irradiance on phytoplankton growth in this turbid area. Procedures developed by Cloern [Aquat. Ecol. 33 (1999)] were used to compare nutrient and light limitation at different sites of the Wadden Sea. The analysis showed that in many cases both spatial and temporal light limitation far exceed effects of nutrient limitation. During the 1990s the dominant influence of high DIN concentrations implies that underwater irradiance by far exceeds effects of nutrients on the production of phytoplankton biomass. Results of this analysis also show how narrowly focussed research may develop when policy-makers direct research priorities.

A new type of sea bed waves

Sandy beds of shallow tidal seas often exhibit a range of rhythmic patterns, from small‐scale ripples a few metres long to large tidal sandbanks with a wavelength of kilometres. For example, on the access route to Rotterdam harbour ships cross a field of sandwaves. The crests of these sandwaves determine the effective navigation depth. To warrant navigability, the North Sea Directorate of the Netherlands Ministry of Transport, Public Works and Water Management continually monitors the bathymetry in the sandwave area, originally using echo sounding. Our analysis of these data has revealed a new rhythmic pattern, in addition to the well‐known sandwaves and tidal sandbanks. The wavelength of this new pattern, labelled here as long bedwaves, is three times the one of sandwaves, and the crest orientation is different. Interference of the three modes leads to the rather complex bathymetry revealed by echo soundings.

Experimental study of the Ekman layer instability in steady or oscillating flows

To investigate the instabilities of steady and oscillating Ekman layers, an 8 m×2 m horizontal plate was moved at controlled speed in homogeneous water at rest in solid body rotation in the “Coriolis” 13 m diameter rotating tank. For a steady Ekman layer two distinct wave types were found, in agreement with previous experimental or numerical studies. Type I was stationary, was oriented positively with respect to the flow direction and had a wavelength of about 10 times the Ekman layer thickness. Type II was oriented negatively with respect to the flow direction and had a wavelength which was more than 20 times the Ekman layer thickness and a phase-speed between 0.3 and 0.5 the forcing interior velocity. The growth rates of both type I and type II waves for various Reynolds numbers Re (computed with the Ekman layer thickness) were estimated and their Re-variations qualitatively agree with previous numerical results. For an oscillating Ekman layer, experimental results depended strongly on Ro t, the temporal Rossby number: only when Ro t<1 was it possible to observe either type I or type II instabilities. Moreover, for all Ro t and average to high Re, there was a noticeable upward turbulent transport occurring during each cycle between the flow maximum and the flow reversal. Such an upward turbulent transport is consistent with observations in the English Channel where maximum upward benthic movements and maximum turbidity were recorded at the flow reversal, hence Ekman layer instabilities and transition to turbulence are likely to occur in shallow tidal seas where they may be relevant for sediment resuspension and transport as well as for some biological processes.

Surface effects of bottom-generated turbulence in a shallow tidal sea

Turbulence in shelf seas strongly affects the spread of pollution (such as oil spills) as well as the distribution of sediment and phytoplankton blooms. Turbulence is known to be generated intermittently close to the sea bed, but little is known of its evolution through the water column, or to what extent it affects the surface. Here we present observations of the surface effects of bottom-generated turbulence in a tidally influenced and well mixed region of the North Sea, as derived from acoustic and visual images. Although the sea bed in the area is flat, we find that at any one time, 20–30% of the water surface is affected by boils—circular regions of local upwelling—of diameter 0.90.2 times the water depth. The signature of individual boils persists for at least 7 minutes and, in accordance with laboratory and numerical studies, shows the appearance of eddies. The boils contribute to the replacement of surface waters from depth in unstratified waters, and may therefore enhance the fluxes of gases between atmosphere and ocean.

Spectral structure of horizontal water movement in shallow seas with special reference to the North Sea, as related to the dispersion of dissolved matter

The spectral structure of horizontal water movements in a shallow sea like the North Sea is reflected in the horizontal spreading phenomena. In the present paper results from tracer experiments in the North Sea are combined with model simulations in order to improve the insight in the relative importance of the variations in the horizontal water movements, the vertical shear dispersion and the 3D turbulence. It is tried to obtain estimates of the kinetic energy spectrum of the horizontal eddies. The analysis of the role of the main mechanisms of mixing and dispersion also applies to other shallow tidal seas, and to an extent, to the mixed upper layer of the oceans. The models used are briefly described.

A Note on Seabed Irradiance in Shallow Tidal Seas

(1) The tidal cycle and that of solar elevation interact to produce patterns in seabed irradiance during the day which change over the springs-neaps cycle. In locations where high water springs is at midday, there is a single peak in seabed irradiance in the middle of the day at neap tides and two peaks in seabed irradiance (one in the morning, the other in the evening) at spring tides.(2) These cycles also interact to produce a springs–neaps cycle of daily mean irradiance, which is relevant to the growth of benthic algae. The pattern of this cycle will also vary from place to place. In locations where low water springs is in the middle of the day the pattern is straightforward: maximum daily irradiance always occurs at spring tides. However, where high water springs is in the middle of the day, the cycle can reverse as the days get longer. The timing of the switch in the cycle depends upon the water clarity.(3) Variations in attenuation over the springs–neaps cycle will also be important. In the Menai Strait, a springs–neaps cycle in K is often (but not always) observed, higher attenuations occurring at spring tides when seabed sediments are stirred up by the stronger tidal currents. This will reduce seabed irradiance at spring tides and tend to favour greater irradiance at neaps. In our model runs, K was kept constant because at present it is difficult to predict these changes. However, in our observations there is evidence of greater seabed irradiance at neap tides associated with greater water clarity. Variations in cloud cover during the day can also affect the regular cycles predicted by the model.The authors are grateful to Professor Ernest Naylor for encouragement and for information on animal behaviour and light. Members of the Marine Optics Group at Menai Bridge helped with the sampling during the experimental work in July 1994.

Chaotic Stirring in a Tidal System

An analysis of a two-dimensional tidal model of the Wadden Sea reveals Lagrangian chaos in the trajectories of water parcels. The associated chaotic stirring results from the transverse intersection of the stable and unstable curves of hyperbolic fixed points in the Lagrangian residual displacement field (the tidal Poincaré map). This tidal dispersion mechanism produces rapid water exchange along the channel axis and could be representative of many shallow tidal seas.

Anomalous diffusion and anomalous stretching in vortical flows**Participation in this Conference has been possible thanks to the financial support of the Dutch foundation of Fundamental Research of Matter and the IUTAM Local Organizing Committee.

The trajectories of particles advected by non-random spatially periodic velocity fields may be chaotic, i.e., extremely sensitive to their initial positions. In the most general case, the area of a cloud of advected particles grows like (time)α where the exponent α ranges between 0 and 2 (shear stretching). These observations could explain many known facts about dispersion processes in shallow tidal seas.