“Traveling Deformation Waves” – What Is It?

So, “traveling deformation waves” – what is it?
We are sure you have been watching them all your life: by looking at wave motions in the water from a thrown stone, or at creeping caterpillar with bend (i.e., wave) rolling along its body. We, the authors of this site, started research of traveling deformation waves by observing and studying wave motion of such creatures as caterpillar, earthworm, snake, and snail. In this site we will tell you how that has helped us to make some discoveries in different fields of science.
Let’s take a closer look on how these land creatures move, even though they have no legs, but only an elongated, deformable body, able to carry deformation waves.

We will prepare and place video films and computer animations of moving mechanisms of mentioned living creatures.

Let’s focus on these two typical and simple models: long, deformable strips lying on solid base. One of them can bend (“caterpillar”), while another one can stretch (“earthworm”).
If we periodically bend one end section of such a strip (i.e., create a transversal wave) and move it towards another strip’s end, the whole strip will “crawl” along the base – this is a model of caterpillar’s movement.
If we stretch some end fragment of the strip (i.e., create a longitudinal wave) and move it towards another strip’s end, the strip will “crawl” as well – a model of earthworm’s movement.
But do not rush to conclusion that those “well-known” phenomena are simple and trivial. This is what we thought when began studying those methods of locomotion from positions of mechanics. Let’s ask ourselves a question: “Why a caterpillar crawls in the same direction as moving deformation wave on its body, but an earthworm moves in the direction opposite to deformation wave’s motion?” Finding answers led us to understanding that there exist only two kinds of traveling deformation waves:
• wave of surplus of mass (example: bend (transversal) wave on caterpillar’s body);
• wave of shortage of mass (example: elongation (longitudinal) wave on earthworm’s body);

Later we will show that all other traveling deformation waves concerned in this site (traveling deformation waves in all media – solid, liquid and gas, and waves of different scales – up to global atmospheric and geospheric waves) are waves of these two kinds – surplus of mass and shortage of mass.
Let’s go back to our “basic biomechanical examples” of traveling deformation waves we started with – methods of transportation of caterpillar and earthworm. From positions of theoretical mechanics, those mechanisms, invented by Nature itself, have many characteristics that are not achievable in man-made devices.
First, this is an extremely economical method of transportation. Because of having massive body and small power for its move, those creatures managed to move themselves “by parts”. As you can see from our models, at every given moment only the wave part of body is moving, while the rest is motionless (“resting”).
Second, there is no sliding friction. This fact seems improbable. How can any legless creature, crawling on solid surface, avoid friction? However, strict analysis shows that:
• for caterpillar, moving part of its body is raised from the ground, thus avoiding friction;
• for earthworm, moving (i.e. stretched) part of its body is raised from the ground as well, because longitudinal stretching of a deformable body leads to its narrowing, i.e., reduction of cross-section (Poisson’s law).

We call such body’s wave movement method, when some of its particles are moving, while others are resting, “discrete-wave” movement.
Let’s define now a concept of mass content for transversal and longitudinal deformation waves. Considering that wave is moving along x-axis, let’s assume a wave length l as a length of the interval along x-axis containing the wave. If mass of deformable body fragment in the wave interval l is , and mass of regular body fragment (not in wave) of the same length l is m, then the mass contents of the wave is
= – m
Another words, mass content of the wave is a difference of mass of body in the wave fragment and mass of non-wave fragment of the same length.

There are two other important characteristics of waves we will need in chapters to follow.
• Wave mass transfer equals to product of mass content  of wave and its traversed path L:
• Momentum (impulse) of traveling deformation wave equals to product of mass content of wave  and its velocity .

Source: Nacionfarma.com

Estuaries: the Ocean’s Nurseries

Ask anyone and they would tell you that water is one of the most important resources for everybody. So why does nature need water? Fishes need water to swim in and lay eggs, plants need water to grow, and some organisms live solely in water and depend on the moisture to survive. Why do we need water? Water is important to help us live, regulate our body temperatures, and grow sex video.

Often viewed as muddy, smelly, mosquito-filled swamps, estuaries and their associated salt marshes and tidal flats are among the most productive habitats in the world. They are mixing zones, where freshwater, delivered by rivers and streams, flows into water from the sea. Animals and plants in this habitat must be able to tolerate wide ranges of salinity and temperature, as well as fluctuating water levels. Nutrient-rich estuaries protect and nurture a variety of shrimp, oysters, crabs, and fishes. Over 490 species of birds live in or migrate through the Coastal Bend of Texas, and many use the estuaries to feed, rest, and find shelter.

Background
Seagrasses are plants that root, pollinate, and spend their entire lives submerged in shallow waters. Special adaptations allow for their survival in the fluctuating conditions of coastal bays and estuaries. The estuaries in the Coastal Bend of Texas contain 40% of Texas’ total seagrass acreage. Seagrasses provide oxygen, nutrients, anchorage, food, habitat, cover, and places for attachment.

SEAGRASS COVER

Bay System Seagrass
Meadow Area* Area of
Bay Bottom* Percent Seagrass
Galveston Bay _____ 391 _____143,153 _____ _____
Matagorda Bay _____ 1,096 _____ 101,368 _____ _____
San Antonio Bay _____ 2,743 _____ 54,335 _____ _____
Aransas Bay _____ 2,455 _____ 47,267 _____ _____
Corpus Christi Bay _____ 5,249 _____ 43,550 _____ _____
Upper Laguna Madre _____ 24,900 _____ 33,100 _____ _____
Lower Laguna Madre _____ 48,200 _____ 68,400 _____ _____

* All measurements are in hectares.

Exercises

The Texas bay systems above are listed in order from north to south. Use the measurements provided to calculate the percent seagrass coverage in each bay.
Rank the measurements in each category. Number one through seven from largest to smallest. Record the rankings in the blanks to the left of each measurement, including percent seagrass coverage.
Examine the rankings. Do you see any relationships between the measurements provided and percent seagrass coverage? How about location north and south? If, so, explain.

Seahorses are among the most unusual-looking animals in the world. Unlike most fishes, they lack the caudal, or tail, fin. Most fish species use the caudal fin to propel themselves through the water. Lacking that, the seahorse uses its dorsal and pectoral fins to propel itself.
The seahorse has a unique tail in that it is prehensile or grasping. Just as monkeys are able to use their prehensile tails to grasp and swing from trees, seahorses are able to use their tails to grasp seagrasses, algae, and other stationary darmowe porno objects.

Humans have thumbs which similarly allow them to grasp objects. This is one adaptation that has contributed to our ability to use tools and manipulate objects easily.

Procedure

Gather a collection of at least ten tools and objects (screwdriver, hammer, coins, etc.).
Divide a sheet of paper into three long columns. List the tools and objects down the page in the first column. Label the second column “with thumb” and the third column “without thumb.”
Manipulate each tool and lift each object. Rate the effort required to perform each task on a scale of one to ten, with ten being very easy and one being very difficult. Write your rating in the second column.
Fold your thumb across your palm. Using the masking tape, tape your thumb in place.
Re-do each of the tasks that you performed earlier. Rate the difficulty of each task on the one to ten scale.
Compare your ratings with and without the use of your thumb. List other tasks that would be affected by the presence or absence of thumbs

North sea Model Advection Dispersion Study

Objective (1), the Realistic Test Case
This focusses on the period November 1988 to October 1989 and spatially on the southern North Sea. The models are taken as they are presently used, i.e. varying from one another in the detail of included physics (2D/3D, barotropic/baroclinic, dispersion formulation), numerical solution techniques, grid sizes, calibration and underlying hydrodynamics. Thus the one constraint is that the models must all have the common spatial coverage of the North Sea basin between 51deg N and 55deg 40’N. To enable model simulations to be carried out a comprehensive [data set] has been constructed which includes bathymetry, tides, time- varying meteorology, boundary forcing and river discharge. Within the intercomparison there are four 2D models and nine 3D models, some of these are tidally-resolving (mesoscale) (9) and some are not (macroscale) (3).

Four experiments were defined:
– Experiment 1 (for 2D models only): continuous release of conservative and non-conservative tracers from the six locations (see figure) for 180 days starting 1 March 1989. Parameters examined include the age and concentration of the tracer.
– Experiment 2: single particle release from each location at four intervals in the year (releases at surface, mid-depth and bottom for 3D models). Parameters examined include distance travelled and relative tracer position.
– Experiment 3: instantaneous release of a 1kg tracer from each location at 2 times, 1 March and 1 August 1989. Parameters examined include trajectory of the centre of mass, total mass and patch shape and area.
– Experiment 4: Salinity and accumulated volume flux across 2 east-west sections at 52.5deg N and 54.5deg N (see figure). Parameters examined include time slice values and spatial variability.
The 2D models were run for the full 12 month period, the 3D models were run for either a) a six-month period, March-September 1989, or b) two 1-month periods, March and August 1989, depending on partners computational ability. Grid sizes of the models ranged from 2.4 km up to 20 km.

Objective (2), the Idealised Test Case
The experiment is the development of a fresh water eddy. A cylinder of fresher water is placed in the surface layer of an ambient fluid and allowed to mix. As the eddy forms under the influence of rotation, instabilities (secondary eddies) develop, the order of which depends on the friction (numerical and interfacial) in the system. The experiment is based on laboratory measurements (Griffiths & Linden, 1981, Journal of Fluid Mechanics, 105, 283- 316) and the numerical design of James (1996, Journal of Marine Systems, in press).
Five partners have participated in this experiment, producing 2 distinct sets of instability related to their numerical schemes.
Together, both experiments have generated more than 900 datasets for intercomparison. The intercomparison is presently in the analysis phase.
NOMADS will produce four Technical Reports:
• TR-1 Project rationale and experimental setup
• TR-2 Overview of the models to be used
• TR-3 Partner interpretations of the simulations
• TR-4 Intercomparison and conclusions.

The NOMADS dataset

The dataset has been constructed to enable partners to run the NOMADS simulations for the period 1 November 1998 to 31 October 1989. It contains the following data:

1) Covering the European Continental Shelf
Gridded bathymetry, 1/12deg latitude by 1/8deg longitude

Ten tidal constants around the shelf break

Gridded meteorological data at 3-hourly intervals (approx. 75km resolution) –

  • Surface winds
  • Atmospheric pressure
  • Relative humidity
  • Air temperature
  • Daily estimates of cloud cover derived from AVHRR imagery

Annual mean discharge of 43 rivers.

2) Covering the Common Area (Southern North Sea, 51deg N to 55deg 40’N)
Thirty tidal constants across north and south boundaries

Residual elevation and current at hourly intervals across the boundaries

Monthly discharges from 16 rivers

Initial conditions for Temperature and Salinity for March and August 1989.

The data is available via anonymous ftp, subject to owner conditions. Please contact the NOMADS co-ordinator for details (@pol.ac.uk).

NEAT GIN – North East Atlantic, Greenland-Iceland-Norwegian sea experiment

The NEAT GIN experiment took place during September-October 1989 at the Norwegian shelf edge near 68°N. Seven moorings, five in a closely-spaced cross-slope section, have proved a valuable precursor to the Shelf Edge Study (SES) west of Scotland. The NEAT GIN data analysis has now been completed.
A mean current (0.2-0.3 m/s) north-eastwards along the slope was found to be a predominant feature and is common to many locations around the north-west European shelf edge. The total transport was estimated to be 4 to 9 106m3/s, values at the upper end of the range of estimates from elsewhere around north-west Europe. Measurements near to the bottom showed slight anti-clockwise veering, consistent with the presence of a bottom Ekman layer.
Rotary motion, coherent down to about 300 m, made another large contribution to the total flow. Most energy occurred in periods exceeding 2 days (« day at the top of the slope). Comparisons with hindcast meteorological data showed little evidence of correlation between this rotary flow and the weather. Hence a stochastic source mechanism is suggested, eg. baroclinic instability.
Tidal analysis of the currents showed modest values; the M2 component was largest, about 0.05 m/s at the top of the slope in 200 m water depth, decreasing to about 0.03 m/s in the deeper waters on the slope. In comparison, tidal models of the region do not fully resolve the slope and exaggerate the increase of tidal currents in shallow water. Attempts to represent the diurnal tidal currents as a trapped wave also show this exaggeration. There was little evidence of internal-wave or internal-tide effects.
A significant finding for subsequent shelf-edge studies was a lateral coherence scale of about 10 km for the currents, comparable with the theoretical Rossby radius of deformation scaling eddies and internal features. This scale gives a basis for future array design. In the temperature field, however, smaller scales were evident from satellite imagery and appeared to contribute a large proportion of the variability. Consequently, a transport balance for temperature (heat) could not be constructed, although movements of the thermocline and changing temperature profiles suggested primarily advective contributions.
Fluctuating contributions to heat flux were calculated from the current meter and thermistor chain records. In common with other locations, eg. north-west of Scotland in 1982-83, these showed a principal contribution along the shelf (to the southwest, against the mean flow) and a small component.

Description of the STOWASUS-2100 project

ABSTRACT

The overall objective of STOWASUS-2100 is to study severe storms, surges and waves in the present climate and in a scenario with increased CO2-concentration. More specifically the project is a joint atmospheric/oceanographic numerical modelling effort aiming at constructing and analysing storm, wave and surge climatologies for the North Atlantic/European region in a climate forced by increasing amounts of greenhouse gases and to compare with present day conditions. It is investigated whether any systematic anomalies regarding frequency, intensity or area of occurrence are found for these extreme events. Also physical mechanisms responsible for possible scenario anomalies are investigated.

INTRODUCTION

Off-shore industries, fisheries, shipping companies, and the insurance business are highly sensitive to extra-tropical strong wind events and the associated ocean waves and surges. It is likely that impacts of possible future changes in the occurrence of extreme type events like these and others will be more severe than modulations of the long term mean climate. This is the rationale behind the STOWASUS-2100 project which aims at setting up climate change scenarios for storms, waves and surges on a variety of spatial scales. On the larger scales, studies on storminess in the North Atlantic region will be performed, while detailed studies on storminess, surges and waves will be carried out in the Adriatic, The North Sea and the Norwegian Sea. On the local scales, storms and surges will be studied in estuaries, low lying coastal areas along the North Mediterranean and North-western European coasts.

The project builds to considerable degree on the results obtained in another project called WASA, which has been described by “The WASA Group” (1998). In WASA it was found that the storm and wave climate has roughened in recent decades, but that the present intensity of the storm and wave climate seems comparable with that at the beginning of the 20th century. The WASA project furthermore analysed and used the output from a high-resolution (T106 spectral truncation) climate change scenario experiment, mimicking global warming due to increase greenhouse gas concentrations. It was found that storm and extreme wave activity was slightly increased in the Bay of Biscay and in the North Sea in a warmer climate, while this activity was slightly weakened at several other places. The experimental set-up of the climate model simulations on which these results were based has been described by Beersma et al. (1997) who pointed out that the projected anthropogenic changes in storm activity fall well within the limits of variability observed in the past considering the length of the (control and scenario) simulations which was only 5-years.

Recently, two so called time slice simulations with the ECHAM4 model also at T106 horizontal resolution have been performed at the Danish Meteorological Institute (DMI) in a collaboration between the Max Planck Institute for Meteorology in Hamburg and DMI. These simulations each covered a period of 30 years, i.e. 6 times longer than the simulations used in WASA. Thus they should be much more suited for studies of storminess and associated impacts since the sampling problem is considerably reduced. The STOWASUS-project therefore uses these new simulations as a backbone to drive very high resolution regional atmospheric climate models and wave and surge models of different resolution. It is these secondary simulations which will be used to set up climate change scenarios of storms, waves and surges along European shelf and in European Estuaries and to compare these with present day conditions. The project is logically divided into 12 working tasks some of which will be described briefly in the following three sections together with preliminary results – to the extend they are available at this early state of the project.

INTENSIVE STORMS

As mentioned above the backbone in STOWASUS-2100 consists of two 30 year time slice simulations with the ECHAM4 atmospheric climate model at T106 horizontal resolution. The experimental design of these simulations which are not part of the project is described in May and Roeckner (1998). The project includes an analysis of the storm and extreme wind climate in these simulations. Fig. 1 (left column) shows the long term mean sea level pressure (MSLP) in winter (DJF) as obtained from the European Re-Analysis data (ERA), from the control simulation and from the scenario simulation. It is seen, that the ECHAM4 model simulates the atmospheric mass field well except for a too high pressure over and immediately to the west of the Iberian peninsula which leads to a too zonal flow over NE Atlantic region. The figure also shows the difference in the MSLP between the scenario and control simulations in the bottom panel, and it is seen that there is a significant increase in the zonality over the northern part of the area associated with a decrease in the high latitude MSLP in the scenario. The right column in Fig. 1 similarly shows the standard deviation of the band pass filtered (2.5-6 day filter) 500 hPa winter height fields which is commonly used as an estimate of storm activity. Also here the model behaves well and a significant increase in storm activity is seen over Northern Europe in the scenario simulation relative to the control simulation together with a corresponding decrease in storm activity around the east coast of US. Fig.2 shows the 1% percentile wind speed for the winters (DJF). Comparing the ERA data and the control run shows that the ECHAM4 model has more severe storms along the south and east coast of Greenland than the ERA data. The difference between the scenario run compared to the control run (fig. 2d) shows more severe storms in the Atlantic north of 60N, and less severe storms south of this latitude. These changes are in accordance with the changes in the 500 hPa variability (fig. 1d). The changes in near surface wind (Fig. 2) are important to the wave and surge simulations (see below) as one can expect that the enhanced wind speeds will also lead to more severe wave and surge activity. This has, however, not yet been shown in the project.

The atmospheric investigations will also cover atmospheric modelling with very high resolution regional climate models (HIRHAM and BOLAM) to perform of intensive systems that are not well resolved at T106 resolution: intensive extra-tropical baroclinic developments, polar lows and highly convective systems (with some apparent similarities to polar lows) in the Mediterranean. Fig. 3 shows the orography in the T106 model and in the BOLAM model over the Mediterranean region and it is seen that one may expect much larger impact from orographic effects at very high resolution than at T106. All the simulations with HIRHAM and BOLAM will take boundary conditions from the T106 time slice simulations and will to considerable degree focus on analysing and understanding the processes associated with possible changes in scenario cases relative to control cases.

The modelling of cohesive sediment transport

The management of coastal zones and estuaries requires more and more accurate and detailed knowledge of cohesive sediment (mud) transport processes to cope with various problems (e.g. wetland protection and restoration, maintenance of navigation channels, dredging and dredged material relocation, effects of construction works on siltation and turbidity levels, dispersion of pollutants, etc.). Detailed mathematical models, including full three-dimensional codes, are necessary tools for the development and application of this knowledge. Presently, this is becoming practically feasible in view of the current developments in soft- and hardware. The physical understanding and mathematical description of the processes, however, is still lagging behind, especially with respect to the presence of concentrated near-bed suspension layers, as explained below.

PHYSICAL PROCESSES

The behaviour of mud in coastal zones and estuaries is the result of horizontal and vertical sediment fluxes, i.e. transport, water-bed exchange processes, including the formation of concentrated suspensions, and processes within the bed.

This whole (semi-)cycle is particularly complicated, because it does not necessarily have to be closed and the processes are interdependent. For instance, settling does not always lead to deposition, i.e. when entrainment dominates, and the sediment then remains in suspension; the consolidation processes within the bed are affected by the flocculation processes in the water column and in turn the erosion processes are governed by the consolidation processes and mediated by biota. The actual transport is the net effect of the interactions of different processes, which, until now, have been studied mainly in isolation.

Concentrated benthic suspensions (CBS) and fluid mud

The capacity to transport sediment in suspension by currents and waves is limited by the amount of energy available in the flow. In many cases the suspended matter is not well mixed over the water column and stratification occurs due to settling when the turbulent energy decreases, resulting in a concentrated near bed sediment suspension. They can be maintained by the turbulent energy of the flow when there is equilibrium between the depositional flux and the vertical turbulent transport flux (e.g. Wolanski et al., 1988). These layers are often thin and therefore frequently remain undetected. The concentrations in these layers can be of the order of 5-10 g/l, but also much higher. Because they include a high proportion of the mobile fine sediment, the total amount of sediment that is transported in these sheet flows can still be enormous. Research has revealed that these near-bed layers are the major mechanism of the transport of fine-grained sediments in coastal zones and estuaries (e.g. Faas, 1984; Odd et al., 1992). Therefore, they must be considered in transport models. These near-bed layers will hereafter be called concentrated benthic suspensions (CBS). This terminology is used for the regime where the sediment/water mixture behaves as a fluid. The concept has a broader meaning than that of “fluid mud”, which is associated with high concentration suspensions with a sharp mud/water interface, which can be detected by echo sounding (Parker & Hooper, 1994). The term “fluid mud”, moreover, is often also used for soft consolidating mud layers, which do not behave as a true fluid, and therefore can be misleading.

At concentrations above a critical value of a few 10 g/l, the particle interactions start to modify the properties of the suspension, i.e. the particle interactions lead to hindered settling and at higher concentrations the rheological behaviour of the suspension becomes non-Newtonian (Faas, 1984). To maintain CBS of higher concentrations (above the critical value), much more energy is required as turbulence is being damped by buoyancy effects and by the dissipation of energy due to interparticle collisions and its resulting effect on the floc structure. Therefore, when the energy level is too low to maintain the CBS, this layer will deposit and form a denser fluid mud layer.

The interface between a CBS layer and the water column above can be very distinct, but also very unstable. Helmholtz-Kelvin instabilities may occur (internal waves), leading to interfacial mixing, which contributes to the entrainment of sediment into the water column and of water into the CBS layer (i.e. diluting it) (Scarlatos & Mehta, 1992; Mehta & Srinivas, 1992; Le Hir, 1994; Winterwerp & Kranenburg, 1994). The vertical fluxes involved in this process are not yet fully quantified.

Pressure gradients (e.g. induced by density differences) may cause gravity current flow of CBS. Lower concentration gravity currents are very unstable and generate turbulence. Density currents of dense, visco-plastic fluid mud layers on the other hand are generally laminar.

When the sediment concentration in a dense suspension exceeds a second critical value, the gel point or structural density, the flocs form a continuous network structure and develop effective stresses: a weak saturated soil is formed. At rest this structure will slowly collapse under its own weight and the interparticle bonds will increase in strength: it consolidates. The compression of the bed and the increase of its strength will be determined both by the development of effective stress and by separate time-dependent processes such as creep and thixotropy (Sills, 1994 & 1995). However, under the influence of internal or external forces (e.g. wave action, particularly in storm conditions), the structure of a weakly consolidated bed may fracture and eventually break-up into mobile aggregates and the sediment behaves again as a dense non-Newtonian suspension: the bed is liquefied under shear forces or fluidized under excess pore pressures. The resulting fluid mud layers can easily be eroded, entrained into the water column and transported as gravity currents: this is a second mechanism for the formation of CBS layers (Mehta et al., 1994).

The transition between CBS and the bed is poorly defined at the moment. The erosion happens by different processes depending on the developing rheology of the CBS and on the degree of consolidation. The entrainment of the CBS contrasts with the erosion of the bed by failure of the interparticle bonds of the flocs on the bed.
Flocculation of fine sediment

The formation of concentrated benthic suspensions, their structure and subsequent evolution is governed by the settling flux of suspended sediment towards the bed. This is the product of the mass concentration and the settling velocity. Both the settling velocity and the size of the flocs are determined by a balance between the forces of particle coagulation and disruption. Coagulation is a function of sediment concentration, salinity, organic material content, particle mineralogy and physical processes like Brownian motion, differential settling and turbulent shearing. At low concentrations a small amount of shear will help to bring small flocs together to form larger ones. Higher shear will tend to pull the flocs apart, and which is enhanced by collisions at high concentrations. The flocs most prone to disruption are the largest ones (macro flocs) that have the lowest density, but which have the greatest settling velocity and contain the greatest mass. Their break-up creates a number of smaller micro flocs which, though they together contain the same total mass, individually have higher densities, but lower settling velocities. The aggregation and disruption functions have not been independently determined for natural suspensions. This is a major shortcoming in predictive models which currently only use relationships between settling velocity and concentration. Though these relationships are determined by laboratory measurements in still water on natural samples, and empirically account for mineralogy, salinity and organic content, they are only a first approximation. Because of the interaction between the processes due to concentration and turbulent shear, their combined effect can only be derived from in-situ measurements.

THE MODELLING OF COHESIVE SEDIMENT TRANSPORT

We identify the research needs for cohesive sediment transport processes from the requirements of the transport models which are used by the managing authorities and engineering consultants.

The modelling of cohesive sediment transport requires the numerical solution of the basic conservation equations of mass, momentum and turbulent energy. Several model parameters are supplied by semi-empirical closure equations for input quantities which depend on position and time (Teisson, 1994), amongst which: the settling velocity of flocs, the eddy diffusivity and the sediment flux at the bed (deposition, erosion). For practical applications fine-sediment suspensions can be modelled as a continuous (single) phase fluid (Le Hir, 1994).

In the state-of-the-art engineering models for simulating the transport and fate of CBS layers, a three-layer approach is often applied in which the lower layer is formed by the consolidated bed, the upper layer by the water column and the layer in between by the fluid mud (e.g. Odd & Cooper, 1989; Kusuda & Futawatari, 1992). The exchange of mass between the two upper layers is described through deposition and entrainment formulae, whereas the exchange of momentum is limited to an adaptation of the internal friction coefficient. The exchange between the two lower layers is described in the form of consolidation and erosion formulae. All formulae are highly empirical often with dimensional empirical coefficients, indicating little physical background. This is cumbersome, as the transport and fate of fluid mud layers, predicted with these models, is highly dependent on the actual value of these coefficients. For instance, the settling velocity is taken constant in general, whereas in reality it is strongly affected by the level of turbulence. The entrainment process was studied by Mehta & Srinivas (1993) and Winterwerp & Kranenburg (1994). The latter derived an integral entrainment model by a rigorous integration of the equation for kinetic turbulent energy over the water depth. However, even in that case many empirical coefficients are still required, especially for the fluid mud properties.

In summary, in the state-of-the-art models the interaction between the water movement and the fluid mud layer is neglected, the properties of the sediment in suspension (settling velocity) and of the fluid mud (viscosity and yield strength) are given by highly empirical relationships and the occurrence and effects of CBS is even entirely ignored.

Turbulence modelling of sediment-laden flow

Turbulence models of various levels of sophistication have been developed, from simple algebraic models to Reynolds stress models (Rodi, 1980; Schumann & Gerz, 1995). Turbulence models for estuarine flows should take into account the damping effect of vertical density stratification. Existing models satisfy this requirement in one way or another. Stratification may not only result from the ubiquitous salinity gradients, but also from gradients in the sediment concentration. In the latter case an interaction exists between turbulence and sediment transport. This interaction in near-bed layers has been analysed numerically by Le Hir (1994) (algebraic mixing-length model), Uittenbogaard et al. (1996) (k-epsilon two-equation model) and Teisson et al. (1992) (Reynolds stress model), amongst others. Uittenbogaard (1995) argues that the production of turbulent kinetic energy by internal waves should be included when modelling CBS. Turbulence modelling in the case of fluid mud is complicated by non-Newtonian rheological behaviour and low Reynolds number effects. As sediment transport processes occur on widely different length and time scales, the numerical aspects of turbulence modelling are complex and require special attention.

In summary, turbulence modelling is needed to determine the quantities required by fine-grained sediment transport models, i.e. to estimate the floc settling velocity and deposition rate, entrainment rates of suspended sediment, surface erosion rates, interfacial stability and mixing at lutoclines and the damping of turbulent energy in concentrated suspensions.

Modelling flocculation

A conceptual model of the effect of shear and concentration on median floc settling velocity has been proposed by Dyer (1989). A heuristic formulation for the process, based on laboratory studies, has been advocated by van Leussen (1994), which relates flocculation and break-up to the dissipation rate of turbulent kinetic energy. This formulation has been incorporated into a numerical estuarine model by Malcherek et al. (1994) and appears to be a major improvement. Flocculation models are most easily formulated in a Lagrangian framework. However, for implementation in general sediment transport models an averaged Eulerian formulation is needed, which requires additional turbulence modelling (e.g. Casamitjana & Schladow, 1993).

The various coefficients need to be obtained from field measurements. This approach requires simultaneous measurement of the settling velocities of the various floc size fractions, the suspended sediment concentration, and the characteristics of the turbulence such as the turbulent shear stresses, the turbulence energy and the eddy dissipation rate. An additional factor that has to be quantified is the influence of organic constituents that can act as ‘glue’ in the flocculation process.

A number of new techniques have recently been developed for in-situ measurements of floc size and settling velocity with minimal disruption (Eisma et al., 1990; van Leussen & Cornelisse, 1993; Fennessy et al., 1994; Dyer et al., 1996). These apparatus have been compared with Owen Tubes in an intercomparison experiment during which it became apparent that the Tube performance was dependent on the operator and the sampling protocol, and that the flocs were disrupted by the sampling. The new techniques are able to distinguish individual flocs, and can provide information on the spectra of floc size, settling velocity and effective density under different conditions.

Modelling the interaction between concentrated benthic suspensions and water

A further understanding and considerable improvement of the modelling of CBS layers are only possible by taking the three-dimensional (3D) effects fully into account. Considerable progress has been made recently by Le Hir (1994), Le Normant (1995), Malcherek (1996) and Galland (1996), amongst others, who studied the three-dimensional behaviour of suspended sediment transport and concluded that simulation of observations is indeed only possible by taking the 3D effects into account. Entrainment of CBS by a turbulent flow can be modelled in a similar way as the entrainment of a dense fluid (Winterwerp & Kranenburg, 1996).

Up to now, the important interaction between water movement (turbulence) and sediment could only be accounted for to a minor degree, because the required physical-mathematical formulations are not yet available. In particular the interaction between (turbulent) water movement, damping of turbulence due to buoyancy effects and its influence on the vertical mixing processes, the effects of flocculation and hindered settling on the formation of fluid mud and CBS and their internal properties (non-Newtonian stress-strain relations), the influence of waves on the generation and erosion of fluid mud layers and the stability of fluid mud layers and CBS are still poorly understood.

The effects of surface waves on the fluid mud layer and vice-versa (e.g wave damping) are important phenomena. Their explicit effects, however, lie beyond the scope of this project. But the indirect effects, such as pore pressure build-up, prior to fluidisation, or interfacial mixing has to be accounted for. Also very little is known about the erosion of a consolidated mud bed by breaking waves, which may occur on tidal flats during a storm event following a period of deposition. This also falls outside the scope of this research project.

Modelling the interaction between fluid mud and the bed

For each of the processes which determine the fate of fluid mud or a mud bed, i.e. consolidation, liquefaction and fluidisation, different models have been developed over the past years: a unified theory for settling and consolidation has been developed (Toorman, 1996) and a poro-elastic model is used for fluidisation (Yamamoto et al., 1978). These models allow the computation of the density and/or stress history within the mud layer. In order to erode a mud bed, the bottom shear stress should be larger than the shear strength of the bed surface. Traditionally, erosion of a consolidated bed has been modelled using empirical formulae and the critical erosion stress has been empirically related to the yield stress, a rheological property which is a measure of the degree of bed structure (Gularte et al., 1979). The yield stress, which is difficult to measure (even in the laboratory), is determined as a function of the density. In this way an empirical link has been established between consolidation theory and rheology. A comprehensive theory, which incorporates liquefaction and fluidisation, is still lacking. An attempt in this direction has been made by van Kesteren et al. (1993), who used a geotechnical approach. As a further step in erosion modelling, this approach should be linked with a hydrodynamic approach. The common factor in the bed history is the structure, which should be parameterized. A possible approach is that of the structural kinetics theory, which has been applied successfully to the modelling of the thixotropic behaviour of mud (Toorman, 1995) and the formation of flocs (Winterwerp, 1996).

Parameterization

Since the processes are very complex, the process models and modules generally are parameterizations of the elaborated mathematical-physical descriptions. This is still a common practice to make the computer codes cost and time efficient in order to be applicable to practical managerial problems.
Measuring methodology

Validation of numerical models requires field and laboratory data. Measuring campaigns have been hampered by a lack of understanding of the physical processes and an isolated approach on the research of mud dynamics. For instance, it may appear necessary to measure turbulence properties simultaneously and some time prior to the settling velocity measurement to obtain reliable results. An improvement of measuring methodologies for cohesive sediments will be one of the spin-offs of the proposed research. Vice versa, insight in measuring methodologies and techniques will prevent the development of process formulations containing unmeasurable quantities.
Conclusions

In summary, it is hypothesized that the transport, fate and subsequent behaviour of cohesive sediment suspensions in many coastal and estuarine environments are largely governed by concentrated near bed suspensions and the structure of the aggregates involved. Classical fluid mud appearances are one of types of CBS identified in the literature. The state-of-the-art review leads to the identification of various gaps in our knowledge, of which the major ones can be summarized as follows:

  • The relationship between floc properties, such as strength, and settling velocity in turbulent flow is poorly understood. A tractable model of history effects on flocculation and floc break-up in turbulent flow is not available.
  • An entrainment model for fluid mud should account for all flow conditions depending on the degree of turbulence damping, i.e. the transition from high to low Reynolds number turbulent flow, down to laminar flow, where the rheological properties of become dominant. Such turbulence models are not available.
  • A physically based bed erosion model should take into account the interaction between turbulence and soil-mechanical properties of the bed. A general model is required which allows for the computation of the strength history of the bed, including the effects of consolidation, liquefaction and fluidisation.

Economic & Social Impact of COSINUS project

Estuaries belong to the most developed areas in many countries. They are under severe stress, as the surrounding land is often densely populated and a concentration of industry, harbour activities and ship traffic is encountered. Many other commercial activities take place, such as fishing, recreation, sand mining, dumping of dredging material, disposal of industrial and domestic waste, etc. On the other hand, estuaries are important natural areas for wildlife, nursery for fish. Often large wetlands are found in estuaries. Through their interaction with the sea, estuaries form an important part of large scale eco-systems.

In serving all these needs many conflicts of interest emerge in the management of estuaries. The managing authorities therefore have a need to weigh the various interests and to predict the consequences of managerial measures in the system. Managing authorities are confronted with progressively more conflicting interests, smaller budgets and more severe legislation. In many of the problems they encounter in estuaries and coastal zones, the transport and fate of cohesive sediment, contaminated or not, plays a key role. Thanks to new developments in numerical modelling and measuring techniques, it is apparent now that this transport and fate is governed in many situations by near bed concentrated mud suspensions. However, our physical understanding is yet insufficient to quantify these processes adequately and formulate them properly in mathematical models. As a result large uncertainties exist in any prediction or recommendation that is made with these mathematical tools. This means that presently it is not possible to improve the physical rationale to optimize managing strategies, the minimization of maintenance costs, nor the evaluation of measures for sustainable development.

An important tool in these evaluations is formed by mathematical models. The shortcomings of the present class of models is discussed in the state-of-the-art. The improvement of these models provides the authorities with means to improve their weighing process. More specific, the impact of a series of measures and interference with the system become better predictable.

The COSINUS project aims at an integration of our perception of various individual processes and of the individual process formulations, and the subsequent integrated validation, with special emphasis on major shortcoming in our understanding, i.e. on the behaviour of near bed concentrated suspensions. An important aspect of this work is related to the practical implications of implementing the various formulae in mathematical models. We believe that in spite of the enormous developments in computational power, it is not yet, nor in the near future, possible to incorporate all these formulae fully in the models, as they then become unpractical to run. Therefore additional studies are required to obtain convenient numerical codes and parameterizations of the physics.

This is a challenge, as it involves the quantification of the flocculation process and the bed structure, turbulence modelling beyond a state that is routine in civil engineering, the interaction between Newtonian and non-Newtonian viscous fluids and a poro-elastic medium, thixotropic effects, implementation of the derived formulations, or their parameterizations in global mathematical models suitable for engineering purpose, and last but not least, the measurements within relatively thin layers of high concentrated near bed suspensions.

The results of the proposed research will contribute to a better assessment of the environmental impact of human interference and regulation in estuaries and coastal zones, improving the modelling tools used for environmental management. The major socio-economic advantages of the COSINUS project consist of:
• A better assessment of the siltation patterns, both with respect to the quantities involved, and the spatial and temporal distributions, enables the authorities to optimize the lay-out and maintenance costs of fairways and harbour basins. At the end this implies lower operational costs of harbours, improving their competitive edge in relation to other ports elsewhere in the world.
• A better assessment of the turbidity levels and accumulation patterns of (contaminated) sediment allows the sustainable development of estuaries and coastal zones; typical examples are the restoration of wetlands and intertidal areas. This contributes to a healthier environment within the Community.
• The commercial institutes working together within this project will increase their competitive edge on the international consulting market through the technology step that will result from the proposed research.

Innovation
Our major innovation will consist of the development of explicit, physically sound mathematical descriptions of the behaviour of concentrated benthic suspensions and its interaction with the bed and the water column, and efficient mathematical formulations to apply this knowledge in everyday advisory work.

The COSINUS project will yield the following innovations:
• Assessment and quantification of the role of concentrated near bed suspensions on the transport and fate of cohesive sediment in estuarine and coastal zones,
• A formulation of the flocculation process of cohesive sediment in a turbulent environment, and its role on the formation of concentrated near bed suspensions and the structure of the bed,
• An integrated model formulation describing the stress response of the video porno, the erosion and re-entrainment process as a function of cyclical loading (waves) and current,
• A unified formulation for the processes of sedimentation, consolidation, liquefaction, fluidization and deformation of the bed.
• Validation, and where necessary modification, of classical turbulence closure models for application in near bed high concentrated suspensions,
• Development of convenient numerical codes and parameterizations enabling engineering applications of the mathematical models, and
• Guidelines for the execution of laboratory and field experiments and procedures for collecting the optimum data set aimed at studying the occurrence and role of near-bed concentrated suspensions.