Coastal hydro- and morphodynamics
Latvia has a 496 km long, mainly sandy coastline (configuration see Fig. 1). The along-shore sediment transport can reach integral values up to 1000000 cubic meters and 50000 cubic meters per annum for the coast of the Baltic Proper and the Gulf of Riga, respectively. The developed harbour industry (the location of 10 seaports of Latvia see on Fig. 1) disturbs the natural load transport processes by means of constructing the hydrotechnical objects as the wave-breakers and sea entrance channels. The redistribution of the seabed topography, sedimentation in the sea entrance channels, dynamic response (growth or erosion) of the coastline is the cost for the operating seaports. Besides, the sedimentation in the sea entrance channels (typical depths are 5 to 7 m for small fishermen harbours up to 17 m for Ventspils harbour serving crude oil tankers) increases the expenses of the navigation requiring regular dredging works (typical price is about 2 $/cubic meter) to ensure the safe navigation depths. Thus, the methods for the forecast of the integral sedimentation/erosion volumes, their spatial and temporal distribution, and dynamics of the coastline are necessary. Besides this, the engineer solutions for the optimum wave breaker configuration, overdredge of the sea entrance channels, configuration and depth of the additional (safety) overdredged areas, location of the load material discharge areas are needed to minimize regular dredgeworks, allow their planning, ensure continuous navigation conditions, and reduce the erosion of the coastline. A set of mathematical models would be suitable for the above goals after the reasonable verification stage.
Fig.1. Coastline of Latvia, including harbours, main rivers, and direction of integral load transport.
2. Physical processes
The principal scheme of the processes related with the along-shore sediment transport and their interaction is shown on the diagram, Fig. 2, whilst the scheme of the scenario of the sedimentation-erosion processes is presented on Fig. 3.
The bed and suspended load transport is driven by the coastal hydrodynamics. The alongshore and wind currents determine the velocity and orientation of mainly longshore load transport that have maximum values at the depths of about 0 to 7 m. The wave field, especially in the zone of breaking waves, is the most important generating the shear-stress and producing the suspension of the grain material in the water column. Wave-field is responsible also for the sediment transport to- and outwards the shoreline. The bottom shear stress is dependent on the water depth (i.e. the bathymetry and the actual water level), whilst the suspension rate as well as the bed load movement depend on the particle size distribution (grain size dispersion, typical mean of the distribution lies within range from 0.1 to 0.3 mm). Besides the bottom sediments, the load flow along the shoreline is being fed or diluted by, respectively, the erosion or growth of the coastline. These processes of the coastal dynamics that can reach the values of several hundred metres per half a century are driven mainly by the wave field action on the beach, that has different impact for different water levels and size distributions of the sand particles.
The sinks (sedimentation) and sources (erosion) of the material load transport are dependent mainly on the bathymetry and the configuration of the natural and artificial (hydrotechnical constructions) obstacles, that, interfering with the hydrodynamics, results in the over- or undersaturation of suspended load, and inability or ability to move the bed load. The above opposite conditions produce, respectively, sedimentation and erosion. These processes have reversive influence on the depth redistribution as well as on the grain size dispersion of the bottom material (coarser particles in the erosion zones but smaller ones in the sedimentation regions). The superposition of the human influence on the depth distribution over the natural processes has to be carefully accounted.
Fig.2. Scheme of processes influencing sedimentation - erosion.
The processes of coastal hydrodynamics driving the load transport are (see Fig. 2):
- water level fluctuations in the synoptic time-scale, due to the action of mainly local winds and the overall atmospheric pressure field; in the cases of the location of the harbour in the river mouth (see Fig. 1) the river run-off (including its possible forcing by hydropower stations regime) also may affect (enlarge) the water level in the regions of the vertical density stratification;
- wind wave field in the open sea and coastal wave transformation zone;
- longshore currents driven through the transformation of the wave field energy due to (i) non-orthogonality of the wave vector in respect to the coastline (energetic currents) and (ii) non-equal seaward depth profiles in different locations along the shoreline (gradient currents); longshore currents prevail in between the wave-breaking line and the coastline;
- wind-driven currents prevailing seawards from the wave breaking zone.
One have to note also the interrelation of above four elements of the coastal hydrodynamics and their structural dependence on the depth distribution and bottom material. The whole hydrodynamic processes are forced by the local (river run-off, wind velocity and direction) and the global (cyclonic and anticyclonic atmosphere structures, non-homogeneous wind field over the whole Sea or Gulf, etc.) meteorological conditions. The scenario of the development of the sedimentation/erosion processes for the particular storm event is summarized on Fig. 3.:
- the fronts of the wind waves transforming in shallow zone reach the wave-breaking line non-parallel to the isobaths;
- energy transformation after breaking the waves produces the long-shore currents with the maximum discharge at the depths of 6 to 7 m along the coast of the Baltic Proper or 3 to 5 m along the coast of the Gulf of Riga;
- the currents carrying the material load incline seawards (to the greater depths) before the wave breakers; here, mainly due to the greater depths, they become oversaturated and the sedimentation occurs;
- the long-shore current becomes even more oversaturated crossing the border of the channel. Due to the fast increase of the depth the bed load transport stops here, whilst the sedimentation of the suspended load depends on the width of the channel;
- passing the seaport, the longshore current is undersaturated; it restores the load transport up to pre-harbour transport capability continuously. This process causes the prolonged erosion of the bottom downwinds from the harbour;
- the decrease of the depths in the upwind side of harbour shifts the wave-breaking zone seawards. The load transport to- and outwards the coastline trends to the growth of the beach (and vice-versa for the downwind region).
The above scheme is valid for a single storm event; these events occur 10 to 20 times per autumn-winter period. Due to the existence of the prevailing wind direction, especially near the coast of the Baltic Sea (the measurements of the wind at Ventspils indicate the 58% repetitiveness of winds producing northwards load transport, but for strong winds over 8 m/s even 63%), the described morphodynamic changes are an overall trend.
Fig.3. Scenario of development of the coastal load transport processes.
3. One-dimensional model
The one-dimensional model of the load transport is developed for the particular Ventspils harbour. The load transport is subdivided into the bed and suspended modes. The critical shear stress for the start of the movement of the bottom particles is determined according to the Shields theory. The parameterization of the bed load flux dependence on the mean current velocity for the superposition of the wave and oriented water flow is performed assuming the uniform bottom particle size d=0.3 mm. The suspended load transport is accounted via the vertically integrated advection/diffusion equation where sink/source terms of the concentration stand for, respectively, sedimentation/erosion processes. The average saturation concentration switching the direction of the process is assumed according to, whilst the empirical concentration depth profile is assumed to be linear. The morphodynamic changes of the seabed are assumed to occur in another time-scale without the direct influence on the load transport. Hence, the model of the dynamics of the depth distribution along a one-dimensional domain is developed, including only universal constants. The hydrodynamic field, and the selection of the one-dimensional domain is the basic problems for the closure of the proposed model.
The selection of the pathline of the longshore current is performed from the analysis of the 4 year monthly depth survey data near Ventspils harbour, indicating the maximum load transport along the 7 m isobath. The velocity of the longshore current is assumed to be proportional to the wind speed and independent on the wind direction according to the experiments described in. The direction of the longshore current is assumed to be dependent on the wind projection on the coastline. The empirical coefficient for the wind/current relationship is found from the best fit for 4 storm periods without dredging works but with complete depth surveys with about a month long delay.
The typical result of calculation is shown on Fig. 4 for the storm period from 27-Dec-1991 until 19-Jan-1992. The depths across the sea entrance channel before (measured) and after (measured and calculated) storms are given on Fig. 4. The comparison indicates good agreement between the survey and the prediction. The interchanging storms (19 and 21 wind event above 10 m/s in, respectively, northern and southern sectors) have caused an interchange of sedimentation/erosion via bed load movement on both sides of the channel, smoothing the bathymetry. Sedimentation of suspended load is observed in the gate of the channel, causing reasonable decrease of the navigation depth.
Fig.4. Comparison of measured and calculated depth distribution.
4. 2D shallow water model
Simple hydrodynamic closure of the load transport model employed in chapter 3 is not sufficient for the spatial resolution of the morphodynamical process. The shallow water model can be used for the calculation of coastal hydrodynamics if the modeling of the short waves is performed in the energetic sense.
The shallow water approach is sensitive to the selection of the computational domain for detailed calculation and the setting of adequate boundary conditions. Usually the linear dimension of the area under interest for the near-harbour sediment transport is 5 to 10 km. Therefore the direct influence of the wind (current and wave generation) is negligible. The wind regime therefore has to be accounted via the appropriate boundary conditions on the borders of the region. These conditions can be obtained either from the large-scale hydrodynamic calculation (for all the water basin) or by means of employing semi-empirical assumptions. The current along the coast nearly follows the isobaths; this can be used by selecting the outer sea boundary along the constant depth line and setting there empirical, wind-dependent flow velocity. The inflow boundary velocity distribution can be obtained, for instance, from the one-dimensional along-shore current model. The outflow boundary can be set at a constant elevation. The steady-state of such a calculation in 5 to 10 km domain can be reached in few hours. Accounting time resolution of the meteorological observations (usually 3 hours) this allows to operate shallow water model in the quasi-steady-state mode and to use a stepwise hydrodynamic forcing for the slow process of sedimentation.
The typical steady-state solution of the shallow water flow for the Engure fishermen's harbour is shown on Fig. 5 (only part of the computational domain!) for the 5 m/s NE wind. Such a wind generates 0.2 m/s current at 5 m depth, i.e. the northern boundary of the computational domain. The calculations indicate recirculation in the stagnation zone downwinds the harbour, the separation of the convective jet 20 to 30 m eastwards from the northern wave-breaker.
Fig.5. Calculated steady state discharge (isolines of modulus and direction) field.
The geographical and geopolitical location of Latvia on the crossing of (European) East-West and North-South routes, the developed rivers network, and prolonged Baltic Sea coastline have stimulated the growth of activities dependent on or influencing natural hydrological processes. Consequently, the observation series for different hydrological parameters are available for approx. 100 years. The broad and interrelated spectrum of hydrological processes are extensively studied for decades; however, contrary to central and western Europe, with minor employment of mathematical models. The relevance of hydrological processes, people awareness, availability of data together with plenty of working hypotheses make hydrological studies in Latvia a real challenge for modeller.
Latvia has approx. 500-km long, mainly sandy coastline. Fine to medium sand means not only recreational beaches but also reasonable littoral drift, coastal abrasion and accumulation. The net annual northward drift along the coast of the Baltic Proper is caused by prevailing westerly south-westerly winds.
The most distinct manifestation of the littoral transport occurs in its interaction with hydroengineering constructions of seaports (wave breakers, jetties, and sea entrance channels). Main qualitative features are beach growth in upwind side of harbours while downwind areas suffer from erosion. Siltation in sea entrance channels is a real problem for navigation safety requiring annual allocations to perform dredging works. The optimisation of the measures to ensure safe navigation at minimum costs is especially actually for Liepaja and Ventspils harbours exposed for the Baltic winds and waves.
The continuos wave action on the sandy coasts produces cross-shore sand transport by oscillatory velocities; longshore currents with maximum of velocities and littoral longshore transport close to the wave-breaking line. The restructuring of the cross-shore profiles has time scale between single storm period (wash out of sand bar and/or beach) and season (restoration of bar structure). The direction and magnitudes of longshore currents vary continuously. The analysis of the mean sand transport volumes along the coastline allows specifying overall trends, accumulation and erosion zones, which on a longer time scale has respective impact on the shoreline development. A simple one-dimensional model for the predicting cross-shore distribution of the longshore littoral drift is developed. It accounts for wave generation (fetch model), transformation (incl. breaking), current distribution, formation of suspension, development of bed macroforms, bed and suspended load transport. The application of the model for the chain of cross-shore profiles along Latvian coastline shows that. The prevalence of the southwestern winds is responsible for the significant (typically more than 1 million m3) northward load transport near the Latvian coast of the Baltic Proper. The combination of the fetch with coastline orientation yields, generally, converging southward sand transport (annual values below 100 thousand cubic kilometers) along the coasts of the Gulf of Riga.
The hydrodynamical processes become essentially two or three dimensional in the vicinity of harbours. Typical engineering constructions, which interact with wave fields, water flow patterns and load transport, are wave-breakers, jetties, sediment traps and sea entrance channels of harbours. Two-dimensional model is developed for applications in near-harbour regions (typically up to 10 km zones). It includes two-dimensional, time-dependent description of wave-field, hydrodynamics, bed and suspended load transport, and morphodynamics (bed level changes). The operation of the model in a hind-casting mode allows its calibration and verification.
The operation of the model in forecasting mode allows prediction of the siltation in sediment traps and sea entrance channels during typical and critical seasons; it helps to draw consequences of reconstruction efforts, and is useful for designing of the sediment traps and finding other engineering solutions such as building additional wave-breakers. The applications of described model are found to assist reconstruction of Ventspils and Liepaja harbours.
Ventspils Free Port Authority