Lagün-deniz etkileşiminin matematiksel modeli

Abstract

Lagünler genelde deniz gibi daha büyük su kütlelerine bağlantılı sığ göllerdir. Lagünler çevreyle ve karışık şekillerde bağlandığı deniz ile doğal denge çerçevesinde etkileşim halindedir. Bir lagünün en önemli karakteristik özelliği açık deniz ile olan bağlantısıdır. Bu bağlantı uzun bir kanal, bir bataklık, rüzgarla oluşmuş kum tepeciği formasyonu, bir akarsu veya sadece bir dar ağız şeklinde olabilir. Bu bağlantı şekli lagünün doğal formasyonuna, sahil şeridinin morfolojik ve ekolojik durumuna etki eder. Bağlantı bölgesinde akıntı mevsimsel olarak tatlı su kaynaklarının azalıp çoğalmasına ve denizdeki dalga koşullarına bağlı olmak kaydıyla her iki yönde de olabilmektedir. Lagündeki tuzluluk konsantrasyonunun değişimi de akün yönüne bağlı olarak değişmektedir. Bu açıdan lagün suları deniz su kalitesinin veya tam tersinin etkisi altındadır. İdealleştirilmiş bir lagün sistemi ele alınıp bilgisayar programı yardımıyla lagün deniz etkileşiminin matematiksel modeli yapılmıştır. Başlangıç koşulları ve sınır değerleriile birlikte lagün ve kanalların boyutsal büyüklükleri verilmiştir. Bu değerler yardımıyla kanallarda oluşan debiler, hızlar, lagünlerdeki su seviyesi değişimleri ile kanal ve lagünlerdeki tuzluluk konsantrasyonu değişimleri hesaplanmıştır. Bu hesaplamalar değişik zaman aralıklarında denizden kabarma dolayısıyla lagün içerisine doğrusu girişi ve lagünü besleyen akarsulardan akım girişi olması koşulları için ayrı ayrı yapılmıştır.

A lagoon is a shallow lake connected with a larger body of water comprised mostly of the sea. Lagoons interact their environment and with the sea with which they are connected in a very complex manner within a naturally balanced framework. The main characteristic of a lagoon is its connection with the open sea which may be a long channel, a wetland, a dune formation, a river, or just a narrow mouth. This type of connections have critical effects on the natural formation of the lagoon and on the morphological and ecological structure of the seacost in the neighborhood of the connection mouth. The hydraulics of the channels have very complex manner, because it has been under effects of the lagoon water level which depends on the hydrological condition of the lagoon basin and under effects of the wave condition around. The mean parameter affecting to the channel flow is the hydraulics slope because of the difference between lagoon water level and mean water level of the sea. The other parameter affecting to the channel flow has been inlet bottom topography. If the inlet is too narrow there's always the problem of water circulation in normal weather conditions. Sometimes seawater reaches to inlet but can not pass through the inlet channels acting as a settling basin. And all the suspended sediments coming from the sea by the water settle down to the channel bottom. The connection area currents may flow in different directions. In wet seasons, when the freshwater sources of the lagoon, such as rivers, have more water, predominant currents flow from the lagoon towards the sea. In the other seasons, however, also depending on wave conditions in the sea, the current flows in the opposite direction from the sea into the lagoon. Therefore lagoon waters are significantly influenced by the water quality of the sea and vice versa. Lagoons are investigated in three parts; 1. Region having fresh water that's near the river part, 2. Tidal zone having salty water near the lagoon mouth, 3. Region where the mixture of salty and fresh water occurs. Lagoons may be completely close to the sea and have fresh water. But in this case, the salinity may increase with the seepage of the sea from the barrier into the lagoon. The formation of the coastal lagoons are related with the mouth of the lagoon or the configuration of the dune that separates the lagoon and the sea. Some lagoons have a wide dune formation (Figure 1). xni Figure 1. Ulawarra Lagoon (Bird 1984) Morphological developments can be observed at the coasts of the lagoons caused by the erosion. As a result of erosion, salt marshes and shallow areas are ceased to exist and channels are filled up. The main causes are identified in engineering structures like jetties and maintenance dredging. The changes in the lagoon morphology also affects human activities. It results in the difficulty of navigation on the natural channels and an heavier wave attact against the defence of villages and agricultural land (Figure 2). BEFORE Figure 2. Change in the cross-section of the lagoon by the time The relation between sedimentation and wave-current is important. In the channels the velocity, in the shallow regions wave motion is effective on the lagoon bottom. And there's a direct proportionality between mean water depth and the mean sediment concentration. Changes in the lagoon is the result of in and out sedimentation. There are various forcings and boundary conditions that control episodic salt intrusion, stratification, mixing and advention of fresh and salt water in the estuary. Generally in the shallow mouth region where the tide and wind causes mixing, xiv incoming of fresh water causes strong stratification. The hydrodynamic motions and salinity regime is more clear in some meteorological and seasonal time periods. The most important reasons causing circulation and salinity structure in the lagoon- type estuaries can be considered as;. low frequency motion and salt intrusion from the coastal sea,. wind forcing over a wide range of frequencies (daily or seasonal),. episodic storms,. freshwater runoff and groundwater seepage,. strong topographic effects,. evaporation and. human impacts in the form of controlled stormwater releases to the estuary. The overcoming of freshwater has a bad effect on the growth of some seaplants because of sudden and severe salinity changes. From the point of view of salinity, stratification changes in some regions of the lagoon. It's more effective near the river and the sea rather than the inner parts. In our country especially in summer season, freshwater coming into the lagoon decrease upto the minimum level. And in this period also with the effect of evaporation salinity escalates to the maximum level by means of sea flowing into the lagoon. The optimal salinity regime of lagoon in the mouth is of importance for the living species in this region. This rapid salinity level changes may cause severe living conditions for some species. In order to investigate the hydrodynamic sturcture of the lagoons, it's possible to make a mathematical model. Models according to their scales can be separated into two such as large scaled and small scaled models. In a lagoon system that's connected to the sea with a channel, there should be a discharge from sea into the lagoon because of the stormy weather conditions and from the lagoon towards the sea when it's returned back to mean water level because of river's discharge into the lagoon. Within this case there will be a problem of discharge in two directions. There will be differentiations in the salinity concenterations and water levels in the lagoons and in the channels that connect lagoons to eachother. An idealized lagoon system is investigated and the mathematical model of the sea and the lagoon relations is considered. In this model it's assumed that the discharge into the lagoon is the lineer function of water level of the sea and the lagoon, the lagoon area is stable and the salinity mixture is uniform. xv A computer programming has been done in order to compute the parameters changing with the new conditions. In the calculations for the water level changes in the lagoon, formulas;.«+1 nn Ql ~Ql A-1. h* + ^LJ« At (1) 4 and h?y = h? + ^3l Ar (2) are used. For the differentiation of the salinity concentration in the channels, formula 1+r 1+r whereas stability factor r should be ^ 1/2 is used. For the differentiation of the salinity concentration in the lagoon, formula is. - 9.{crc) (4) dt V ' is used. Interpretations on the results of the mathematical model: Because of the increase in the sea level, the discharges in the channels and the concentrations in the lagoons are observed. The discharges in the channels, with the increase of the time period, advances into the lagoon more. After sometimes the direction of the discharge has turned back to the seaward. After a while it has become neutralized and in the small time period little, in the big time periods wider oscillations takes place. xvi With the advance of sea and the discharge of river into the lagoon at the same time, water coming into the lagoon from the sea facing with the discharge of the river changes its direction back to the sea having the discharge of river by the time. Concentrations in the lagoons with the salinity coming from the sea increases somewhat and by the last of the current coming from the sea decrease to a value and oscillate around. Concentrations in the lagoons decrease down till having the same ratio with that of the coming discharge caused by the river.