Akarsuların, Denizlerdeki Kıyı Çizgisine Ve Yapılarına Etkisinin Bir Matematik Modelle İncelenmesi

Abstract

Akarsuların taşıdığı katı maddelerin iri olanları, akarsuyun denize döküldüğü nehir ağzında çökelir. Daha ince olanları dalgaların etkisi ile kıyı boyunca hareket ederken, bir kısmı ise kıyıya dik hareket eder. Akarsulardan gelen bu katı maddelerin uzun vadede kıyılarda bazı değişikliklere sebep olduğu bilinmektedir. Ayrıca bu katı madde hareketleri mevcut deniz yapılarına da oyulma veya yığılmalar dolayısı ile önemli etkilerde bulunur. Bu çalışmada, denize dökülen akarsuların taşıdığı katı maddelerin kıyı çizgisine ve deniz yapılarına etkileri matematik bir modelle incelenecektir. Akarsuyun getirdiği katı madde enkesitte uniform kabul edilerek kıyı boyu katı madde süreklilik denklemine, sabit birim genişlikten geçen katı madde miktarı olan (q) ilave edilmiştir. Bu durumda katı madde süreklilik denklemindeki türevler yerine ileriye doğru sonlu farkları yazılmış, kıyı boyu katı madde debisini tahmin eden bir formül yardımıyla, başlangıç ve sınır şartlan belli olan bir kıyı şeridi için çözüme gidilmiştir. Akarsuyun genişliği 50 m, 100 m ve 125 m alınarak 1000 metrelik bir kıyı şeridinde meydana gelen değişiklikler incelenmiştir. Bu incelemede akarsuyun konumu sabit alınmıyarak, hesap sınırının başında, ortasında ve sonunda olmak kaydıyla yeri değiştirilmiş ve taşıdığı katı madde debisi q=1.10"3 m3/sn/m, q=1.10-4 m3/sn/m, q=1.10-5 m3/sn/m ile q=1.10-6 m3/sn/m şeklinde değiştirilerek akarsuyun kıyıdaki yeri ve debisinin etkisi açısından bir genelleme yapılmaya çalışılmıştır. Mendirek gibi bir deniz yapısının sağından soluna doğru veya solundan sağma doğru bir katı madde geçişi söz konusu değildir. Aynı zamanda kıyı yapısından belli bir mesafe sonra kıyının yapıdan etkilenmediği ve doğal durumunu koruduğu görülür. Bu incelemede mendireğin hemen bitişiği hesap sınırının başlangıcı olarak kabul edilmiş ve başlangıç sınır şartı olarak bu noktada katı madde debisi sıfir alınmıştır. Mendirekten 1000 m ötede kıyının yapıdan etkilenmediği göz önüne alınarak, bu noktadaki katı madde miktarı bir önceki noktaya eşit alınmak suretiyle hesaplar yapılmıştır. Mendireğin hemen yam başında, mendirek yüksekliği rüzgarın esişini engellediği için bu kısımda ölü bir nokta meydana gelmektedir. Dolayısıyla akarsuyun mendireğin hemen yam başmda denize dökülmesi halinde, akarsu tarafindan taşman katı madde kıyı boyunca kısmen taşınmaktadır. Ancak akarsuyun döküldüğü yer, mendirekten uzaklaştıkça mendireğin kıyıya etkisi azalmakta dolayısıyla akarsuyun taşıdığı katı madde kıyı boyunca daha çok taşınmaktadır. Ayrıca çalışmada elde edilen sonuçlar tablo ve grafikler halinde değerlendirilmiştir.

Beach is defined as the coast contained choeisionless materials such as sand and gravel. Along some beaches man-made structures such as harbors, seawalls, breakwaters and shore-connected breakwaters are constructed. The beach itself is constantly in motion and slowly changing its configuration. On a natural beach, the longshore sand transport is usually in equilibrium. If, however, the longshore sand transport is interrupted by a coastal structure, sand will deposit on the updrift side of the structure and erosion will occur on the downdrift side. Coastal sediment transport is either perpendicular to the shoreline (onshore-offshore transport) or parallel to it (longshore transport). Onshore- offshore sediment movements produce short-term variations on the beach profiles, while alongshore movements produce long-term variations. Nearshore currents are the main causes for the movement of sediment. Currents are generated by waves, winds, tides and river outflows. The most important current that cause the movement of sand is the one that flows alongshore in the surf zone which is created by waves breaking at an angle to the shore. On some coasts, alongshore currents annually transport thousands of cubic meters of sand, eroding one beach and building another. Alongshore sediment transport is usually sand moved in the beaches under action of waves and currents. The rate Q that is moved parallel to the shoreline, is the longshore transport rate. There are two possible directions of motion. One of them is from right to left and another of them is from left to right. So sediment transport from right to left is indicated by subscript (It), the other motion is indicated by subscript (it). Gross longshore transport rate (Q ) is the sum of parallel sediment transport on the shoreline in a given time period. Similarly, net longshore transport rate (Qn) is difference between Qrt and Q^. These transport rates may be expressed as follows. Qg = Qrt + Qit Qn = Qrt-Qlt The purpose of this study is to analyse relationship between shoreline, longshore sediment transport and effect of a river. It can be divided into six main parts. The brief summary of these parts have been given as follows. In Chapter II, the types of most important models were analysed. And the model of CERC (Coastal Engineering Resource Center) was used in this xin study. As such as, the longshore transport rate (Q) is usually calculated from the CERC formula. It has been given below. Q = K'(H2.Cg)b.Sin2obs !C * (if \6{ys-\)a\r) Where, K : Non dimensions empirical coefficient (of order 0.4) H : Significant wave height Cg : Wave group velocity ot- : Angle of breaking waves to the shoreline y : Ratio of sand density to water density a : Ratio of volume of solids to total volume r : Conversion factor from root mean Square (RMS) to significant wave height, if necessary (equals, 1.416 ) The subscript (b) indicates quantities at wave breaking. The group velocity at breaking is calculated from; Where, V r ) g : Acceleration of gravity Y : Ratio of wave height to water depth at breaking, approximately equal to 0.78 The a. is the angle of the breaking waves to the shoreline. It is equal to the difference between the angle the breaking waves makes with the x-axis and the angle the shoreline makes with the x-axis; abs = ab'a Where, ov : Angle of breaking waves to x-axis \âcj This condition shows as follows, XIV Direction of Significant v Wavers. NS ^bs^s^oreline Figure 1. x - y Axis and the Condition of Shoreline In Chapter HI, Continuity, momentum equations and equations of wave were described. The conservation of the mass of sand is described by the continuity equation. ât D âc In which. y : Shoreline position t : Time Q : Volume rate of longshore sediment transport x : Distance alongshore D : Vertical distance between the top of the bank and the lowest line where material is moved Effect of a river on shoreline is shown below by the continuity equation ây 1 âO - + - = q a D âc * q : Sediment quantity per unit width of river Also some important equations for sinusoidal wave are snown below -a.C.Cosh[k{y+d)} In fact this equation is velocity potential. In which; Where; XV <|) : Velocity potential a : Amplitude of wave C : Celerity of wave or the phase velocity k : The number of wave d : Water depth y : The distance of y-axis a : Circular frequency Also Bernoulli's equation for unsteady flow, expressing the conservation of energy, can be written as; *¥ U2+V2 p at 2 p where; P : Pressure p : Density of the fluid g : Acceleration due to gravity U : Horizontal velocity of a particle V : Vertical velocity of a particle Wave celerity can be written by equation of velocity potential, ms { l ) In Chapter IV, Equations, which were used of in this study, were explained by use of the explicit scheme of finite differences. In a standard explicit scheme, the continuity equation with effect of river is discretized as For an explicit scheme, there is a stringent limitation on the size of the largest possible time step, other variables being held constant. For small breaking wave angles, in the present case this condition is where, ** = 2K'.At(H2.Cg)b D.{Axf XVI Rg was called, as the stability parameter by Kraus and Harikai. This equation is an adequate indicator of stability in most applications, since breaking wave angles are usually small (Hanson and Kraus, 1986). Present equation is solved by initial and boundary conditions. According to the rule for diffusion equations, we need a boundary condition at each boundary on both sides of the reach. There are few possibilities. One of them is sediment transport which is zero or constant at a construction such as a breakwater and shore-connected breakwater. So we can write as Another boundary condition is far away from a construction. It means that x-»oo. So we can write as aQ or dy_ ds. - Const. X=±00 = Const. X=±00 The shoreline evolution can be calculated with continuity equation and CERC formula. This study was continued with Chapter V which contains applications and evaluation. A mathematical model was setup for the problem and a computer program written in FORTRAN 77 to solve the model was used. The results found in this study were presented in diagrams and in tables. Some assumptions were made been make in this research. These are; 1) The width of river were taken as 50 m, 100 m and 125 m. Also the position of river was at the beginning, middle and end of system. 2) Sediment material of river was selected as 1.10, 1.10, 1.10 and 1.10 outflow per unit width (m3/sn/m). 3) Changes of shoreline were analysed after 1, 3 and 6 years in the mathematical model. 4) The flow chart of computer program is given in Chapter V. The names of parameters and variables are; the angle (theta); denoted as Z, and the empirical coefficient K; denoted as Kl in the computer program. Also the grid XVII spacing is DX (in meters) and the time step is DT (in hours), the wave period is denoted by T (seconds), NTIMES specifies the number of time steps and IT1 and IT2 denote time steps, DENOM is value of physical quantities in the denominator of the CERC's equation, evaluated for quartz sand. 5) It has been assumed that waves coming from NNW, N and NE winds transport sediment material along the shoreline. 6) Strip, 1000 m, was taken into the consideration for computational boundary on the shore and discretized 40 elements. 7) CERC formula was employed for the sediment material computation. The results of the experiments and mathematical model have been summarised in Chapter VI. Finally, the results of the computations were compared with laboratory experiments and natural conditions. 450m Figure 2. Changes in Shoreline at Laboratory -Model (NE, H=2.8 m, 1=6 sec, after 2 hours) A pool having length of 32 m, width of 19.1 m and height of 0.7 m was constructed in the Hydraulics Laboratory of İTÜ. The model of Efirli-Ordu Harbor was built by using of scale of 1/150 in the pool. In this model, XVIII polstryrene, which is equivalent to sand dimension, was used as the sediment material. Changes in the model occurred for two hours are shown in Figure 2 for the wave height of 2.8 m and the wave period of 6 sec and the results observed is presented in Figure 3. Figure 3. Changes in Shoreline According to the Natural Condition The main results of this research can be summarised as follows: 1) Because the sediment transported by the river is relatively less, the main cause of deposition on the shoreline is waves travelling in direction of NE 2) Since sediment transport does not exist across the groin, initial boundary at this point will be taken a zero. So, an eroding process will take place just after groin. 3) Because of height of groin NNW and N winds can not cause any changes on the surface of sea at the just after the eastern side of groin, this region is called as dead zone. Hence sediment transport does not exist in this zone. 4) As moving away from groin, the effect of groin decreases along the shoreline as shown in Figure 4. It will be observed that if amount of deposition is 100 % at the beginning of boundary, 37.5 % at the middle of computation boundary and 33 % at the end of computation boundary. 5) New position can be occurred by changing of the boundary conditions. Hence these conditions can be taken account into future studies.