Akarsu deltaları oluşumunun matematik modellenmesi

Özet

Akarsular üzerine yapılan çeşitli düzenleme yapıları, bu akarsuların taşıdığı katı madde miktarını değiştirmektedir. Bu değişikliklerin olumsuz etkilerinin en belirgin olarak görüldüğü yer, akarsuların çıkış ağızlarında oluşan deltalardır. Denge halinde bulunan bir akarsu kesiminde bir barajın yapılması sonucunda, baraj gölünün yukarısında, su kabarması görülen nehir kısmında, su hızı düştüğü için akarsuyun taşıdığı katı maddelerin önce iri malzemeleri çökelir. Daha sonra biraz daha ince olan kum ve çakıl gibi malzemeler baraj gölünün menba kesiminde çökelir ve bu çökelmeler delta oluşturur. Kil ve silt iriliğindeki malzemeler ise baraj gölünde akmaya devam eder ve baraj gövdesine yakın bölgede çökelirler. Böylece barajlarda üç türlü yığılma söz konusu olur. a)- suyun kabardığı akarsu kesimindeki yığılmalar, b)- kum ve çakılın oluşturduğu deltalar ve c-) kil ve siltin oluşturduğu taban yığılmaları. Yığılma şekilleri, kil malzemesinin mineral karakteristiğine ve suyun hareket şekline bağlıdır. Taban malzemesine baraj gölünün her yerinde rastlanır. Fakat en çok akım hızının düşük olduğu baraja yakın yerlerde ve su yüzünün salınım yaptığı yerlerde çökerler. Bununla beraber, bunlar tam yığılıp tabakalaşmadan önce bu ince malzemeler yoğunluk akımlarıyla hareket edebilir. Haznenin toprakla dolmasında, su yüzünün ve tabanın profillerinin nicelik olarak belirlenmesi önemlidir. Olayı matematik olarak inceleyen metotlar; su ve katı madde denklemlerinin birlikte çözüldüğü modeller ve suyun kabarması etkisinden faydalanan modellerdir. Bu çalışmada, durgun bir su ortamına deşarj olan bir akarsu deltası matematik olarak modellenmiştir. Akarsu debisi, katı madde miktarı, akarsu deltası radyal genişleme açısının akarsu deltasına etkisi matematiksel ve sayısal olarak belirlenmiştir.

Abstract

Rivers form deltas wherever they flow into a water body such as a lake, a reservoir, a sea or the ocean. All rivers transport sediment as well as water. Dam construction impacts the transport of both water and sediment. Because the great majority of rivers transport much more water than sediment, a much longer time is required to fill a reservoir with sediment than with water. As a result the gradual accumulation of sediment in reservoirs often receives less attention that it merits. Sediment deposition in a reservoir reduces its storage capacity, so limiting the effective life of the dam as well as the benefits it provides. Natural river reaches are usual in a state of morphological equilibrium where the sediment inflow in average balances the sediment outflow. Dam constructions dramatically alter this balance due to change in the hydraulic conditions as well as trapping of the sediment in the reservoir. The storage of water and sediment has a number of various environmental impacts, which need to be investigated in the design, construction, operation and maintenance. Understanding the mechanisms of formation of deltas and the bed profiles of sediments is of fundamental importance to the fields of hydraulics, hydrology and water resources. Deltas are cone-shaped deposits formed at the confluence of rivers with standing bodies of water. Deltas commonly display three distinct zones; (a) a lowslope topset deposit that forms as the coarse sediment load deposits on the river bed, (b) a high-slope foreset deposit (delta face) that forms as the coarse sediment load avalanches down the delta face into deeper water and (c) a low-slope bottomset deposit that forms as the fines settle out on the bed of the lake or reservoir. This structure is illustrated in Figure 1. Rivers generally carry a broad range of sediment sizes. Here the problem is abstracted to sand-bed rivers that predominantly transport two grain sizes, sand and mud. Such rivers typically have beds that are composed almost exclusively of sand. The mud carried by a sand-bed stream typically forms only a negligible fraction of the bed material because its deposition on the river bed is inhibited by the relatively high ratio of boundary shear velocity to particle fall velocity. For this reason it is often referred to as wash load. In the deltas of sand-bed streams, therefore, the topset and foreset deposits are built mostly out of sand, while the bottomset deposit consists mostly of mud. The mud may be deposited by one of three mechanisms. The first of these consists of surface plumes and the second consists of interflows. Both of these form when the sediment-laden river inflow has a density that is less than the highest density of water in the lake or reservoir. The third mechanism is a muddy bottom turbidity current which forms when the sediment-laden river inflow is sufficiently heavy to plunge. Some assumptions and approximations are introduced in order to develop the delta formation of a river. The delta and its associated deposits are allowed to prograde in the longitudinal direction but not allowed to flare out in the transverse direction. This approach allows for a relatively simple experimental test of the model. The model can be easily generalized to a quasi 2-D laterally expanding model of river deltas in lakes and reservoirs. The model assumes a single characteristic grain size D, which may be sand or gravel. Sediment transport calculations are based on the assumption that this size allows for a computation of bed material load, but not wash load, which is excluded from the calculation. In a gravel-bed river the bed material load is typically mostly gravel, even when the great majority of the load is sand. In a sand-bed stream the bed material load is typically mostly sand, even when the great majority of the load is mud. The analysis presented here represents a delta formation processes in a standing water such as a lake or reservoir by using finite difference methods. Firstly one dimensional form of the delta formation is developed. Secondly two dimensional formulation is calculated according to flow regime of the river. A standing body of water is created in a river of constant width and by means of a vertical barrier (dam). The river flow upstream of the barrier is Froude-subcritical and the barrier creates an M1 backwater curve.