Modeling of tsunami waves in the Sea of Marmara

Abstract

Istanbul is the most important city of Turkey in the view of economical, social and cultural aspects. Because of the active faults in the Sea of Marmara, there is always an expectation of an important earthquake that will be harmful for the city and also for the other big cities that are located around the Sea of Marmara such as Bursa, İzmit, Tekirdağ and Yalova. In addition to the earthquake, a tsunami which occurs in the Sea of Marmara can also be a very destructive hazard for Istanbul and other cities around the Sea of Marmara. There are many tsunamis that happened in the Sea of Marmara in the history. The main reason of these tsunamis is the slumps and the landslides that were triggered by an earthquake. One of the most important reasons of the tsunamis on the earth is the submarine landslides. Movement at the sea bottom stirs the above water mass. This causes tsunami waves and these waves damage the coastal areas seriously. The aim of this study is to find the maximum wave heights of possible tsunamis around Tuzla coasts using different scenarios. A submarine landslide that may be occurred after an earthquake or because of any other reason in the Sea of Marmara at the region near to northeast Marmara coasts is taken as the reason of the tsunami in the simulations that are performed in the study. As the solution method, one hybrid method was developed. The main objective of this method is to combine an analytical solution presenting near-field tsunami amplitudes above the submarine mass failure with a numerical solution indicating the tsunami amplitudes in the coastal regions. An analytical model that is frequently used in the literature was applied to find the amplitudes of tsunami waves at the surface of Sea of Marmara above the submarine landslide region. These tsunami waves will be directly affected from the water depth of the Sea of Marmara. It will be also affected by the shore profile when traveling to the coasts. Because of this reason, a computational fluid dynamics model which is based on finite elements method is used in the regions that are very close to the coasts. The model solves the Navier-Stokes equations. Analytical and numerical models were used together in this study. The analytical model is used from the submarine up to sea surface and the numerical model is used for modeling of the movement of the tsunami waves at the sea surfaces. In the border of two models the outputs of analytical model is used as the inputs of numerical model that means the initial and boundary conditions of numerical model is obtained from the analytical model. The output of the analytical model is the tsunami wave amplitudes for each minute of a 900 seconds period. The submarine landslide type that is named as Model2 in the literature was applied in this study. The model was applied to the submarine landslide region that is located between 400m and 800m depth of water surface around Tuzla coast. Time series of the wave amplitudes at the top of the water mass over the landslide region for the landslide model were calculated by using analytical model. These time series were used as inputs of the numerical model. Then the numerical model is performed for simulating the wave propagation in the shallow waters of shore of Tuzla. The simulations for 13 different landslide velocities are performed for the previously determined landslide model on the selected mesh. These velocities were ranging between Cr=10 m/s and Cr=300 m/s. As a result of this, the effects of landslide model and different landslide velocities to the amplitudes of the tsunami waves were observed clearly. In another stage the landslide type and submarine landslide velocities were taken as constant and the thickness and width of the sliding mass were changed. The results of these simulations show that there is a linear relation for the thicknesses and the widths with the wave heights. The equations used in numerical modeling were Saint Venant equations that are derived from Navier-Stokes equations. The equations used in numerical modeling were also changed in this study in order to see the effects of both dispersive and non-dispersive waves to the coast.

Özet

Bu çalışmada Marmara Denizi 'nde Tuzla açıklarında bulunan heyelan bölgesindeki bir hareketlenme sonucunda sahilde seçilen belli noktalarda oluşan tsunami dalga yükseklikleri literatürde çok kullanılan bir denizaltı heyelan modeli ile analitik olarak modellenmiş ve heyelan bölgesinin üzerinden itibaren Tuzla kıyılarına kadar nümerik olarak modellenmiştir. Denizaltı heyelanının değişik hızlardaki hareketine göre Tuzla kıyılarındaki dalga yükseklikleri hesaplanmıştır. Çalışmada ele alınan heyelan bölgesi Tuzla açıklarında, 400 m ile 800 m 'lik derinlikteki yamaçtadır. Seçilen heyelan modeli için heyelanın üzerindeki su kütlesi yüzeyinde oluşacak dalga genliklerine ait zaman serileri analitik yöntemlerle iki ve üç boyutlu olarak elde edilmiştir. Elde edilen zaman serileri sınırdaki hareketi modellemekte ve bu hareket nümerik yönteme zorlayıcı etki olarak eklenmiş ve kıyıya kadar taşınarak kıyıdaki dalga genlikleri bulunmuştur. Ayrıca çalışma alanında üç boyutlu olarak, tsunami dalgalarının ilerleyişi görselleştirilerek tsunami dalgalarının çeşitli bölgelerdeki etkileri anlaşılmaya çalışılmıştır. Kıyıdaki kritik noktalarda oluşabilecek maksimum dalga yükseklikleri hesaplanmıştır. Proje sahası içerisinde seçilen lineer doğrultular boyunca Tsunami dalgalarının ilerleyişi gözlenerek batimetrinin dalga yüksekliği üzerindeki etkisi ortaya konulmuştur. Analitik model Cr=10 m/s ile Cr=300 m/s arasındaki farklı heyelan hızları için çalıştırılarak yüzeyde elde edilen dalga genlikleri nümerik modelde kullanılarak farklı heyelan hızlarında kıyıda meydana gelecek dalga yükseklikleri gözlemlenmiştir. Bu çalışmada dünya literatüründe yeni olduğu düşünülen, analitik yöntemle nümerik yöntemin birleştirilmesi gerçekleştirilmiştir.