Sediment mathematical model for sand ridges and sand waves
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Sediment mathematical model for sand ridges and sand waves LI Daming1*, WANG Xiao1, WANG Xin1, 2, LI Yangyang1 1 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China 2 National Ocean Technology Center, State Oceanic Administration, Tianjin 300112, China
Received 3 April 2015; accepted 15 October 2015 ©The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2016
Abstract
A new theoretical model is formulated to describe internal movement mechanisms of the sand ridges and sand waves based on the momentum equation of a solid-liquid two-phase flow under a shear flow. Coupling this equation with two-dimensional shallow water equations and wave reflection-diffraction equation of mild slope, a two-dimensional coupling model is established and a validation is carried out by observed hydrogeology, tides, waves and sediment. The numerical results are compared with available observations. Satisfactory agreements are achieved. This coupling model is then applied to the Dongfang 1-1 Gas Field area to quantitatively predict the movement and evolution of submarine sand ridges and sand waves. As a result, it is found that the sand ridges and sand waves movement distance increases year by year, but the development trend is stable. Key words: internal movement mechanisms, sand ridges and sand waves, two-dimensional coupling model, migration Citation: Li Daming, Wang Xiao, Wang Xin, Li Yangyang. 2016. Sediment mathematical model for sand ridges and sand waves. Acta Oceanologica Sinica, 35(5): 141–149, doi: 10.1007/s13131-016-0853-6
1 Introduction Since the submarine pipelines were introduced in 1954, it has been widely used in offshore oil and gas transmission due to its efficiency and economic reliability. However, waves and tidal current, in combination with the sand wave terrain ups and downs, can easily lead to the suspension, exposure and subsiding of pipelines, thus affecting the stability of pipelines. Therefore, it is crucial to ensure the safety of laying the submarine pipeline under the dynamic conditions of the underwater environment. What’s more, it is necessary and valuable to investigate the sand waves movement and understand the underlying mechanisms. Extensive studies were carried out by foreign scholars on the morphological features, development environment and the migration regularity of sand ridges and sand waves. Earliest study on the appearance of sediment sorting patterns along tidal sand waves mainly depended on field observations (Terwindt, 1971). With the time going on, numerical and theoretical models had been becoming more and more popular. Rubin and McCulloch (1980) used a three-dimensional model with vertical circulations. Hulscher (1996) found that the formation of sand waves and net convergence of sand can occur at the top of the sand waves over an entire M2 tidal cycle. Németh et al. (2002) extended the previous work and established a vertical two-dimensional flow and morphological numerical model describing the behavior of
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