研究亮點:
(1)尋找到一個變數變換,使得泥沙擴散係數為線性函數的懸沙方程可以解析求解。
(2)獲得了底部泥沙濃度邊界條件為Dirichlet和Neumann條件時泥沙濃度時空變化的解析解,得到實驗數據的良好驗證。
圖1振盪流情形理論解與實驗數據的比較
圖2振盪流情形泥沙濃度的週期變化過程理論解與實驗數據的比較
尋找到一個變數變換,使得泥沙擴散係數為線性函數的懸沙方程可以解析求解,從而獲得了底部泥沙濃度邊界條件為Dirichlet和Neumann條件時泥沙濃度時空變化的解析解。通過與不同實驗數據比較,討論了兩種理論解對懸沙濃度分佈的預測能力。結果表明,兩種理論解均能較好地描述波浪作用下懸沙濃度的變化過程,包括懸沙濃度的振幅、相位和垂向分佈。此外,相比採用Dirichlet邊界條件,採用Neumann邊界條件得到的理論解在懸沙濃度的相位變化上與實驗數據符合更好。
Two kinds of analytical solutions are derived through Laplace transform for the equation that governs wave-induced suspended sediment concentration with linear sediment diffusivity under two kinds of bottom boundary conditions,namely the reference concentration(Dirichlet)and pickup function(Numann),based on a variable transformation that is worked out to transform the governing equation into a modified Bessel equation.The ability of the two analytical solutions to describe the profiles of suspended sediment concentration is discussed by comparing with different experimental data.And it is demonstrated that the two analytical solutions can well describe the process of wave-induced suspended sediment concentration,including the amplitude and phase and vertical profile of sediment concentration.Furthermore,the solution with boundary condition of pickup function provides better results than that of reference concentration in terms of the phase-dependent variation of concentration.
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