일반화된 Galerkin-Eigenfunction 을 이용한 3차원 해양에서 부유물질을 위한 해석해 연구

Abstract

Recent efforts of the suspended sediment dynamics study have largely been focused on the investigation on the sediment profile and the boundary layer flows via the use of a set of numerical models equipped with sophisticated turbulence model. There is however a continuing need to develop analytical solutions because of its fundamental importance; analytical solutions of the advection-diffusion equation are valuable not only for its own right but for the better understanding on the dynamic processes of suspended sediments. Furthermore, the solution might be of practical value for the verification of numerical schemes. The time-harmonic analytical solution of the one-dimensional vertical (1DV) advection-diffusion equation for the finite water depth was previously solved by the first author using a transformation of the dependent variable and then applying the Galerkin-Eigenfunction method developed by Heaps(1972). In this talk an analytical solution for the 1DV advection-diffusion equation of suspended sediment in a three-layered finite water depth is to be presented which is relevant to the study of the local time-build up of the suspended sediment field. The settling velocity is assumed to be constant throughout the water column and the eddy diffusivity is assumed to be time-invariant but vary in step-like manner. No flux condition is imposed at the sea surface, while erosion and depositional rates are given at the sea bed. The solution has been derived using a generalized Galerkin-Eigenfunction method in which trial and test functions are different each other and the transformation of dependent variable is not required. Results are briefly presented with emphasis on the influence of the pycnocline upon the time build-up of suspended sediment concentration.