A New Analytical Solution for Tide-Induced Groundwater Fluctuations in An Unconfined Aquifer with A Sloping Beach  

作　　者：孔俊 宋志尧 辛沛 沈城吉 

机构地区：[1]College of Harbor, Coastal and Offshore Engineering, Hohai University [2]Key Laboratory of Virtual Geographic Environment under Ministry of Education,and Jiangsu Key Laboratory for Numerical Simulation of Large-Scale Complex System,Nanjing Normal University [3]National Centre for Groundwater Research and Training, The University of Queensland

出　　处：《China Ocean Engineering》2011年第3期479-494,共16页中国海洋工程（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 51009059);the Natural Science Foundation of Jiangsu Higher Education Institutions of China (Grant No. 09KJA170003);the Fundamental Research Funds for the Central Universities (Grant No. 2010B02914);the Special Commonweal Research Foundation of the Ministry of Water Conservancy (Grant No. 200901032);the Priority Academic Program Development of Jiangsu Higher Education Institutions

摘　　要：Deriving analytical solutions for tide-induced groundwater fluctuations in unconfined aquifers confronts two problems： （1） As the Boussinesq equation itself contains nonlinear terms, the ＂secular term＂ would be generated in derivation, thus making perturbation solution unable to be deduced to higher order; （2） for aquifers with sloping beaches, the perturbation parameter in existing analytical solution integrating the beach slope and hydrogeological property would be sometimes larger than 1. So the application of perturbation solutions is relatively limited. Furthermore, as the beach slope decreases, the error of analytical solution would gradually increase. Given that water table over-height would increase the aquifer thickness and speed up wave propagation, this paper integrates over-height into the perturbation parameter and adjusts boundary conditions to settle the problem of ＂secular term＂ and to derive a new high-order analytical solution for nonlinear Boussinesq equation in terms of sloping beaches. Results show that the new analytical solution is more reasonable, and the analytical accuracy is obviously improved in comparison with the existing analytical solution for a gentle slope. The new analytical solution provides a theoretical basis for analyzing the propagation characteristics （e.g., wave length and over-height variation） of tide-induced groundwater wave in unconfined aquifers, particularly those with sloping beaches.Deriving analytical solutions for tide-induced groundwater fluctuations in unconfined aquifers confronts two problems： （1） As the Boussinesq equation itself contains nonlinear terms, the ＂secular term＂ would be generated in derivation, thus making perturbation solution unable to be deduced to higher order; （2） for aquifers with sloping beaches, the perturbation parameter in existing analytical solution integrating the beach slope and hydrogeological property would be sometimes larger than 1. So the application of perturbation solutions is relatively limited. Furthermore, as the beach slope decreases, the error of analytical solution would gradually increase. Given that water table over-height would increase the aquifer thickness and speed up wave propagation, this paper integrates over-height into the perturbation parameter and adjusts boundary conditions to settle the problem of ＂secular term＂ and to derive a new high-order analytical solution for nonlinear Boussinesq equation in terms of sloping beaches. Results show that the new analytical solution is more reasonable, and the analytical accuracy is obviously improved in comparison with the existing analytical solution for a gentle slope. The new analytical solution provides a theoretical basis for analyzing the propagation characteristics （e.g., wave length and over-height variation） of tide-induced groundwater wave in unconfined aquifers, particularly those with sloping beaches.

关 键 词：TIDE GROUNDWATER analytical solution over-height perturbation method 

分 类 号：P641[天文地球—地质矿产勘探]