'Methods to Derive the Differen tial Equation of the Free Surface Boundary,' by Chongxi Chen,Xingxing Kuang,and Jiu Jimmy Jiao,May-June 2010,v.48,no.3:329-332.

摘要

Recently Chen et al. (2010) (hereafter CKJ) challenged the classical dynamic boundary condition at the free surface in an unconfined aquifer as derived by Boul-ton (1954) and Bear (1972, 1978). However, we believe that the classical derivation is correct. In the CKJ derivation there is some confusion over the type of derivative applied at the free surface because we cannot take a simple partial derivative of the free-surface boundary condition. The fact that the particle is on the free surface allows us to take only the material derivative of the free-surface boundary condition as in the classical derivation. As a result, only the material derivative of the head, h, is known at the free surface, and we cannot calculate explicitly partial derivatives of h with respect to t (time) and z (vertical coordinate) from the dynamic boundary condition.