This paper presents a new perturbation solution of the non-linear Boussinesq equation for one-dimensional tidal groundwater flow in a coastal unconfined aquifer. Built upon the work of Parlange et al. [Parlange, J.-Y., Stagnitti, F., Starr, J.L., Braddock, R.D., 1984. Free-surface flow in porous media and periodic solution of the shallow-flow approximation, J. Hydrol., 70, 251–263], the solution adopts a new perturbation parameter that is by definition less than unit, and thus is applicable to a wider range of physical conditions within the constraint of the Boussinesq approximation. This approach avoids a secular term in the third-order perturbation equation of Parlange et al. (1984), enabling the derivation of the third- and higher-order solutions. In comparison with a numerical (“exact”) solution, the new perturbation solution is shown to be slightly more accurate than that of Parlange et al. (1984) with the second-order approximation. The obtained third-order solution exhibits considerable improvement in accuracy. In relatively simple analytical forms, the present perturbation solution will help to understand better the non-linear characteristics of tidal water table fluctuations in as modeled by the non-linear Boussinesq equation coastal unconfined aquifers. 相似文献
Magmatism in SE China was dormant during 204–180 Ma, but was reactivated in 180–170 Ma (early J2), and then became more and more intensive towards the end of early Cretaceous. The small-scale early J2 magmatism is the incipience to long-term and large-scale magmatism in this region. A near east-west (EW) trend volcanic belt
was distributed across south Hunan, south Jiangxi and southwest Fujian was formed during early J2 time. Along this belt from the inland toward the coast, the lithology of basalts changes from alkali into tholeiite, and
the amount of erupted volcanic rocks and the proportions of rhyolites coexisting with the basalts increase. On the basis of
geochemical characteristics of these basalts, we infer that the melting degree of source rocks and the extent of fractional
crystallization and crustal contamination all increased whereas the depth of mantle source decreased from the inland to the
coast, which led to the variations of geological characteristics of the volcanic belt. In early J2, the western spreading Pacific plate began to subduct underneath SE China continental block, reactivating near EW trend deep
fault that was originally formed during the Indosinian event. The stress of the western spreading Pacific plate and the extent
of asthenosphere upwelling increased from the inland to the coast, which is consistent with the generation and evolution of
early J2 basalts. 相似文献