Skip to main content
Log in

Similarity solution to unconfined flow in an aquifer

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

In this study we refer to a non-steady state, one-dimensional unconfined flow in an aquifer described by the Boussinesq equation. A closed-form analytical solution is derived for a semi-infinite porous medium possessing a boundary condition of the power law type.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abramowitz M. and Stegun I.A. (1970). Handbook of Mathematical Functions. Dover, New York, 1046

    Google Scholar 

  • Barenblatt G.I. (1979). Similarity, Self-Similarity and Intermediate Asymptotics. Consultants Bureau, New York

    Google Scholar 

  • Bear J. (1988). Dynamics of Fluids in Porous Media. Dover, New York, 764

    Google Scholar 

  • Chen Z.-X., Bodvarsson G.S., Witherspoon P.A. and Yortsos Y.C. (1995). An integral equation formulation for the unconfined flow of groundwater with variable inlet conditions. Transport Porous Med. 18(1): 15–36

    Article  Google Scholar 

  • Kamke E. (1959). Differentialgleichungen Losungsmethoden und Losungen. Chelsea, New York

    Google Scholar 

  • Lockington D.A., Parlange J.Y., Parlange M.B. and Selker J. (2000). Similarity solution of the Boussinesq equation. Adv. Water Resour. 23(7): 725–729

    Article  Google Scholar 

  • Pulido-Velazquez, D., Sahuquillo, A., Andreu, J.: A two-step explicit solution of the Boussinesq equation for efficient simulation of unconfined aquifers in conjunctive-use models. Water Resour. Res. 42, DOI: 10.1029/2005WR004473 (2006)

  • Rupp, D.E., Selker, J.S.: Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile. Water Resour. Res. 41(11), DOI: 10.1029/2005WR004241(2005)

  • Telyakovskiy S., Braga G.A. and Furtado F. (2002). Approximate similarity solutions to the Boussinesq equation. Adv. Water Resour. 25(2): 191–194

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arieh Pistiner.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pistiner, A. Similarity solution to unconfined flow in an aquifer. Transp Porous Med 71, 265–272 (2008). https://doi.org/10.1007/s11242-007-9124-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-007-9124-5

Keywords

Navigation