Environmental Processes

, Volume 5, Issue 3, pp 519–537 | Cite as

Propagation of Tidal Wave in Coastal Terrains with Complex Bed Geometry

  • Bushra Y. Shaikh
  • Rajeev K. Bansal
  • Samir K. Das
Original Article


Transient interaction of tides and groundwater has a direct impact on marine ecosystems and plays an important role in coastal aquifer management. The literature is replete with studies that analyze the influence of periodic tidal waves on the adjacent aquifers of various configurations underlain by horizontal or sloping bases. However, water table fluctuations in coastal aquifers whose base extends horizontally as well as sloping in a definite lateral domain cannot be addressed with existing studies. This paper presents a new model for tide induced groundwater flow in a coastal aquifer system whose base has mixed features of both horizontal and sloping terrains. Variations in water table are simulated by combining a linear diffusion equation with an advection-diffusion equation. Validity of spatial and temporal variables as well as performance of new analytical solution is assessed with numerical solution of nonlinear Boussinesq equations. Sensitivity of the solution is analyzed in both homogeneous and heterogeneous aquifer systems. Numerical experiments based on Tchebycheff and L2 norms indicate that the new analytical solution provides acceptable results in a large range of aquifer parameters.


Boussinesq equation Horizontal and sloping bases Tide Unconfined aquifer Water table 



The authors thank the anonymous reviewers whose insightful comments improved the organization and clarity of the paper.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Bushra Y. Shaikh
    • 1
  • Rajeev K. Bansal
    • 2
  • Samir K. Das
    • 1
  1. 1.Department of Applied MathematicsDefence Institute of Advanced Technology (Deemed University)PuneIndia
  2. 2.Department of MathematicsNational Defence AcademyPuneIndia

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