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Exact analytical expressions for the piezometric profile and water exchange between stream and groundwater during and after a uniform rise of the stream level
Author(s) -
Boufadel Michel C.,
Peridier Vallorie
Publication year - 2002
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2001wr000780
Subject(s) - aquifer , hydraulic head , head (geology) , groundwater , geology , boundary (topology) , piezometer , hydrology (agriculture) , volume (thermodynamics) , volumetric flow rate , water level , soil science , groundwater model , groundwater flow , geotechnical engineering , mechanics , mathematics , geomorphology , mathematical analysis , physics , thermodynamics , geography , cartography
We consider an archetypical problem relevant to a confined aquifer in contact with a stream. The model problem consists of an idealized one‐dimensional region 0 ≤ x ≤ L, where the left boundary at x = 0 is held at a fixed piezometric head h 0 , and the right boundary's piezometric head at x = L is increased from h L to h 0 at a constant rate. Exact solutions for all times, all points in the aquifer, and for any possible constant rate of change of the right boundary piezometric head are presented for the piezometric head and the instantaneous flow rate. An exact expression for the exchange volume at the groundwater/stream interface for an arbitrary time is also provided. This expression shows that there is a specific critical rising rate of the stream level above which the net exchange volume is into the aquifer and below which it is out of the aquifer. The solution shows that regardless of the rise rate, a certain water volume, inversely proportional to the rise rate, enters the aquifer.