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What happens near a quasi‐linear point source?

 

作者: J. R. Philip,  

 

期刊: Water Resources Research  (WILEY Available online 1992)
卷期: Volume 28, issue 1  

页码: 47-52

 

ISSN:0043-1397

 

年代: 1992

 

DOI:10.1029/91WR02600

 

数据来源: WILEY

 

摘要:

The quasi‐linear continuous point source has been central to many studies of multidimensional flow in unsaturated soil. Immediately next to the source, however, the water pressure Ψ is positive and indefinitely large, so the quasi‐linear flow equation (limited to Ψ ≤ 0) fails in principle. We investigate whether this is a serious problem in practice. Exact analysis would be complicated and difficult, since the problem is of mixed saturated‐unsaturated flow with an unknown free boundary between the two regions. When the source strength is not too large, the saturated region is close to spherical. A simple approximate analysis follows with exterior and interior flow velocities matched on the boundary. The correction, taking into account the saturated region, shifts the quasi‐linear source a small distance above the actual source location. In practical applications the correction is usually negligibly small. Physical reasons why the approximation works well and the correction is small are indicated. In addition, these physical reasons suggest that the scope of the quasi‐linear analysis is wider than supposed hitherto. The solution in potential theory for the eccentric point source needed for the study is given in

 

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