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A many‐valued hodograph in an interface problem

G. De Josselin de Jong

Open publisher page 22 citations

Abstract

The hodograph method for determining patterns of flow of groundwater in a coastal aquifer with a drain requires the treatment of double‐sheeted hodograph planes. This many‐valuedness does not prohibit the use of Schwarz‐Christoffel analysis if the hodograph domain is simply connected. In the two‐fluid case of fresh water flowing over stationary salt water the hodograph is simply connected, and the hodograph method is shown to give a solution. This solution was verified by a test that showed a stable interface in the predicted position.

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What this paper is about

The hodograph method for determining patterns of flow of groundwater in a coastal aquifer with a drain requires the treatment of double‐sheeted hodograph planes. This many‐valuedness does not prohibit the use of Schwarz‐Christoffel analysis if the hodograph domain is simply connected. In the two‐fluid case of fresh water flowing over stationary salt water the hodograph is simply connected, and the hodograph method is shown to give a solution. This solution was verified by a test that showed a stable interface in the predicted position.

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Available abstract

The hodograph method for determining patterns of flow of groundwater in a coastal aquifer with a drain requires the treatment of double‐sheeted hodograph planes. This many‐valuedness does not prohibit the use of Schwarz‐Christoffel analysis if the hodograph domain is simply connected. In the two‐fluid case of fresh water flowing over stationary salt water the hodograph is simply connected, and the hodograph method is shown to give a solution. This solution was verified by a test that showed a stable interface in the predicted position.

Key concepts: Hodograph, Interface (matter), Groundwater, Position (finance), Aquifer, Flow (mathematics), Plane (geometry), Mechanics

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