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ARS Home » Plains Area » Bushland, Texas » Conservation and Production Research Laboratory » Soil and Water Management Research » Research » Publications at this Location » Publication #231820
Title: The transition of flow patterns through critical stagnation points in two-dimensional groundwater flow

Author
item JIN, WEI - KANSAS STATE UNIV
item STEWARD, DAVID - KANSAS STATE UNIV

Submitted to: Advances in Water Resources
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/20/2006
Publication Date: 10/1/2006
Citation: Jin, W., Steward, D. 2006. The transition of flow patterns through critical stagnation points in two-dimensional groundwater flow. Advances in Water Resources. 30:16-28.

Interpretive Summary:

Technical Abstract: A flow pattern is characterized by aquifer features and the number, type, and distribution of stagnation points (locations where the discharge is zero). This article identifies a condition for transition of flow patterns in two-dimensional groundwater flow obeying Darcy's law by examining changes in stagnation points, using the Taylor series expansion of the discharge vector. It is found that the three standard types of stagnation points (minimums, maximums, and saddle points) are completely characterized by the first-order term containing the discharge gradient tensor. However, when the determinant of the tensor becomes zero, stagnation points of other types characterized by higher-order terms come into existence. In this article, we call these zero-determinant stagnation points as critical stagnation points; they may emerge suddenly, split to a set of new stagnation points, or disappear from the flow, resulting in transitions of flow patterns. Examples of both transient and steady flows are used to illustrate the usefulness and significance of critical stagnation points.