Steady-State Topography-Driven Flow

Developed by Paul Hsieh, USGS

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Introduction

A topography-driven flow system is one in which ground water flows from higher-elevation recharge areas (where hydraulic head is higher) to lower-elevation discharge areas (where hydraulic head is lower). See figure below.

The boundaries of the flow domain are as follows:

  • The top boundary (AB) is the water table, which is assumed to lie close to land surface.
  • The two vertical boundaries (BC and AD) are no flow boundaries.
  • The bottom boundary (CD) is also a no-flow boundary.

The no-flow boundaries might represent low-permeability bedrock that bounds the basin. Alternatively, the vertical boundaries might also represent ground-water flow divides. Important Note: By specifying the position of the water table, it is assumed that the pattern of recharge and discharge is such that the water table is maintained at steady state.

Governing Equation

The steady-state ground-water flow equation to be solved is

where h is hydraulic head, and Kxx and Kzz are the principal values of the hydraulic conductor tensor. The principal directions are assumed to be parallel to the xand z axes.

Boundary Conditions

Assuming we know the position of the water table, the boundary condition along the water table (AB) is

where z is the elevation of the water table.

Along the vertical boundaries BC and AD, the no-flow boundary condition is

Along bottom boundary CD, the no-flow boundary condition is

After solving for hydraulic head h, the x and z components of the linear velocity vector are computed by

where n is porosity. The velocity vectors are used for calculating flow paths and the advective movement of fluid particles.


Running the Model

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Running the model involves 7 steps. To begin each step, click the corresponding button at the top of the window. A dialog box appears for you to enter the necessary input data. The three buttons on the second row allow you to zoom in, zoom out, and quit the model.

    Step 1: Start -- Specify model dimension
    Step 2: Water Table -- Specify the position of the water table
    Step 3: Mesh -- Specify the dimension of the model mesh
    Step 4: Properties -- Specify hydraulic conductivity and porosity
    Step 5: Head -- Compute hydraulic head

    After hydraulic head is computed, two options are available. You may proceed to

    Step 6a: Flow (Path) -- Track flow paths from selected points
    Step 7a: Animation -- Animate the evolution of flow paths

    or

    Step 6b: Flow (Particle) -- Set up initial distribution of fluid particles
    Step 7b: Animation -- Animate the advective movement of fluid particles

Updated on July 11, 1999.