A topographically-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). The boundaries of the flow domain are as follows (Figure Box 6-1):<\/p>\r\n\r\n
- \r\n \t
- The top boundary (AB) is the water table, which is assumed to lie close to land surface.<\/li>\r\n \t
- The two vertical boundaries (BC and AD) are no flow boundaries.<\/li>\r\n \t
- The bottom boundary (CD) is also a no-flow boundary.<\/li>\r\n<\/ul>\r\n
![\"Diagram](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/uploads\/sites\/15\/2021\/01\/image47.png\")
<\/p>\r\nFigure Box 6-1<\/strong> - Diagram of the TopoDrive flow system.<\/p>\r\n
The no-flow boundary A-D-C-B might represent low-permeability bedrock that bounds the basin. Alternatively, the vertical BC boundary might represent a groundwater flow divide on a ridge. Also, point A may represent the center of a river, thus groundwater on both sides of the river flows towards the river forming a no-flow boundary along AD. Important Note:<\/strong> 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.<\/p>\r\n\r\n
Governing Equation<\/h1>\r\n
The steady-state ground-water flow equation to be solved is:<\/p>\r\n
[latex]\\displaystyle \\frac{\\partial }{\\partial x}\\left (K_{xx} \\frac{\\partial h}{\\partial x} \\right )+\\frac{\\partial }{\\partial z}\\left (K_{zz} \\frac{\\partial h}{\\partial z} \\right )=0[\/latex]<\/p>\r\n
where h<\/em> is hydraulic head, and K<\/em>xx<\/em><\/sub> and K<\/em>zz<\/em><\/sub> are the principal values of the hydraulic conductivity ellipse. The principal directions are assumed to be parallel to the x <\/em>and z<\/em> axes.<\/p>\r\n\r\n
Boundary Conditions<\/h1>\r\n
Assuming we know the position of the water table, the boundary condition along the water table (AB) is<\/p>\r\n
h<\/em> = z<\/em><\/p>\r\n
where z<\/em> is the elevation of the water table.<\/p>\r\n
Along the vertical boundaries BC and AD, the no-flow boundary condition is<\/p>\r\n
[latex]\\displaystyle \\frac{\\partial h}{\\partial x}=0[\/latex]<\/p>\r\n
Along bottom boundary CD, the no-flow boundary condition is<\/p>\r\n
[latex]\\displaystyle \\frac{\\partial h}{\\partial z}=0[\/latex]<\/p>\r\n
After solving for hydraulic head h<\/em>, the x<\/em> and z<\/em> components of the linear velocity vector are computed by<\/p>\r\n
[latex]\\displaystyle v_{x}=K_{xx}\\frac{\\partial h}{\\partial x}[\/latex] [latex]\\displaystyle v_{z}=K_{zz}\\frac{\\partial h}{\\partial z}[\/latex]<\/span><\/p>\r\n
Where n<\/em> is porosity. The velocity vectors are used for calculating flow paths and the advective movement of fluid particles.<\/p>\r\n\r\n
<\/a>Running the Model<\/h1>\r\n
Open the model by linking to https:\/\/tdpfonline.net<\/a> and click the \u201cLaunch TopoDrive\u201d button to start the TopoDrive software. TopoDrive will appear in a new browser window (Figure Box 6-2).<\/p>\r\n
![\"TopoDrive](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/uploads\/sites\/15\/2021\/01\/image48.jpg\")
<\/p>\r\nFigure Box 6-2<\/strong> - TopoDrive software window.<\/p>\r\n
Running the model involves 7 steps. To begin each step, click the corresponding button at the top of the window (Figure Box 6-3). A dialog box appears for you to enter the necessary input data. The three buttons on the second row allow you to zoom in and zoom out. To quit the model, simply close the browser window.<\/p>\r\n
![\"TopoDrive](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/uploads\/sites\/15\/2021\/01\/image49.jpg\")
<\/p>\r\nFigure Box 6-3<\/strong> - TopoDrive software buttons.<\/p>\r\n
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<\/p>\r\nAfter hydraulic head is computed, two options are available. You may proceed to 6a\/7a or 6b\/7b<\/p>\r\n
Step 6a: Flow (Path) -- Track flow paths from selected points
Step 7a: Animation -- Animate the evolution of flow paths<\/p>\r\nOr:<\/p>\r\n
Step 6b: Flow (Particle) -- Set up initial distribution of fluid particles
Step 7b: Animation -- Animate the advective movement of fluid particles<\/p>\r\nAdditional buttons can be used to zoom in and zoom out. The web browser\u2019s \u201cPrint\u201d command can be used to print the image in the window. Closing the browser window terminates the program.<\/p>\r\n
If you are feeling uncertain about how to proceed, here are some suggested inputs:<\/strong><\/p>\r\n\r\n
Example 1:<\/h1>\r\n
Step 1: Click the <\/em>Start<\/em><\/strong> button then input:\u00a0\u00a0\u00a0\u00a0 Domain length: <\/em>1000<\/em><\/strong> \u00a0\u00a0\u00a0 Vertical Exaggeration: <\/em>1<\/em><\/strong><\/p>\r\n
Step 2: Click <\/em>Water Table<\/em><\/strong> button then place the cursor to the left of the left axis fairly low and click, move the cursor to the right within the model area and click, continue to move the cursor to the right within the model area and click creating a shape for the water table, finally move the cursor to the right of the right axis click to complete the upper boundary of the model. The upper portion of the vertical boundary on each side will be clipped to terminate at the line you drew. Your line now defines the water table and thus the heads at the top of the model.<\/em><\/p>\r\n
Step 3: Click the <\/em>Mesh<\/em><\/strong> button then input:\u00a0\u00a0\u00a0 Number of columns: <\/em>60<\/em><\/strong> \u00a0\u00a0\u00a0 Number of Rows: <\/em>30<\/em><\/strong><\/p>\r\n
Step 4: Click the <\/em>Properties<\/em><\/strong> button: Initially the entire mesh is set at the medium value of hydraulic conductivity (indicated by white). Click on the blue rectangle, OK. Place the cursor within the mesh and draw a polygon by clicking at the vertices. Double clicking the last vertex completes the polygon. You now have a high hydraulic conductivity zone in the model. Next, click the <\/em>Properties<\/em><\/strong> button again and click on the pink rectangle. Draw another polygon on the mesh to define a zone of low hydraulic conductivity. An alternative way to finish the polygon is to single-click the last vertex and then click the <\/em>Done Polygon<\/em><\/strong> button. Notice you can change the values of hydraulic conductivity for each color, you can choose anisotropic and specify different hydraulic conductivity in the horizontal and vertical directions. You can also change the porosity which will not affect the flow lines but will affect the velocity of flow.<\/em><\/p>\r\n
Step 5: Click the <\/em>Head<\/em><\/strong> button then input:\u00a0\u00a0\u00a0\u00a0 Number of contour intervals: <\/em>40<\/em><\/strong> \u00a0\u00a0\u00a0 Then click <\/em>Compute<\/em><\/strong><\/p>\r\n
Step 6: Click the <\/em>Flow<\/em><\/strong> button then choose:<\/em> \u00a0\u00a0\u00a0 \u25cf Flow Path Tracking<\/em><\/strong> \u00a0\u00a0\u00a0 \u25cf Forward and Backward<\/em> \u00a0\u00a0 OK<\/em><\/strong><\/p>\r\n
Step 7: <\/em>Click locations within the flow field<\/em><\/strong> and the flow path will be drawn in both the forward and backward directions from that locations.<\/em><\/p>\r\n
One possible example of a finished product is shown in Figure Box 6-4. The blue zone has 100 times the hydraulic conductivity of the white zone. The pink zone has 1\/100 times the hydraulic conductivity of the white zone.<\/em><\/p>\r\n
![\"Example](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/uploads\/sites\/15\/2021\/01\/image50.jpg\")
<\/p>\r\nFigure Box 6-4<\/strong> - Example of one final product of a TopoDrive simulation.<\/p>\r\n\r\n
Example 2:<\/h1>\r\n
Follow steps 1 through 5 for example 1. Alternatively, if you still have the TopoDrive Window open, you can go back to step 6 and choose different options as follows:<\/p>\r\n
Step 6: Click the <\/em>Flow<\/em><\/strong> button then input:\u00a0\u00a0\u00a0\u00a0 \u25cf <\/em>Particle Movement<\/em><\/strong> \u00a0\u00a0\u00a0 Initial particle spacing: <\/em>5 m<\/em> \u00a0\u00a0\u00a0 OK<\/em><\/strong><\/p>\r\n
Now use the cursor to draw a polygon anywhere in the model and double click when you have completed the shape. You will see dots in the shape that are 5 m apart (Figure Box 6-5).<\/em><\/p>\r\n
![\"Starting](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/uploads\/sites\/15\/2021\/01\/image51.jpg\")
<\/p>\r\nFigure Box 6-5<\/strong> \u2013 Starting positions of a group of particles within the TopoDrive model.<\/p>\r\n
Step 7: Click on the Animation button then input: <\/em><\/p>\r\n
1 sec of animation time=<\/em>50<\/em><\/strong> days\u00a0\u00a0\u00a0\u00a0 animation smoothness=<\/em>10<\/em><\/strong> frames per sec \u00a0 \u00a0 <\/em>OK<\/em><\/strong><\/p>\r\n
Click anywhere within the model and the particles will begin to move, if you click within the model again the particles will pause, then click again to continue and so on<\/em> (Figure Box 6-6).<\/em><\/p>\r\n
If you setup different properties then your particles may move too fast or slow. If this is the case, adjust the amount of time represented by 1 second of animation.<\/em><\/p>\r\n
The particle locations for example 2 are shown after 1460 days (four years) in Figure Box 6-7. Note that the elapsed time is shown in the bottom of the TopoDrive window.<\/em><\/p>\r\n
![\"Particle](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/uploads\/sites\/15\/2021\/01\/image52.jpg\")
<\/p>\r\nFigure Box 6-6<\/strong> - Particle positions at two times during the animation: a) 365 days (1 year); and, b) 730 days (2 years).<\/p>\r\n \r\n
![\"Particle](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/uploads\/sites\/15\/2021\/01\/image53.jpg\")
<\/p>\r\nFigure Box 6-7<\/strong> - Particle positions after 1460 days (4 years). Many particles have exited the aquifer. A strand of particles is moving around the left side of the low hydraulic conductivity zone (pink region) and a few particles have moved into the low hydraulic conductivity zone.<\/p>\r\n
Return to where text links to Box 6<\/a><\/p>","rendered":"
Introduction<\/h1>\n
The online version of TopoDrive is designed to run in a web browser and does not require any plug-ins.<\/p>\n
IF YOU ARE READY TO GO DIRECTLY TO INFORMATION ON HOW TO USE THE TOPODRIVE MODEL, PROCEED TO Running the Model<\/a><\/p>\n
A topographically-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). The boundaries of the flow domain are as follows (Figure Box 6-1):<\/p>\n
- \n
- The top boundary (AB) is the water table, which is assumed to lie close to land surface.<\/li>\n
- The two vertical boundaries (BC and AD) are no flow boundaries.<\/li>\n
- The bottom boundary (CD) is also a no-flow boundary.<\/li>\n<\/ul>\n<\/p>\n
Figure Box 6-1<\/strong> – Diagram of the TopoDrive flow system.<\/p>\n
The no-flow boundary A-D-C-B might represent low-permeability bedrock that bounds the basin. Alternatively, the vertical BC boundary might represent a groundwater flow divide on a ridge. Also, point A may represent the center of a river, thus groundwater on both sides of the river flows towards the river forming a no-flow boundary along AD. Important Note:<\/strong> 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.<\/p>\n
Governing Equation<\/h1>\n
The steady-state ground-water flow equation to be solved is:<\/p>\n
![\"\displaystyle \frac{\partial }{\partial x}\left (K_{xx} \frac{\partial h}{\partial x} \right )+\frac{\partial }{\partial z}\left (K_{zz} \frac{\partial h}{\partial z} \right )=0\"](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/ql-cache\/quicklatex.com-beb8a0786ef5b18bf62568c499c42c29_l3.png\" "\\"Rendered")
<\/p>\nwhere h<\/em> is hydraulic head, and K<\/em>xx<\/em><\/sub> and K<\/em>zz<\/em><\/sub> are the principal values of the hydraulic conductivity ellipse. The principal directions are assumed to be parallel to the x <\/em>and z<\/em> axes.<\/p>\n
Boundary Conditions<\/h1>\n
Assuming we know the position of the water table, the boundary condition along the water table (AB) is<\/p>\n
h<\/em> = z<\/em><\/p>\n
where z<\/em> is the elevation of the water table.<\/p>\n
Along the vertical boundaries BC and AD, the no-flow boundary condition is<\/p>\n
![\"\displaystyle \frac{\partial h}{\partial x}=0\"](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/ql-cache\/quicklatex.com-b30bbb1be4aa1968d325a300e15afe74_l3.png\" "\\"Rendered")
<\/p>\nAlong bottom boundary CD, the no-flow boundary condition is<\/p>\n
![\"\displaystyle \frac{\partial h}{\partial z}=0\"](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/ql-cache\/quicklatex.com-90c089a26b4afbc9d511a64186bd196c_l3.png\" "\\"Rendered")
<\/p>\nAfter solving for hydraulic head h<\/em>, the x<\/em> and z<\/em> components of the linear velocity vector are computed by<\/p>\n
![\"\displaystyle v_{x}=K_{xx}\frac{\partial h}{\partial x}\"](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/ql-cache\/quicklatex.com-8c2dcfbcf915af241882dd4b40f7e230_l3.png\" "\\"Rendered")
![\"\displaystyle v_{z}=K_{zz}\frac{\partial h}{\partial z}\"](\"https:\/\/books.gw-project.org\/graphical-construction-of-groundwater-flow-nets\/wp-content\/ql-cache\/quicklatex.com-f3952a3133505a78b3dd3096d3641bfc_l3.png\" "\\"Rendered")
<\/span><\/p>\nWhere n<\/em> is porosity. The velocity vectors are used for calculating flow paths and the advective movement of fluid particles.<\/p>\n
<\/a>Running the Model<\/h1>\n