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Curvilinear Theory of Lake LBJ

Curvilinear Theory of Lake LBJ. Bridget Wadzuk April 26, 2001. Review. Purpose – manipulate bathymetry to be used in models Idea – straighten the bathymetry Less computationally expensive Sinuosity can be neglected Changes – now using Lake LBJ instead of Lake Travis. Lake LBJ Stats.

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Curvilinear Theory of Lake LBJ

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  1. Curvilinear Theory of Lake LBJ Bridget Wadzuk April 26, 2001

  2. Review • Purpose – manipulate bathymetry to be used in models • Idea – straighten the bathymetry • Less computationally expensive • Sinuosity can be neglected • Changes – now using Lake LBJ instead of Lake Travis

  3. Lake LBJ Stats • Lake LBJ is significantly smaller, but still takes a while to process! Data from www.lcra.org

  4. Data Acquisition • LBJ Contours - Dr. Maidment and Kevin Donnelly • Convert contour lines • Buffer and shapefile • TIN • Grid

  5. TIN Grid GIS Data

  6. ELCOM Bathymetry

  7. Curvilinear Space Theory • Geometric space uses a square Cartesian grid mesh = Many cells! • Curvilinear spaces uses a representative mesh of streamwise and cross-stream flow • Applicable to Lake LBJ because the channel width is much less than the radius of curvature – effects of curvature become negligible

  8. Δr Δs r = 0 Ro δθ Schematic of Channel Geometry Ro = radius of curvature of centerline R(s,r) = radius of curvature of radial line Δs = chord length, rep arc length at small angle Δr = radial distance off centerline δθ = infinitely small angle R(s,r) ** Radii of curvature are orthogonal to channel lines

  9. 1 4 2 3 Geometric Space Radial lines: Arc lengths: Arc (chord) lengths vary in geometric space, but are the same in curvilinear space due to the ratios of the radii of curvature Ro R(s,r) Radial lines y x =

  10. The fact that Δs is the same over the channel width enables the lake to be straightened. Δr determines the channel edge – this may be a problem 1 4 Δs Δr 3 Radial lines Ro R(s,r) Curvilinear Space 2

  11. Possible Problems with Curvilinear Approach • Non-uniformity of channel width may be problematic because the edge may become jagged • If grid resolution is poor, there may be alterations in flow solutions

  12. Upcoming Events • Use ELCOM to develop thalweg and bathymetry file • Use ArcView to construct centerline, compare methods • Points of comparison: • Resolution • Will GIS capture the hydrodynamics of Lake LBJ? • Will the GIS method be able to be easily applied to a general system?

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