Curvilinear Theory of Lake LBJ

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
GIS Data

• TIN

• Grid

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ELCOM Bathymetry
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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

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Schematic of Channel Geometry
Ro radius of curvature of centerline R(s,r)
radius of curvature of radial line ?s chord
length, rep arc length at small angle ?r radial
distance off centerline d? infinitely small
angle
R(s,r)
Radii of curvature are orthogonal to channel
lines
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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

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Curvilinear Space

• The fact that ?s is the same over the channel
  width enables the lake to be straightened.
• ?r determines the channel edge this may be a
  problem

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?