Curvilinear Theory of Lake LBJ
Bridget Wadzuk
April 26, 2001
Review
Purpose – manipulate bathymetry to be used in models
Idea – straighten the bathymetryLess computationally expensiveSinuosity can be neglected
Changes – now using Lake LBJ instead of Lake Travis
Lake LBJ Stats
Lake LBJ is significantly smaller, but still takes a while to process!
Lake LBJ Lake Travis
Length
(mi)21.15 63.75
Area (ac) 6,375 18,929
Maximum Depth (m)
20 156
Data from www.lcra.org
Data Acquisition
LBJ Contours - Dr. Maidment and Kevin Donnelly
Convert contour lines Buffer and shapefile TIN Grid
GIS Data
TIN Grid
ELCOM Bathymetry
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
Schematic of Channel Geometry
R(s,r)Ro
δθ
r = 0
Δs
ΔrRo = 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
** Radii of curvature are orthogonal to channel lines
Geometric Space
221
22121 )()( yyxxrr
Radial lines
214
21414 )()()(
),(yyxxss
R
rsR
o
Ro R(s,r)
223
22323 )()()(
),(yyxxss
R
rsR
o=
1
2 3
4
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
y
x
Curvilinear Space
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
2
4
3
1
Radial linesRo R(s,r)
ΔsΔr
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
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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