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 Lake LBJ is significantly smaller, but still takes a while to process! Lake LBJLake Travis Length (mi) Area (ac)6,37518,929 Maximum Depth (m) Data from

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

GIS Data TINGrid

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) RoRo δθ r = 0 Δs Δr R o = 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 Radial lines RoRo R(s,r) = 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 Radial lines RoRo R(s,r) Δs Δr

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?