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?