Analysis of Dispersion Tensor for 2-D Advection-Dispersion Model in Meandering Channels

  • Il won Seo, Dept. of Civil Engineering, Seoul National Univ, Korea
  • In hwan Park, Dept. of Civil Engineering, Seoul National Univ, Korea
  • Sung won Park, Dept. of Civil Engineering, Seoul National Univ, Korea

In this research, dispersion coefficient tensor is calculated by using proposed formula by Alavian and Fischer to analyze change of dispersion coefficients in meandering channel. Velocity distribution and dispersion coefficient for calculation referred to previous experiment result. Measuring points of velocity are composed to 8 points in vertical direction, 19 points in transverse direction, and 10 points in longitudinal direction. First dispersion coefficient tensor formula which is suggested by Fischer is calculated by triple integration of vertical-direction velocity and eddy viscosity. The first formula should use vertical direction longitudinal and transverse velocity distribution; however, on account of insufficient velocity data cause of the limitation of experiment apparatus, result of calculation didn’t produce a meaningful conclusion. Second formula suggested by Alavian is composed to transverse, longitudinal dispersion coefficients and magnitude of velocity. The second formula can draw a reasonable result due to use relatively easy calculation method.
From the calculation result, dispersion coefficient tensors tend to change according to the relative direction of primary flow and x, y-axis in Cartesian coordinate. Moreover, dispersion coefficient tensors have tendency to increase where the maximum velocity of primary flow occurs. Thus, dispersion effect will be more activated in where primary flow’s maximum velocity occurs. In the aspect of application of tensor form dispersion coefficient, Alavian’s formula is more useful rather than Fischer’s formula on the account of Alavian’s formula use easier calculation process and needs less information about velocity distribution. For this reason, Alavian’s formula is more applicable to 2-dimensional advection-dispersion model.