5:15 PM - 6:30 PM
[HCG26-P01] Discriminant functions for formative conditions of bedforms in open-channel flows
Keywords:Bedform, Discriminant analysis
This study provides boundary surfaces of bedform stability regions defined as discriminant functions of dimensionless parameters. In previous studies, the lines were described manually without quantitative examination. Thus, previous studies that apply these diagrams to sedimentary structures lack sufficient statistic basis. To this end, this study obtained boundary lines as polynomial equations of dimensionless parameters.
First of all, we defined a new bedform existence diagram based on 3272 existing laboratory and field data. We used three parameters in dimensionless form. Some of diagrams in previous studies were not sufficient in the number or kinds of parameters. This study produces a new bedform stability diagram, which defines bedform stability regions by three dimensionless parameters: dimensionless grain size D*, Shields mobility parameter τ* and Froude number Fr.
On the basis of the diagram described above, discriminant functions are derived by following procedures. At first, a polynomial function with arbitrary coefficients which divides parametric space is supposed as a candidate of a discriminant function. Then, the ratio of data points of bedform experiments that was judged incorrectly by the polynomial function is calculated. At last, in order to minimize the ratio, coefficients of polynomial function is optimized.
The discriminant functions of bedforms obtained in this study can serve quantitative paleo-flow analysis of sedimentary structures. Their form is Fr = ƒ (D*, τ*). This function can be recast in the form U = ƒ (D, h), where U = flow velocity; D = sediment particle size; h = flow depth. Thus, when we obtain the data of sediment particle size and flow depth from sedimentary structures, we can estimate paleo-flow velocity. The discriminant functions are useful and objective for estimation of paleo-flow conditions.