Predicting the bulk drag coefficient of flexible vegetation in wave flows based on a genetic programming algorithm

Abstract

The prediction of the bulk drag coefficient (CD) for aquatic vegetation is of great significance for evaluating the influence of vegetation on the hydrodynamic processes in wave environments. Different CD empirical formulas have been mostly proposed as functions of either Reynolds (Re) number or Keulegan–Carpenter (KC) number in the literature, and the influences of other wave and vegetation parameters on CD were often ignored. The difference in formulas is largely attributable to inconsistent uses of characteristic velocity and length scales in the definitions of Re and KC. By considering the vegetation and hydrodynamic characteristics in this study, new Re and KC numbers were redefined using the mean pore velocity and vegetation-related hydraulic radius. Besides, a genetic programming algorithm was adopted to develop a robust relationship between CD and possible dimensionless variables based on extensive experimental data. Ultimately, a new CD predictor that has a similar form to that of the classical expression was obtained without any prespecified forms before searching. It turns out that the new predictor depends on not only the new KC number but also the submergence ratio and Ursell number. Compared with the existing predictors, the proposed CD predictor exhibits a considerable improvement in predictive ability for a wider parameter space.