人民黄河2025，Vol.47Issue(11)：41-49,59,10.DOI:10.3969/j.issn.1000-1379.2025.11.006
Einstein河流动床阻力公式的剖析和修正
Analysis and Modification of Einstein Formula for Movable Bed Resistance of Flowing Rivers
摘要
Abstract
Research on movable bed resistance is a pivotal subject in river dynamics.Building upon a review of the current state of movable bed resistance studies in alluvial rivers,this paper identified issues in Einstein mobile bed resistance formula.First,the original empirical curve did not cover the high-energy regime.The second was that the hydraulic radius of the sand particles in the Yellow River calculated by trial was approximately 30%greater than the measured water depth,resulting in a physical paradox where the hydraulic radius of the sand waves calculated according to the definition formula of hydraulic radius division was negative.By expanding the dataset with measured Yellow River data,the empirical curve was extrapolated,and a new relational expression was fitted.The analysis using field data demonstrates the applicability of Einstein formula:it remains valid for international rivers where the hydraulic radius of sand waves is non-negative and the hy-draulic parameter exceeds 0.3.After appropriate modifications,the formula is preliminarily applicable to the lower Yellow River.By introdu-cing Zhang Hongwu's longitudinal stability index relationship for riverbeds to estimate the bed slope-replacing the measured water surface slope-the validation accuracy of the formula improved while reducing the frequency of negative sand wave hydraulic radii.This confirms that Einstein movable bed resistance formula,following refinement,is applicable to relevant calculations for the Lower Yellow River.关键词
动床阻力/Einstein公式/水力半径/比降/黄河下游Key words
movable bed resistance/Einstein formula/hydraulic radius/slope/Lower Yellow River分类
建筑与水利引用本文复制引用
师翠香,张红武,刘晓民,卜海磊..Einstein河流动床阻力公式的剖析和修正[J].人民黄河,2025,47(11):41-49,59,10.基金项目
内蒙古自治区科技重大专项(2024JBGS0016) （2024JBGS0016）
国家重点研发计划项目(2023YFC3208603) （2023YFC3208603）
国家自然科学基金资助项目(52169016,U2443224) （52169016,U2443224）
