Stochastic Theory for Irregular Stream Modeling. Part I: Flow Resistance

A stochastic theory is developed for predicting flow resistance in natural rivers. Irregularly varying river width and bed elevation are represented as one‐dimensional spatial random fields. Large‐scale random flow acceleration and deceleration in response to boundary variations are described by the stochastic differential flow equation. Analytical stochastic flow solutions are developed for the case when boundary variations are small and statistically homogeneous. In particular, closed‐form expressions for the effective flow resistance coefficient and flow variance are obtained. The results indicate that flow resistance in natural rivers is strongly influenced by cross‐sectional nonuniformity and mean flow condition, in addition to relative boundary roughness and mean cross‐sectional shape. The results also show that effective resistance is always greater than uniform resistance in a corresponding mean straight channel. This difference increases as the mean Froude number increases for a given mean bed slope or as mean bed slope decreases for a given mean Froude number. Part II of this paper will be published in the future.