A unified flow resistance formula for open-channels with natural and
engineered submerged obstacles
Abstract
Stream obstacles, naturally formed like boulders or engineered like
weirs, are the major source of flow resistance; however, to quantify
their flow resistance, a resistance formula needs to be selected in
accordance with the specific obstacle type, i.e. obstacle type
dependency. So far, whether a unified resistance formula that adequately
characterizes the roughness of distinctive obstacle types is elusive.
Here, we conduct flume experiments with various natural and engineered
submerged obstacles, including boulders, weirs, log jams, and transverse
stones. We combine them with existing datasets containing rigid
vegetation, step-pool, and riffle-pool to identify a unified metric for
a general resistance relation. We test three roughness metrics, the
widely used roughness metrics D84 (84th percentile of bed grain size
distribution), a bathymetric-line-based metric σz,centerline (the
standard deviation of bed centerline elevation), and the new metric
σz,bed (the standard deviation of elevation of the entire bed) as bed
roughness, respectively. σz,bed is proposed to incorporate the roughness
inhomogeneity in the transverse direction which widely exists in both
natural and engineered channels, complementing the insufficiency of
line-based metric σz,centerline. We show that the resistance equation
based on σz,bed demonstrated a more consistent and superior velocity
prediction capacity than D84 and σz,centerline throughout almost all
types of obstacles. Interestingly, when applied to vegetated channels,
the resistance formula based on only σz,bed can compare with those based
on multiple parameters related to vegetation characteristics. This study
shows the viability of unifying the flow resistance formula in
open-channels with submerged obstacles, avoiding obstacle-type
dependency.