Critical Resistance Affecting Sub- to Super-Critical Transition Flow by Vegetation

Abstract

In order to design a vegetation structure to mitigate floods resulting from extreme events like tsunamis, vegetation density and thickness (width) are important parameters. Flow passing through vegetation faces great resistance, which results in a backwater rise on upstream (U/S) vegetation, increases the water slope inside the vegetation, and for some cases, forms a hydraulic jump downstream (D/S) of the vegetation, thus transforming a subcritical flow to supercritical [Pasha, G. A. and Tanaka, N. [2017] “Undular hydraulic jump formation and energy loss in a flow through emergent vegetation of varying thickness and density,” Ocean Eng. 141, 308–325.]. Like the concepts of critical velocity and critical slope, this paper introduces the concept of “critical resistance of vegetation,” which is defined as “resistance offered by vegetation that transforms a subcritical flow to supercritical.” An analytical approach to find the water depths U/S, inside, and D/S of vegetation is introduced and validated well by laboratory experiments. Critical resistance was determined against vegetation of variable densities ([Formula: see text], where [Formula: see text] of each cylinder in the cross-stream direction, [Formula: see text] of the cylinder), thicknesses (dn, where [Formula: see text] of a cylinder and [Formula: see text] of cylinders in a stream-wise direction per unit of cross-stream width), and the initial Froude number (Fro). A subcritical flow ([Formula: see text], without vegetation) was transformed to a supercritical flow (D/S vegetation) with a range of Froude numbers of 1.6–1.9, 1.1–1.2, and 0.85–0.98 against [Formula: see text] ratios of 0.25, 1.09, and 2.13, respectively, thus defining [Formula: see text] as the critical resistance. However, altering vegetation thickness did not change the results.