Stationary Wave Trains in Steep Channels: Experimental Hydraulics and Velocity Estimation

Abstract

Stationary wave trains have been interpreted as indicators of near-critical flow and associated with undular hydraulic jumps (UHJs) in steep rivers. However, the hydraulic conditions under which these waves form, and the extent to which their observable properties reflect flow characteristics, remain incompletely understood. This study investigates stationary wave trains as a hydraulically definable class of surface gravity waves characterized by consistent wavelength across multiple downstream undulations and a mean water surface parallel to the bed slope. Controlled flume experiments were conducted across a range of slopes and discharges to quantify wave geometry, flow depth, and velocity, and to evaluate the applicability of wave-based velocity estimation methods derived from linear wave theory. Stationary wave trains were observed under both subcritical and near-critical flow regimes, with wave nonlinearity increasing systematically with slope. Despite this increase in wave nonlinearity, intermediate-depth dispersion relationships provided the most accurate estimates of mean flow velocity for all slopes tested. These results demonstrate that stationary wave trains are not restricted to classical UHJs and do not require strict critical flow conditions. Instead, they represent organized surface gravity waves that can persist across subcritical to near-critical regimes in steep, rough-bed channels. The findings support the use of wave-based approaches for velocity estimation and provide the hydraulic conditions for interpreting stationary wave trains in natural rivers.