Outer region scaling using the freestream velocity for nonuniform open channel flow over gravel

The theoretical basis for outer region scaling using the freestream velocity for nonuniform open channel flows over gravel is derived and tested for the first time. Owing to the gradual expansion of the flow within the nonuniform case presented, it is hypothesized that the flow can be defined as an equilibrium turbulent boundary layer using the asymptotic invariance principle. The hypothesis is supported using similarity analysis to derive a solution, followed by further testing with experimental datasets. For the latter, 38 newly collected experimental velocity profiles across three nonuniform flows over gravel in a hydraulic flume are tested as are 43 velocity profiles previously published in seven peer-reviewed journal papers that focused on fluid mechanics of nonuniform open channel over gravel. The findings support the nonuniform flows as equilibrium defined by the asymptotic invariance principle, which is reflective of the consistency of the turbulent structure's form and function within the expanding flow. However, roughness impacts the flow structure when comparing across the published experimental datasets. As a secondary objective, we show how previously published mixed scales can be used to assist with freestream velocity scaling of the velocity deficit and thus empirically account for the roughness effects that extend into the outer region of the flow. One broader finding of this study is providing the theoretical context to relax the use of the elusive friction velocity when scaling nonuniform flows in gravel bed rivers; and instead to apply the freestream velocity. A second broader finding highlighted by our results is that scaling of nonuniform flow in gravel bed rivers is still not fully resolved theoretically since mixed scaling relies to some degree on empiricism. As researchers resolve the form and function of macroturbulence in the outer region, we hope to see the closing of this research gap.