Abstract
AbstractSteady turbulent near‐critical free‐surface flow over a slightly inclined bottom with an oblique roughness discontinuity is considered. An asymptotic analysis for Froude numbers close to the critical value 1 and large Reynolds numbers results in an extended Korteweg–de Vries (KdV) equation describing the free‐surface elevation without the need of turbulence modeling. Two new integral relations can be derived from the extended KdV equation. For enlarged downstream bottom roughness, a new type of undular jump solutions with fully developed flow both upstream and downstream exists. Numerical solutions of the extended KdV equation show that an increasing downstream bottom roughness enhances the development of undulations.
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