Near-critical turbulent free-surface flow over a wavy bottom

Abstract Steady plane turbulent free-surface flow over a slightly wavy bottom is considered for very large Reynolds numbers, small slopes, and Froude numbers close to the critical value 1. As in previous works, slope deviation from number are assumed be coupled such that turbulence modeling not required. The amplitudes of periodic elevations, however, half an order magnitude larger than case bumps or ramps finite length. Asymptotic expansions give steady-state version extended Korteweg–deVries (KdV) equation surface elevation. extension consists forcing term due unevenness damping friction at bottom. Other quantities, as pressure, velocity components, local force, can expressed terms Exact solutions KdV equation, describing stationary cnoidal waves, obtained bottoms particular shapes. limiting case, solitary waves ramp re-obtained accord with results.