Surprising behaviour in the large-wavelength approximation of turbulent flow past a wavy bottom

Knowledge of the stress exerted by turbulent flow over a wavy bottom is an essential ingredient in the analysis of sediment transport by rivers, open channels and tides, in addition to being relevant to the understanding of turbulent flow per se and of some proposed drag-reduction devices. In a geophysical context this kind of flow is often studied in either the short-wavelength limit, where a boundary-layer type of structure applies (Jackson & Hunt 1975) or the large-wavelength limit, where a shallow-water type of analysis is generally used. Target of the analysis, in the case of a small sinusoidal perturbation of the bottom, is in particular the quadrature component of the induced modulation of the bottom shear stress, which has implications on the morphological evolution of a sandy bottom. For a general overview, see e.g. Charru, Andreotti & Claudin, Annu. Rev. Fluid Mech. (2012)