Do shear-driven and pressure-driven simulations of the oscillatory flow over ripples provide different results ?

Numerical simulations of the two-dimensional oscillatory flow generated by a uniform, oscillating pressure gradient over a wavy wall are made and the results show that simulations, carried out for the same geometrical characteristics of the bottom waviness and the same hydrodynamic parameters, can converge to different states and can generate different steady streaming. Indeed bifurcations, that occur when the Reynolds number becomes larger than critical values, cause the flow to converge towards different states. Although the numerical simulations are made for moderate values of the Reynolds number so that a laminar flow is expected to provide reliable results, the numerical simulations of Sishah and Vittori (2022) and the experimental measurements of Ridler and Sleath (2000) suggest that a similar phenomenon is present even when the flow regime is turbulent and the Reynolds averaged flow field is considered. Hence, it is likely that the differences observed by Ciri et al., (2024) when comparing ( i ) the oscillatory flow generated over a rippled bed by an external uniform pressure gradient that oscillates in time (pressure-driven flow) and ( i i ) the flow generated by the oscillations of a rippled bed in a still fluid (shear-driven flow) are due to the growth of different initial perturbations of very small amplitudes that make the flow to converge to different states.