Large-eddy simulation (LES) of open channel flow driven by an oscillating pressure gradient with zero surface shear stress was performed. The flow is representative of an oscillating tidal boundary layer. Under neutrally stratified conditions, during certain phases of the oscillating pressure gradient corresponding, for example, to peak tide, the flow develops secondary structures, characterized by coherent, full-depth, streamwise-elongated counter-rotating cells. These structures are similar to the classical Couette cells found in Couette flow driven by parallel no-slip plates moving in opposite direction. A constant cooling flux at the surface with an adiabatic bottom wall leads to more intense and coherent streamwise-elongated cells characterized by greater crosswind width, which we term convective supercells. The signature of the convective supercells is observed even during times when the oscillating mean flow is decelerating, unlike in cases without surface cooling. Investigation of these coherent structures (with and without surface cooling) is deemed important due to their strong influence on vertical mixing and their potential role in determining the wake behind tidal turbines.