Overbank flows in rivers, also termed compound open-channel flows, are rarely uniform in the streamwise direction. Flow nonuniformity involves transverse currents directed from the river main channel (MC) to adjacent floodplains (FPs) or vice versa. Depending on their direction and magnitude, the transverse currents can laterally displace the planform shear layer that forms at the interface between MC and FP. They can also modify the cross-sectional distribution of the helical secondary currents (SCs). This paper reports a numerical study that focuses on assessing the ability of a hybrid RANS (Reynolds Averaged Navier-Stokes)-LES (Large Eddy Simulation) approach, namely, the Scale Adaptive Simulation (SAS), to capture the evolving structure of both depth-uniform and nonuniform flows in a straight compound open-channel. The simulated flows have recently been studied in an 18 m long and 3 m wide laboratory flume by Proust and Nikora (2020, https://doi.org/10.1017/jfm.2019.973). The originality of the study lies in the modeling of flows over the entire flume length and in the estimate of the length-scales of the large Kelvin-Helmholtz-type coherent structures (KHCSs). The SAS approach can accurately predict the longitudinal evolution of: (i) the streamwise time-averaged flow, including the planform shear layer width, (ii) the SC patterns, and (iii) the turbulence statistics. The emergence and development of the KHCSs are qualitatively retrieved and are confirmed to be controlled by dimensionless velocity shear irrespective of flow depth. The simulations also show that SC patterns depend on the magnitude and direction of the transverse currents and also on the development of KHCSs.