Depth-integrated wave–current models. Part 2. Current with an arbitrary profile

The depth-integrated wave–current models developed by Yang & Liu ( J. Fluid Mech. , vol. 883, 2020, A4) are extended to investigate currents with an arbitrary vertical profile in the water column. In present models, horizontal velocities decomposed into two components. first part deduces prescribed current velocity when waves absent. second is approximated a polynomial form. resulting obtained applying weighted residual method. absence of currents, identical those and validated several three-dimensional (3D) benchmark laboratory experiments. A theoretical analysis conducted study frequency dispersion relation linear on exponential results compared numerical solutions Rayleigh equation. Using new validations investigations then for periodic solitary one-dimensional (1DH) space. Furthermore, applied interactions two-dimensional (2DH) Two scenarios considered: (1) wave propagation over vortex-ring-like (2) obliquely incident 3D sheared varying bathymetry. shear have significant effects modifying various properties, which well captured models. However, time-averaged under interaction shows small differences velocity, except region between trough crest.