Interfacial shear-layer dynamics in partially obstructed shallow flows

Shallow flows partially obstructed by arrays of rigid elements develop a lateral shear layer that controls momentum exchange, turbulence production, and scalar transport. We investigate this interfacial region through a tractable two-layer theoretical framework, laboratory measurements in an unusually wide (4 m) flume and GPU-accelerated weakly compressible SPH simulations. The depth-averaged velocity across the interface collapses onto a hyperbolic-tangent profile, enabling closed-form predictions for the mixing-layer thickness, outer-edge velocity, and interfacial shear stress via a momentum balance that incorporates detrainment, pressure gradients, and obstacle-induced dissipation. Coherent motions consist of quasi-periodic vortices that organise a sweep--ejection cycle and dominate the Reynolds shear stress; conditional statistics reveal a robust phase-locked structure, while Lagrangian trajectories exhibit ballistic, inertial, and diffusive dispersion regimes whose anisotropies reflect the vortex scale and lifetime. Classical Rayleigh analysis shows that the depth-averaged velocity profiles are neutrally stable, indicating that the interfacial rollers do not arise from the inviscid Kelvin--Helmholtz instability. Instead, a reduced temporal model reproduces the characteristic instability window of drag-modified shallow shear layers, and the shallow-water Modified Rayleigh Equation shows that all configurations fall well within the unstable regime. The vortices therefore represent the nonlinear manifestation of a drag-induced lateral instability intrinsic to partially obstructed shallow flows. Together, these results provide a unified description of interfacial momentum balance, coherent-structure dynamics, Lagrangian dispersion, and drag-modified stability, and offer physically grounded diagnostics for mixing in environmental and engineered porous-flow interfaces.