Wake dynamics and flow mechanisms of narrow-gap flow beneath a slender rectangular cylinder under unsteady inflow

Narrow-gap flow beneath a slender rectangular cylinder is relevant to small-opening discharge in hydraulic structures, yet the mechanisms governing wake dynamics and turbulence evolution remain unclear. A coupled volume of fluid-large eddy simulation framework is employed to investigate the flow characteristics and hydrodynamic responses under different opening ratios E and hydraulic head differences P*. The results show that E regulates narrow-gap flow through geometric confinement and downstream momentum transport. Smaller openings intensify gap-jet acceleration and extend transient shear-layer development, whereas larger openings promote wake expansion and turbulent transport. The downstream wake is divided into three regions: the narrow-gap-influenced region, approximate self-similarity region, and far-downstream confinement region. Furthermore, increasing E advances the onset of approximate self-similarity, which occurs at x/D ≈ 5 for E = 0.2. Meanwhile, the enhanced downstream turbulence is accompanied by reduced local shear production and subgrid-scale dissipation near the gap. Spectral proper orthogonal decomposition reveals that the transient wake is governed by multiple energetic coherent structures rather than a single periodic vortex shedding process. These flow features modify surface pressure distribution, with upstream mean pressure decreasing by approximately 44% as E increases. In contrast, P* primarily controls transient hydraulic forcing. A larger P* enhances pressure-driven acceleration, strengthens shear-layer instability and vortex development, and increases pressure fluctuations and hydrodynamic loading. The maximum drag coefficient increases approximately threefold as P* rises from 0.1 to 0.3. These findings clarify the effects of geometric confinement and hydraulic forcing on transient narrow-gap flow and hydrodynamic response.