Hydrodynamic Response of a Bubble Curtain Under Transverse Current: Free-Surface Elevation and Parametric Effects

This study investigates the near-surface hydrodynamic response of bubble curtains under transverse currents, utilizing the spatially averaged net free-surface elevation as the primary metric. Recirculating-flume experiments were conducted to examine five control parameters: gas flow rate, gas supply pressure, inflow velocity, orifice diameter, and orifice spacing. A five-factor full-factorial design comprising 3000 operating conditions was analyzed through variance decomposition and two-factor interaction assessment. Gas flow rate and inflow velocity emerged as the dominant controls, with main-effect contributions of 41.80% and 32.79%, respectively, jointly accounting for 74.59% of the total response variation. This highlights the competition between gas-driven forcing and ambient-current inertia. When gas flow rate was independently controlled, the main and interaction effects of supply pressure were both below 1%, justifying its exclusion from the predictive model. Orifice spacing exhibited a weak main effect but interacted strongly with inflow velocity and orifice diameter. Following variable screening, an empirical correlation was formulated in terms of a gas-supply Reynolds number, a transverse Froude number, and a geometric opening parameter. The correlation yielded R2 = 0.7875 for the fitting set and R2 = 0.7974 for the independent validation set, with a validation MAPE of 11.64%. Normalized-response analysis indicated that increasing gas-input intensity raised the relative elevation response by approximately 90.5%, whereas increasing transverse-current intensity reduced it by approximately 36.4%. These results quantify the coupled dependence of bubble-curtain-induced free-surface elevation on operating and geometric parameters and provide a hydrodynamic basis for subsequent modeling and quantitative assessment of pneumatic oil-barrier performance.