ALBERT

Description: Self-similar propagation of gravity currents through vegetation-like obstruction arrays was elucidated. We conducted a theoretical analysis by using an approximate model for one-layer and two-layer situations. This model incorporates a balance between the driving buoyancy (i.e., pressure) force and the resisting obstruction-induced drag force that is proportional to u λ (where u —speed in the layer and λ —a constant). We focused our attention on solutions with λ ≥ 1. We considered both gravity currents in a deep ambient fluid (including both continuous-flux release currents and constant-volume currents) and lock-exchange currents and demonstrated that a variety of such flows are governed by physically acceptable similarity solutions. For gravity currents in a deep ambient fluid, our theoretical analysis revealed four distinct classes of similarity solutions. Class I solutions predict gravity currents with a triangular profile (i.e., linear current interface with a constant negative slope) and a front/nose position that is a linear function of time. The physical presence of such self-similar currents was reported in recent experimental observations for currents sustained by a continuous-flux release source. We showed that theoretical predictions of Class I solutions capture the behavior of these experimental currents well. Class II solutions predict gravity currents with a non-linear profile/interface and a constant height at the source. Though physically acceptable, we could not relate this class of solutions to presently known currents. Class III solutions correspond to constant-volume currents and predict a linear increase of velocity within the current toward the nose. We discussed this class of similarity solutions using previously reported experimental observations of such currents. Class IV solutions cover the rest of the parameter domain for all other continuous-flux release gravity currents (except those that fall under Classes I-III). Next, using a two-layer variation of the model, we developed physically acceptable similarity solutions for lock-exchange currents (released by a full-depth gate). We confirmed our theoretical results by performing comparisons with previously reported experimental data for such currents. These comparisons, while showing a good qualitative agreement, revealed a quantitative ambiguity on the value of λ for the dependency of the obstruction-induced drag force on u . We also extended our similarity solutions for the currents in a deep ambient fluid to the axisymmetric geometry. We expect our similarity solutions to provide useful insights for both “deep” and lock-exchange type of gravity currents propagating through aquatic vegetation-like obstacles and a guidance for adequate design of relevant experiments.