ANALYSIS OF THE EFFECT OF THE BEAVERS-JOSEPH INTERFACE CONDITION ON FLOW IN KARST CONDUITS

摘要

In this study, we derive an approximate analytic solution for the distribution of flow velocity in a cylindrical conduit and the surrounding media, and analyze the effect of differing parameters (e.g., conduit radius) on the velocity of conduit flow. The solution is then employed to estimate the thickness of the boundary layer inside the media. The results reveal that when conduit radius is large, the Beavers-Joseph condition has only a minor effect on the velocity of conduit flow (such that the nonslip condition on the conduit wall still works pretty well), and the boundary layer is so thin that the wall can still be treated as the interface between fast water in the conduit and slow water in the media. The solution indicates that the velocity of conduit flow is the superposition of the velocity profile in the nonslip situation onto the slip velocity on the wall. Our study theoretically shows that the coupled continuum pipe flow model in MODFLOW-2005 constructed by the U.S. Geological Survey is reasonable in that there is no need to consider the Beavers-Joseph condition when simulating flow in karst conduits. The role of the boundary layer in transport and its effect on the hyporheic zone is not clear, which is a suitable topic for future study.