On the front condition for compositional gravity currents

A two-dimensional potential flow is employed to derive the front condition of the gravity current. The derivation starts from the balance between the static pressure of the gravity current and the form drag imposed on the gravity current by the ambient fluid. After employing Bernoullis equation along the interface of the gravity current near the head, we end up with a front condition that is in better agreement with experiment than previous theoretical models. This condition is a function of the density ratio between current and ambient fluids, which was different from previous theoretical models, while it has been widely used in experimental studies. The present front condition suggests that the form drag may account for a significant part of the resistance force applied on the current head.