Evolution of freely propagating, two‐dimensional surface gravity current fronts

Abstract

This work addresses the two‐dimensional propagation and shape evolution of surface gravity current fronts with a surface density outcrop frontal line. The problem is formulated using the reduced gravity shallow water equations, and the gravity currents are assumed to advance into a fluid at rest. We formulate a nonlinear analytical model for the gravity current plume front morphology by applying the shock tube theory of compressible fluids, which casts the problem in the form of an initial value calculation to be solved numerically. The simulations are initiated by assuming three different plan forms for the initial plume front and their subsequent evolutions followed in time. The paper is concerned exclusively with gravity current fronts having initially a uniform frontal propagation speed locally normal to the plume front, and a number of interesting results emerge. We find that an initially concave region of the front can lead to a nonlinear focusing that results in an energetic bulge in the frontal plan view. These bulges form sharp angles, or kinks, where they are joined to the front at their edges on either side. As they evolve, these angles increase toward 180° (a straight line), and the front becomes smoother in time. The orientation of the bulge and kink features predicted by the model is in agreement with visual and radar imagery observations. The kinks are always oriented toward the lighter plume material. When a plume has two or more such concave regions, the resulting energetic bulges can interact at a later time. The issue of determining plume speeds by tracking these features on sequential images of gravity currents is also dealt with.