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

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 equation s, 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 art initial value calculation to be solve d numerically. The simulations are initiated by assuming three different pl an forms for the initial plume front and their subsequent evolutions follow ed 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 in itially concave region of the front can lead to a nonlinear focusing that r esults in an energetic bulge in the frontal plan view. These bulges form sh arp angles, or kinks, where they are joined to the front at their edges on either side. As they evolve, these angles increase toward 180 degrees (a st raight line), and the front becomes smoother in time. The orientation of th e bulge and kink features predicted by the model is in agreement with visua l 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 d etermining plume speeds by tracking these features on sequential images of gravity currents is also dealt with.