NONSTEADY COMPUTATIONS OF UNDULAR AND BREAKING BORES

Abstract

A bore occurs when water with local depth /t1? say, moves over shallower water with depth hi, necessarily moving at a lower speed, in a scale in which horizontal distances are a few times bigger than either h\ or hi- The bore is the region of transition between the two uniform depths and speeds. If the slopes are initially gentle, the bore gets gradually steeper and develops into one of three types depending on the ratio A = hl^hi - For small enough values of A, A <~ 0.3, the bore front develops into a smooth succession of long waves. The difference between the upstream and downstream levels is fitted with undulations which are long at the front and short at the back. These are called undular bores. For big enough values of A, A >~ 0.7, bore fronts break and the whole bore takes the aspect of a turbulent breaking zone extending over some depths and advancing at a constant speed (over a flat bed); outside this turbulent zone the water is flat. For intermediate values of A breaking and turbulence at the front precede a train of smooth undulations. Here the difference in level between upstream and downstream is fitted partially with breaking and turbulence in the front and partially with undulations, these bores are called undular breaking bores.