A dissipative nonlinear theory for generation and propagation of explosion-generated waves in shallow water

The process of water wave generation due to underwater explosions is investigated in detail. This study is focussed on large explosions in shallow water, $h\over W\sp{1\over 3}$ $\u3c$ 1, where h is the water depth in ft. and W is the explosion yield in lbs. of TNT. A number of small scale tests were studied in slow motion which allowed deciphering of the complex wave generation and propagation phenomena. The process was split up into a sequence of events which are analysed and modelled individually.An underwater explosion in shallow water creates a large crater which extends to the bottom and a visible plume of water is observed on the free surface. The crater collapses and the water rebounds on itself at the center creating a dissipative bore propagating outwards following the leading wave generated by the fall of the plume. The bore transforms itself into an undular bore and then into a wave train of high frequency trailing waves. Mathematical modelling of the above sequence of events is done by selecting a cylindrical cavity with a lip as the initial condition created by the explosion. The collapse of the cavity on dry bed is solved using nonlinear long-wave equations and method of characteristics. Dissipative bore formation is analysed by iteratively solving the momentum and the continuity equations as in the case of a translatory wave. The propagation of nonlinear waves is achieved by the application of KdV equation and the split step Fourier algorithm. Transition of near-field nonlinear waves to far-field linear waves is achieved by using an extended form of KdV equation proposed during this study. Since the phenomenon is assumed to be axisymmetric, all the computations were done in cylindrical coordinate system with zero dependence on $\theta$.Theoretical model was tested with the data obtained from the small scale explosion tests conducted. The model was also tested with the available large yield data and the calibrations were performed. Hydrodynamic dissipation was computed and found to be a constant. Efficiency of shallow water explosions was determined. Thus capability of predicting the entire wave field in shallow water, given the yield of explosion and the water depth, was achieved.Additional work was also done in improving the range and flexibility of the existing linear model by incorporating Fast Fourier Transforms in the computational schemes. An inverse method was also developed which allowed the computation of linear equivalent initial conditions in the form of a crater and a velocity distribution, by Fourier analysis of the far field linear wave records