Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 5 1 1998 10.5194/npg-5-27-1998 http://www.nonlin-processes-geophys.net/5/27/1998/ http://www.nonlin-processes-geophys.net/5/27/1998/npg-5-27-1998.html http://www.nonlin-processes-geophys.net/5/27/1998/npg-5-27-1998.pdf 27 38 0000-00-00 The run-up of weakly-two-dimensional solitary pulses M. Brocchini Istituto di Idraulica, Università di Genova, Via Montallegro 1, 16145 Genova, Italy The run-up of solitary-type pulses propagating at a small angle with respect to the shore normal is analysed by means of a weakly-two-dimensional extension of a solution of the nonlinear shallow water equations for a non-breaking, solitary pulse incident and reflecting on an inclined plane beach similar to that of Synolakis (1987). A simple analytic expression for the longshore velocity of the solitarytype pulse is given along with examples of computations. The proposed solution can be employed in modelling run-up flow properties of solitary-type pulses (e.g. <em>tsunamis,</em> primary waves of wave groups propagating in shallow waters, ...). The hodograph transformation that is used and the flow properties are illustrated in terms of contour plots. A limiting pulse amplitude is defined such that breakdown of the solution occurs. A solution for the run-up of multiplesolitary-pulses in shallow waters is also described. Some of the salient characteristics are illustrated and discussed. Breakdown conditions are analytically defined also for the multiple-solitary-pulses solution. A strong condition is given which couples information on both pulses amplitudes and distances. An easier (but weaker) version of the criterion is given in terms of a pair of decoupled formulae one for the Pulses amplitudes and the second for their initial positions. Very large run-up is achieved because of the merging of two or more solitary pulses which are smaller than the limiting Pulse. The role of pulse separation within a group of solitary Pulses is also analysed in terms of both a 'nonlinearity parameter' <i>N</i> and a 'groupiness parameter' <i>G</i>. It is found that a critical distance exists between two pulses which minimizes the back-wash velocity and, as a consequence, the nonlinearity parameter <i>N</i>.