Experimental study of the evolution of a solitary wave at an abrupt junction

<jats:p>This paper describes physical and numerical experiments that were carried out to investigate the scattering of nonbreaking solitary waves of moderate amplitude on encountering an abrupt discontinuity in depth from <jats:italic>h</jats:italic><jats:sub>1</jats:sub> to <jats:italic>h</jats:italic><jats:sub>2</jats:sub>. It is shown that in the neighborhood of the step from deeper to shallower depth the wave amplitude undergoes a rapid evolution which depends on the amount of reflection and energy losses and on dispersive and nonlinear wave effects. On the shallower shelf, the wave amplitude reaches a minimum value after the step. It is proposed that the wave characteristics (shape and volume) recorded at this point be used to predict the far field wave evolution on the shelf. From the experimental results an evolution modes diagram is drawn which distinguishes four types of wave evolution on the shelf: (1) fission, (2) fission and peaking of the first soliton, (3) transition, and (4) plunging. The diagram includes lines of constant breaking index <jats:italic>a<jats:sub>b</jats:sub></jats:italic>/<jats:italic>h</jats:italic><jats:sub>2</jats:sub>, where <jats:italic>a</jats:italic><jats:sub><jats:italic>b</jats:italic></jats:sub> is the breaking wave amplitude and <jats:italic>h</jats:italic><jats:sub>2</jats:sub> is the shelf depth. Following Mei (1985), an energy loss coefficient <jats:italic>f<jats:sub>e</jats:sub></jats:italic> is presented. For large values of <jats:italic>a</jats:italic><jats:sub>1</jats:sub>/(<jats:italic>h</jats:italic><jats:sub>1</jats:sub>–<jats:italic>h</jats:italic><jats:sub>2</jats:sub>), the experimental data conform with the values given by the steady state formula of Daily and Harleman (1966).</jats:p>