Kurkin A. A., Semin S. V., Stepanyants Y. A.
A brief overview of works on transformation of surface and internal gravity waves over a bottom step is presented. The generalization of Lamb formulae for the transformation coefficients derived in the longwave approximation is discussed for waves of arbitrary length in the fluid of a finite length. The rigorous approach to calculate the transformation coefficients in the linear approximation is described both for the surface and internal waves in two-layer fluid. The problems associated with the application of the rigorous approach are noticed. The various approximate approaches are considered, as well as their compliance with the rigorous theory and numerical and experimental results. Within the framework of the rigorous approach the transformation coefficients of travelling waves and the excitation coefficients of evanescent modes are calculated. It is shown that wavelength of a quasi-monochromatic wavetrain changes after transformation on a bottom step proportionally to the phase speed, whereas the length of the envelope changes proportionally to the group speed. A comparison of theoretical results with numerical data and laboratory experiments is presented.