Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 16 1 2009 10.5194/npg-16-23-2009 http://www.nonlin-processes-geophys.net/16/23/2009/ http://www.nonlin-processes-geophys.net/16/23/2009/npg-16-23-2009.html http://www.nonlin-processes-geophys.net/16/23/2009/npg-16-23-2009.pdf 23 32 2009-01-29 Nonlinear long-wave deformation and runup in a basin of varying depth I. Didenkulova ira@cs.ioc.ee Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia Institute of Applied Physics, Uljanov Street 46, 603950 Nizhny Novgorod, Russia Nonlinear transformation and runup of long waves of finite amplitude in a basin of variable depth is analyzed in the framework of 1-D nonlinear shallow-water theory. The basin depth is slowly varied far offshore and joins a plane beach near the shore. A small-amplitude linear sinusoidal incident wave is assumed. 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