Generation of Long Waves in Laboratory

Abstract

A consistent theory is presented for generating arbitrary, finite‐amplitude, long waves at any location in a two‐dimensional, constant‐depth wave tank using a vertical paddle‐type wavemaker. The theory consists of solving an inverse evolution problem of the Korteweg‐de Vries equation; given specific initial data the boundary motion that produces that data is determined. The theory also suggests the appropriate method for calculating the force on the wavemaker. Application of this theory allows for the laboratory generation of very detailed single waveforms at arbitrary lengths away from the wave‐maker; this formalism obliterates the limitations of the existing shallow‐water wavemaker algorithms which can only reproduce wave motions either of periodic or of constant form. A series of laboratory experiments is described where relatively arbitrary single waves are specified as initial data, the theory calculates the correct boundary motion, the waves are generated and then compared with the initial data as appropriate. The experiments also demonstrate the limitations of this theory, which, even though capable of generating the leading wave emerging after a long wave breaks, it cannot model the details of the tail of the breaking wave.