ANALYSIS OF PROPAGATION OF LONG WAVES IN SHALLOW WATER USING THE KDV-BASED NONLINEAR FOURIER TRANSFORM (KDV-NLFT)

摘要

Hydraulic model tests and numerical simulations show that long sinusoidal waves that are generated in very shallow waters are not stable but show modifications of the free surface as function of propagation in time and space. First, with increasing distance from the wave maker the wave becomes asymmetric and develops into a bore-shaped wave. Second, with further increasing distance more and more additional wave crests appear from the front of the bore (undular bore). The shallower the water depth, the more additional wave components can be observed. In extremely shallow water, the periodic sine waves completely disintegrate into periodic trains of solitons. At Leichtweiss-Institute for Hydraulic Engineering and Water Resources (LWI), TU Braunschweig, a nonlinear Fourier transform based on the Korteweg-deVries equation (KdV-NLFT) is implemented and successfully applied in Bruehl that provides an explanation for this nonlinear phenomenon and allows the prediction of the dispersion and propagation of long sinusoidal waves in shallow water.