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Undular bores and solitons in a tsunami


The setup is a long wave (solitary wave) propagating onto a shelf. These results are numerically convergent, but have no dissipation (bottom friction) which appears to be very important here in controlling both the number of fission waves generated, and their height. By the end of the animation, this waveform is a basically undular bore. The initiation of the fission appears to be a nonlinear - nondispersive process, while the evolution of the fission-waves (the undular bore) is a nonlinear - weakly dispersive process.  This expected and known - most mathematical work on this type of phenomenon uses the KdV-type equations. The wavelength of the fission waves in this example is around 20 water depths (T=30s in 20 m of water). To generate this type of fission train, there usually needs to be a long mild shelf and/or a strong opposing current, but this depends on the nonlinearity of the wave. So, the deep water, initial wave is a soliton.  Under certain conditions, it will turn into an undular bore.  If let propagate/transform further, the undular bore could in fact turn it a train of solitons (solitary waves).

Additional notes

Thanks to Patrick J. Lynett (Assistant Professor - Sustainable Coastal Margins Program - Coastal and Ocean Engineering Division - Department of Civil Engineering - Texas A&M University)