Abstract
Abstract
Highlights
Long wavelength linear elastic waves experience an effective dispersion that arises due to the periodic variation in the material coefficients (Sun, Achenbach & Herrmann 1968)
We have shown that bathymetric variation in an infinite periodic domain leads to an effective dispersion of water waves, and have related this to the already-studied phenomenon of dispersion of waves in non-rectangular channels
This dispersion is distinct from the dispersion accounted for in wave models like Korteweg–de Vries (KdV), and can on its own lead to solitary wave formation, which we call bathymetric solitary waves, even when the dominant behaviour would normally be wave breaking
Summary
The importance of laminates and composite materials in engineering led to the study of elastic waves in periodically varying media. The induced dispersion due to reflections leads to the formation of solitary waves that behave to those arising in nonlinear dispersive wave equations like the Korteweg–de Vries (KdV) equation (Korteweg & De Vries 1895) This behaviour depends on the degree of variation in the impedance; if it is not strong enough there is little effective dispersion and shocks tend to develop, as they would in a homogeneous medium (Ketcheson & LeVeque 2012; Ketcheson & Quezada de Luna 2020). We refer to this as bathymetric dispersion These effective equations describe waves varying in two horizontal dimensions; if restricted to plane waves propagating transverse to the variation in bathymetry (as depicted in figure 1a) they are similar to those derived in Chassagne et al (2019).
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