Propagation of Long Water Waves through Branching Channels

Solitary waves in forked channel regions

“…Many other relevant articles can be found, for example, in the references of the above publications. Surprisingly, another topic in this class of problems does not feature much in the literature, regarding either its physical or mathematical aspects: solitary waves propagating in intricate channel networks (Harbitz 1992;Shi, Teng & Wu 1998;Shi, Teng & Sou 2005;Harbitz et al 2014). A problem that is addressed here for the first time concerns the reduction of a two-dimensional (2D) nonlinear dispersive wave model into an effective one-dimensional (1D) system, defined on a network.…”

“…Previous studies in Cartesian coordinates were restricted (for meshing reasons) to angles that were multiples of π/4 (Shi et al 2005 (iii) A new three-point nonlinear compatibility condition is presented. It proves to be more general and more accurate than the existing/standard one-point linear compatibility condition (Stoker 1957;Jacovkis 1991;Bona & Cascaval 2008).…”

“…We have normalized the reference shallow water speed to be c o = √ gh 0 = 1. An approximate solitary wave solution is available for this model (Shi et al 2005):…”

“…In Shi et al (2005) the effective wavelength λ e of the solitary wave is defined as being the length within which the solitary wave elevation is larger than 1 % of its amplitude a. Based on our previous numerical experience (Nachbin & Simões 2012) we take the amplitude to be a = 0.3, while the wavelength is respectively λ e ≈ 13.…”

“…This is achieved by having a slightly wider branching region mapped, followed by choosing the nearest ζ -level curve as the channel's boundary. In the Cartesian configuration, Shi et al (2005) report having to perform an ad hoc averaging near the inner branching corner to avoid spurious oscillations. We observed and removed these oscillations with a very mild smoothing of the corner through the mapping of a slightly wider region.…”