Shoaling of a shallow-water undular bore

River_Ribble_bore The paper “Transformation of a shoaling undular bore“, co-authored by G. El, R. Grimshaw, and W. Tiong, has appeared in the J Fluid Mechanics.  The paper considers the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variable-coefficient Korteweg–de Vries equation. When the undular bore advances in the direction of decreasing depth, its interaction with the slowly varying topography results, apart from an adiabatic deformation of the bore itself, in the generation of a sequence of isolated solitons – an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore. Using nonlinear modulation theory the paper constructs an asymptotic solution describing the formation and evolution of this solitary wavetrain. The analytical solution is supported by direct numerical simulations.  A link to the paper is here.

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