Exact solutions for the initial stage of dam-break flow on a plane hillside or beach

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Abstract

Inviscid, incompressible liquid is released from rest by a sudden dam break, accelerating under gravity over a uniformly sloping impermeable plane bed. The liquid flows downhill or up a beach. A linearised model is derived from Euler's equations for the early stage of motion, of duration, where H is the depth scale and is the acceleration due to gravity. Initial pressure and acceleration fields are calculated in closed form, first for an isosceles right-angled triangle on a slope of. Second, the triangle belongs to a class of finite-domain solutions with a curved front face. Third, an unbounded domain is treated, with a curved face resembling a steep-fronted breaking water wave flowing up a beach. The fluid goes uphill due to a nearshore pressure gradient. In all cases the free-surface-bed contact point is the most accelerated particle, exceeding the acceleration due to gravity. Physical consequences are discussed, and the pressure approximation of shallow water theory is found poor during this early stage, near the steep free surface exposed by a dam break.

Original languageEnglish
Article numberR7
Number of pages11
JournalJournal of Fluid Mechanics
Volume972
DOIs
Publication statusPublished - 11 Oct 2023
EventBritish Applied Mathematics Colloquium 2024: Reception and Poster Session for 37 posters - Newcastle University, Newcastle, United Kingdom
Duration: 9 Apr 202411 Apr 2024
https://conferences.ncl.ac.uk/bamc2024/

Keywords

  • gravity currents
  • surface gravity waves
  • wave-structure interactions

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