TY - JOUR

T1 - Exact solutions for the initial stage of dam-break flow on a plane hillside or beach

AU - Cooker, Mark J.

N1 - JFM Rapids is a subset of short papers published in the Journal of Fluid Mechanics. Volume 972 contains several Rapids papers of which this article is numbered R7.

PY - 2023/10/11

Y1 - 2023/10/11

N2 - 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.

AB - 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.

KW - gravity currents

KW - surface gravity waves

KW - wave-structure interactions

UR - http://www.scopus.com/inward/record.url?scp=85175298252&partnerID=8YFLogxK

U2 - 10.1017/jfm.2023.752

DO - 10.1017/jfm.2023.752

M3 - Article

VL - 972

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

M1 - R7

ER -