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An analytical model for bore-driven run-up


We use a hodograph transformation and a boundary integral method to derive a new analytical solution to the shallow-water equations describing bore-generated run-up on a plane beach. This analytical solution differs from the classical Shen–Meyer runup solution in giving significantly deeper and less asymmetric swash flows, and also by predicting the inception of a secondary bore in both the backwash and the uprush in long surf. We suggest that this solution provides a significantly improved model for flows including swash events and the run-up following breaking tsunamis.

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T. E. Baldock , M. G. Hughes , K. Day & J. Louys 2005 Swash overtopping and sediment overwash on a truncated beach. Coastal Engng 52, 633645.

P. A. Guard & T. E. Baldock 2007 The influence of seaward boundary conditions on swash zone hydrodynamics. Coastal Engng 54, 321331.

S. Hibberd & D. H. Peregrine 1979 Surf and run-up on a beach: a uniform bore. J. Fluid Mech. 95, 323345.

A. J. Hogg 2006 Lock-release gravity currents and dam-break flows. J. Fluid Mech. 569, 6187.

A. J. Hogg & D. Pritchard 2004 The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501, 179212.

P. A. Luccio , S. I. Voropayev , H. J. S. Fernando , D. L. Boyer & W. N. Houston 1998 The motion of cobbles in the swash zone on an impermeable slope. Coastal Engng 33, 4160.

D. H. Peregrine & S. M. Williams 2001 Swash overtopping a truncated plane beach. J. Fluid Mech. 440, 391399.

D. Pritchard & L. Dickinson 2008 Modelling the sedimentary signature of long waves on coasts: implications for tsunami reconstruction. Sed. Geol. 206, 4257.

D. Pritchard & A. J. Hogg 2005 On the transport of suspended sediment by a swash event on a plane beach. Coastal Engng 52, 123.

M. C. Shen & R. E. Meyer 1963 Climb of a bore on a beach. Part 3. Run-up. J. Fluid Mech. 16, 113125.

H. Yeh 2006 Maximum fluid forces in the tsunami runup zone. J. Waterway Port Coastal Ocean Engng 132 (6), 496500.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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