Publication Cover
Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 12
36
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A bound on oscillations in an unsteady undular bore

&
Pages 1701-1712 | Received 30 Oct 2008, Accepted 01 Oct 2009, Published online: 17 Nov 2009

References

  • Rowbotham , F . 1970 . The Severn Bore , Newton Abbot, , UK : David & Charles .
  • Pan , C-H , Lin , B-Y and Mao , X-Z . 2007 . Case study: Numerical modeling of the tidal bore on the Qiantang River, China . J. Hydraulic Eng. , 133 : 130 – 138 .
  • Favre , H . 1935 . Ondes de Translation , Paris : Dunod .
  • Keulegan , GH and Patterson , GW . 1940 . Mathematical theory of irrotational translation waves . Natl. Bur. Standards J. Res. , 24 : 47 – 101 .
  • Binnie , AM and Orkney , JC . 1955 . Experiments on the flow of water from a reservoir through and open channel: II . Proc. R. Soc. A , 230 : 237 – 246 .
  • Benjamin , TB and Lighthill , MJ . 1954 . On cnoidal waves and bores . Proc. R. Soc. , A 224 : 448 – 460 .
  • Sturtevant , B . 1965 . Implications of experiments on the weak undular bore . Phys. Fluids , 6 : 1052 – 1055 .
  • Johnson , RS . 1972 . Shallow water waves on a viscous fluid–the undular bore . Phys. Fluids , 15 : 1693 – 1699 .
  • Dutykh , D and Dias , F . 2007 . Dissipative Boussinesq equations . C.R. Mecanique , 335 : 559 – 583 .
  • El , GA , Grimshaw , RHJ and Kamchatnov , AM . 2005 . Analytic model for a weakly dissipative shallow-water undular bore . Chaos , 15 : 037102
  • Johnson , RS . 1997 . A Modern Introduction to the Mathematical Theory of Water Waves , Cambridge : University Press .
  • El , GA , Grimshaw , RHJ and Kamchatnov , AM . 2007 . Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction . J. Fluid Mech. , 585 : 213 – 244 .
  • Peregrine , PG . 1966 . Calculations of the development of an undular bore . J. Fluid Mech. , 25 : 321 – 330 .
  • Bona , JL and Schonbek , ML . 1985 . Travelling-wave solutions to the Korteweg-de Vries-Burgers equation . Proc. R. Soc. Edinb. , A 101 : 207 – 226 .
  • Bona , JL , Rajopadhye , SV and Schonbek , ML . 1994 . Models for propagation of bores: I. Two-dimensional theory . Diff. Integral Equ. , 7 : 699 – 734 .
  • Katznelson , Y . 1976 . An Introduction to Harmonic Analysis, 2nd corrected ed. , New York : Dover .
  • Foias , C and Temam , R . 1989 . Gevrey class regularity for the solutions of the Navier-Stokes equations . J. Funct. Anal. , 87 : 359 – 369 .
  • Grujić , Z . 2000 . Spatial analyticity on the global attractor for the Kuramoto-Sivashinsky equation . J. Dyn. Differ. Equ. , 12 : 217 – 227 .
  • Bona , JL , Colin , T and Lannes , D . 2005 . Long wave approximations for water waves . Arch. Ration. Mech. Anal. , 178 : 373 – 410 .
  • Craig , W . 1985 . An existence theory for water waves and the Boussinesq and Korteweg de Vries scaling limits . Comm. Partial Differ. Equ. , 10 : 787 – 1003 .
  • Rudin , W . 1987 . Real and Complex Analysis , New York : McGraw-Hill .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.