The Burgers equation model and the monoclinal wave phenomenon in conveyance channels

References

• Abramowitz , M. and Stegun , I. A. 1965 . Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 295 – 307 . New York, , USA : Dover Publications .
   Google Scholar
• Burgers , J. M. 1950 . Correlation Problems in a Onedimensional Model of Turbulence . Proc. Roy. Netherlands Acad. Sci. Amsterdam , 53 : 247 – 260 .
   Google Scholar
• Chow , V. T. 1959 . Open-channel Hydraulics. McGraw- Hill 528 – 535 . New York, , USA
   Google Scholar
• Cole , J. D. 1951 . “ On a Quasi-linear Parabolic Equation Occurring in Aerodynamics ” . In Quarterly of Applied Mathematics 9 225 – 236 .
   Google Scholar
• Ferrick , M. G. and Goodman , N. J. 1998 . Analysis of Linear and Monoclinal RiverWave Solutions . J. Hydraul. Engng. ASCE , 124 ( 7 ) : 728 – 741 .
   Web of Science ®Google Scholar
• Hayami , S. 1951 . On the Propagation of Flood Waves , Vol. 1 , 1 – 16 . Japan : Bulletins, Disaster Prevention Research Institute, Kyoto University .
   Google Scholar
• Hope , E. 1950 . “ The Partial Differential Equation ut + uux = µuxx ” . In Commun. Pure Appl. Math. 3 201 – 230 .
   Google Scholar
• Kajisa , T. 1990 . Discharge Response in a Water Conveyance System . J. Irrig. Engng. Rural Planning , 19 : 7 – 17 .
   Google Scholar
• Kubo , N. and Shimura , H. 1988 . Theoretical Analysis of Transient Phenomena of Conveyance Waves with Small Froude Number . Trans. Jpn. Soc. Irrig. Drain. Reclam. Engng. , 138 : 25 – 36 . in Japanese
   Google Scholar
• Odai , S. N. 1999 . ANonlinear Kinematic-wave Model for Predicting Open-channel Flow Rate . J. Hydraul. Engng. ASCE , 125 ( 8 ) : 886 – 889 .
   Web of Science ®Google Scholar
• Odai , S. N. , Kubo , N. , Onizuka , K. and Osato , K. 2006 . Analytical Solution of the Burgers Equation for Simulating Translatory Waves in Conveyance Channels . J. Hydraul. Engng. ASCE , 132 ( 2 ) : 194 – 199 .
   Web of Science ®Google Scholar
• Onizuka , K. and Odai , S. N. 1998 . Burgers' Equation Model for Unsteady Flow in Open Channels . J. Hydraul. Engng. ASCE , 124 ( 5 ) : 509 – 512 .
   Web of Science ®Google Scholar
• Price , R. K. 1994 . “ Flood Routing Models ” . In Computer Modeling of Free-surface and Pressurized Flows , Edited by: Chaudhry , M. H. and Mays , L. W. 375 – 407 . Dordrecht, , The Netherlands : Kluwer Academic Publishers .
   Google Scholar
• Tsai , C. W.-S. 2003 . Applicability of Kinematic, Noninertia, and Quasi-steady Dynamic Wave Models to Unsteady Flow Routing . J. Hydraul. Engng. , 129 ( 8 ) : 613 – 627 .
   Web of Science ®Google Scholar
• Tsai , C. W.-S. and Yen , B. C. 2001 . Linear Analysis of Shallow Water Wave Propagation in Open Channels . J. Engng. Mech. ASCE , 127 ( 3 ) : 459 – 472 .
   Web of Science ®Google Scholar
• Tsai , C. W.-S. and Yen , B. C. 2004 . Shallow Water Wave Propagation in Convectively Accelerating Open-Channel Flow Induced by the Tailwater Effect . J. Engng. Mech. ASCE , 130 ( 3 ) : 320 – 336 .
   Web of Science ®Google Scholar