References
- Akan , A. O. 2006 . Open channel hydraulics , Oxford, , UK : Elsevier .
- Balmforth , N. J. and Mandre , S. 2004 . Dynamics of roll waves . J. Fluid Mech , 514 : 1 – 33 .
- Benjamin , T. B. 1957 . Wave formation in laminar flow down an inclined plane . J. Fluid Mech , 2 : 554 – 574 .
- Benney , D. J. 1966 . Long waves on liquid films . J. Math. Phys , 54 : 150 – 155 .
- Briggs , R. J. 1964 . Electron-steam interaction with plasmas , Cambridge, MA : MIT Press .
- Brock , R. R. 1969 . Development of roll-waves trains in open channel . ASCE J. Hydraulics Div , 95 ( HY4 ) : 1401 – 1427 .
- Brock , R. R. 1970 . Periodic permanent roll waves . ASCE J. Hydraulics Div , 96 ( HY12 ) : 2565 – 2580 .
- Chang , C. 1994 . Wave evolution on a falling film . Ann. Rev. Fluid Mech , 26 : 103 – 136 .
- Chen , G.-Q. , Levermore , C. D. and Liu , P. 1994 . Hyperbolic conservation laws with stiff relaxation terms and entropy . Commun. Pure Appl. Math , 47 ( 6 ) : 787 – 830 .
- Chow , V. T. 1959 . Open channel hydraulics , New York : McGraw-Hill .
- Colebrook , C. F. and White , C. M. 1937 . Experiments with fluid friction in roughened pipes . Proc. R. Soc. Lond. A , 161 : 367 – 381 .
- Cornish , V. 1910 . Ocean waves and kindred geophysical phenomena , Cambridge, , UK : Cambridge University Press .
- Coussot , P. 1994 . Steady, laminar, flow of concentrated mud suspensions in open channel . J. Hydraulic Res , 32 ( 4 ) : 535 – 560 .
- Dafermos , C. M. 2000 . Hyperbolic conservation laws in continuum physics , Berlin : Springer .
- Di Cristo , C. and Vacca , V. 2005 . On the convective nature of roll waves instability . J. Appl. Math , 3 : 259 – 271 .
- Di Cristo , C. , Iervolino , M. , Vacca , A. and Zanuttigh , B. 2008 . Minimum channel length for roll-wave generation . J. Hydraulic Res , 46 ( 1 ) : 73 – 79 .
- Dressler , R. F. 1949 . Mathematical solution of the problem of roll waves in inclined channel flows . Commun. Pure Appl. Math , 2 ( 2–3 ) : 149 – 194 .
- Huerre , P. and Monkewitz , P. A. 1990 . Local and global instabilities in spatially developing flows . Ann. Rev. Fluid Mech , 22 : 473 – 537 .
- Hwang , S.-H. and Chang , C. 1987 . Turbulent and inertial roll waves in inclined film flow . Phys. Fluids , 30 ( 5 ) : 1259 – 1268 .
- Jeffreys , H. 1925 . The flow of water in an inclined channel of rectangular bottom . Philos. Mag. Ser. 6 , 49 : 793 – 807 .
- Jin , S. and Katsoulakis , M. A. 2000 . Hyperbolic systems with supercharacteristic relaxations and roll waves . SIAM J. Appl. Math , 61 ( 1 ) : 273 – 292 .
- Julien , P. Y. and Hartley , D. M. 1986 . Formation of roll waves in laminar sheet flow . J. Hydraulic Res , 24 ( 1 ) : 5 – 17 .
- Kapitza , P. L. and Kapitza , S. P. 1949 . Wave flow of thin viscous liquid films . Zh. Exper. i Teor. Fiz , 19 : 105 – 120 .
- Katsoulakis , M. A. and Jin , S. 2000 . Hyperbolic systems with super-characteristic relaxations and roll waves . SIAM J. Appl. Math , 61 ( 1 ) : 273 – 292 .
- Kranenburg , C. 1992 . On the evolution of roll waves . J. Fluid Mech , 245 : 249 – 261 .
- Liu , P. 1987 . Hyperbolic conservation laws with relaxation . Commun. Math. Phys , 108 ( 1 ) : 153 – 175 .
- Liu , H. and Natalini , R. 2001 . Long-time diffusive behavior of solutions to a hyperbolic relaxation system . Asymp. Anal , 25 ( 1 ) : 21 – 38 .
- Needham , D. J. and Merkin , J. H. 1984 . On roll waves down an open inclined channel . Proc. R. Soc. Lond. A , 394 ( 1807 ) : 259 – 278 .
- Ponce , V. M. and Simons , D. B. 1977 . Shallow water propagation in open channel flow . ASCE J. Hydraulics Div , 103 ( HY12 ) : 1461 – 1476 .
- Yih , S. 1963 . Stability of liquid flow down an inclined plane . Phys. Fluids , 6 : 321 – 333 .