The formation of river channels

SIAM Journal on Applied Mathematics

Volumn 67, Issue 4, 2007, Pages 1016-1040

  Fowler, A C ^a   Kopteva, Natalia ^b   Oakley, Charles ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF LIMERICK   (Ireland)

Author keywords

Channel formation; Mathematical geomorphology; Nonlinear diffusion; River networks

Indexed keywords

GEOMORPHOLOGY; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; TOPOGRAPHY;

CHANNEL FORMATION; MATHEMATICAL GEOMORPHOLOGY; NONLINEAR DIFFUSION; RIVER NETWORKS;

FLUID DYNAMICS;

EID: 34548214095     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050629264     Document Type: Article

References (21)

1. B. BIRNIR, T. R. SMITH, AND G. E. MERCHANT (2001), The scaling of fluvial landscapes, Comput. Geosci., 27, pp. 1189-1216.
2. G. F. CARRIER, M. KROOK, AND C. E. PEARSON (1966), Functions of a Complex Variable, McGraw-Hill, New York.
3. A. D. HOWARD (1994), A detachment-limited model of drainage basin evolution, Water Resour. Res., 30, pp. 2261-2285.
4. N. IZUMI AND G. PARKER (1995), Inception and channelization and drainage basin formation: Upstream-driven theory, J. Fluid Mech., 283, pp. 341-363.
5. N. IZUMI AND G. PARKER (2000), Linear stability analysis of channel inception: Downstream-driven theory, J. Fluid Mech., 419, pp. 239-262.
6. N. V. KOPTEVA (1996), On the convergence, uniform with respect to a small parameter, of a four-point scheme for a one-dimensional stationary convection-diffusion equation, Differ. Uravn., 32, pp. 951-957 (in Russian); Differential Equations, 32 (1997), pp. 958-964 (in English).
7. S. KRAMER AND M. MARDER (1992), Evolution of river networks, Phys. Rev. Lett., 68, pp. 205-208.
8. S. LOEWENHERZ (1991), Stability and the initiation of channelized surface drainage: A reassessment of the short wavelength limit, J. Geophys. Res., 96, pp. 8453-8464.
9. S. LOEWENHERZ-LAWRENCE (1994), Hydrodynamic description for advective sediment transport processes and rill initiation, Water Resour. Res., 30, pp. 3203-3212.
10. E. MEYER-PETER AND R. MÜLLER (1948), Formulas for bed-load transport, in Proceedings of the International Association for Hydraulic Structures Research, 3rd Annual Conference, Stockholm, Sweden, pp. 39-64.
11. G. PARKER (1978), Self-formed straight rivers with equilibrium banks and mobile bed. Part 1. The sand-silt river, J. Fluid Mech., 89, pp. 109-125.
12. A. A. SAMARSKII, V. A. GALAKTIONOV, S. P. KURDYUMOV, AND A. P. MIKHAILOV (1995), Blow-Up in Quasilinear Parabolic Equations, de Gruyter Exp. Math. 19, de Gruyter, Berlin.
13. R. SLINGERLAND, J. W. HARBAUGH, AND K. P. FURLONG (1994), Simulating Clastic Sedimentary Basins: Physical Fundamentals and Computer Programs for Creating Dynamic Systems, Prentice-Hall, Englewood Cliffs, NJ.
14. T. R. SMITH AND F. P. BRETHERTON (1972), Stability and the conservation of mass in drainage basin evolution, Water Resour. Res., 8, pp. 1506-1529.
15. T. R. SMITH, B. BIRNIR, AND G. E. MERCHANT (1997a), Towards an elementary theory of drainage basin evolution: I. The theoretical basis, Comput. Geosci., 23, pp. 811-822.
16. T. R. SMITH, B. BIRNIR, AND G. E. MERCHANT (1997b), Towards an elementary theory of drainage basin evolution: II. A computational evaluation, Comput. Geosci., 23, pp. 823-849.
17. T. R. SMITH, G. E. MERCHANT, AND B. BIRNIR (2000), Transient attractors: Towards a theory of the graded stream for alluvial and bedrock channels, Comput. Geosci., 26, pp. 541-580.
18. K. STEWARTSON AND J. T. STUART (1971), A non-linear instability theory for a wave system in plane Poiseuille flow, J. Fluid Mech., 48, pp. 529-545.
19. G. E. TUCKER AND R. L. SLINGERLAND (1994), Erosional dynamics, flexural isostasy, and long-lived escarpments: A numerical modeling study, 3. Geophys. Res., 99, pp. 12229-12243.
20. E. W. WELSH, B. BIRNIR, AND A. L. BERTOZZI (2006), Shocks in the evolution of an eroding channel, Appl. Math. Res. Express, 71638.
21. G. WILLGOOSE, R. L. BRAS, AND I. RODRÍGUEZ- ITURBE (1991), A coupled channel network growth and hillslope evolution model: I. Theory, Water Resour. Res., 27, pp. 1671-1684.