TY - JOUR

T1 - A generalized, non-linear, diffusion wave equation: theoretical development and application

AU - Sivapalan, M.

AU - Bates, B.C.

AU - Larsen, J.E.

PY - 1997

Y1 - 1997

N2 - The derivation of a generalized, non-linear, diffusion wave equation, which explicitly includes inertial effects, is presented. The generalized equation is an approximation to the Saint-Venant equations of order epsilon, where epsilon is a characteristic ratio of the water surface slope to the bed slope. The derivations are carried out using a general expression for how resistance, representing both friction and form drag. Some simplified forms of the generalized diffusion wave equation, useful for different practical applications, are given, A numerical finite difference model, solving a particular simplified form of the generalized equation, is used to simulate a number of observed floods in a natural river reach, The model is then used to investigate the effects of non-linearity on the characteristics of flood wave propagation. (C) 1997 Elsevier Science B.V.

AB - The derivation of a generalized, non-linear, diffusion wave equation, which explicitly includes inertial effects, is presented. The generalized equation is an approximation to the Saint-Venant equations of order epsilon, where epsilon is a characteristic ratio of the water surface slope to the bed slope. The derivations are carried out using a general expression for how resistance, representing both friction and form drag. Some simplified forms of the generalized diffusion wave equation, useful for different practical applications, are given, A numerical finite difference model, solving a particular simplified form of the generalized equation, is used to simulate a number of observed floods in a natural river reach, The model is then used to investigate the effects of non-linearity on the characteristics of flood wave propagation. (C) 1997 Elsevier Science B.V.

U2 - 10.1016/S0022-1694(96)03116-2

DO - 10.1016/S0022-1694(96)03116-2

M3 - Article

SN - 0022-1694

VL - 192

SP - 1

EP - 16

JO - Journal of Hydrology

JF - Journal of Hydrology

IS - 1-4

ER -