Models of nonlinear stream aquifer transients

SummaryThe phenomenon of stream aquifer interaction was investigated via mathematical modeling using the Boussinesq equation. The effect of highly fluctuating transient stream level on the subsequent propagation of hydraulic transients in the adjacent aquifer was quantified using various solutions to the linearized and the nonlinear Boussinesq equation. The semigroup solution of the linearized equation, the spatial-partial decomposition solution of the nonlinear equation, the temporal-partial decomposition solution of the nonlinear equation, and a quasi nonlinear solution were investigated subject to a transient, large-amplitude, periodic boundary condition. The models were verified with a limited numerical solution to the nonlinear Boussinesq equation.The results indicated that the linearized model compared well with the temporal-partial solution and with a numerical solution, whereas the spatial-partial solution did not adequately reproduce the expected damping in the water table amplitude with distance. The linearized solution was sensitive to the chosen linearized transmissivity. The quasi nonlinear solution did not exhibit the natural attenuation of the head amplitude as distance increased, but could lend itself to practical applications of stream-aquifer interaction calculations subject to discrete-time irregular flood hydrographs. The temporal-partial nonlinear solution is simpler to derive than the linearized solution.