Aquifer Cutaway - 2D Cross-Section: Dupuit Water Table, Well Drawdown and River Baseflow

Setting up the lab bench...

Presets

Live readouts

Graphs

Water table: solver now (blue) against the steady closed form (orange)

Head history at well A and observation well B

Darcy flux q(x) toward the river (negative = river feeds the aquifer)

Water budget over time: river baseflow, recharge and pumping

What is happening now

Starting.

Numerical checks

running...

How to use

Pick a scenario, then drag the sliders and watch the blue water table respond. Try: (1) Over-pumping: flow reverses near the river and the river feeds the well; (2) Drought or Flood: the mound drains or recharges over years (raise the time speed); (3) press Storm for a 10 day burst of recharge and watch well B; (4) Find the sustainable pumping rate: it sets Q' to the closed-form limit that keeps the head at well A at 5 m, and the numerical checks confirm it. White arrows are Darcy seepage velocities, yellow dots are tracers; the orange dashed line is the steady closed form.

The science

Model. Water in the saturated sand-gravel obeys Darcy's law, q = −K h dh/dx (flux per metre of width, m²/d). With the Dupuit-Forchheimer assumption (horizontal flow, uniform with depth) the saturated thickness h(x,t) above a flat impermeable base is the only unknown, and mass conservation gives the Boussinesq equation:

S_y ∂h/∂t = ∂/∂x ( K h ∂h/∂x ) + R − Q' δ(x − x_w)

No flow at the divide (x = 0), fixed head h = h_r at the river (x = L = 1000 m). It is solved with backward-Euler finite differences (dx = 5 m, 3 Picard passes for the K·h nonlinearity), so any time step is stable.

Steady state, closed form. Integrating once:

h(x)² = h_r² + (R/K)(L² − x²) − (2Q'/K)(L − max(x, x_w))

The page checks the solver equilibrium against this formula for four pumping rates, the mass balance (recharge − pumping = river baseflow) and the divide head sqrt(h_r² + R L²/K). Sustainable pumping: setting the head at the well to h_min gives Q'_max = K [h_r² + (R/K)(L² − x_w²) − h_min²] / (2 (L − x_w)), verified against the solver.

Tracers drift with the seepage velocity u = q / (S_y h) at a fixed fraction of the local saturated thickness: a schematic of where water goes, not measured pathlines.

Honest simplifications. A 1-D section: the pumping "well" is a line of wells across the width (a gallery); a single well would add a logarithmic Thiem cone. Homogeneous isotropic aquifer, flat base, no unsaturated-zone delay (recharge arrives instantly), constant S_y, no evapotranspiration, a fully penetrating river without bed clogging. Dupuit is inaccurate within about one aquifer thickness of the river and the well. The water table is capped at 38 m (the aquifer top); the excess leaves as surface runoff. The picture exaggerates the vertical scale about 8 times. K ranges are typical textbook values (gravel 10-1000, clean sand 1-50, silt 0.01-1 m/d); recharge values and well positions are illustrative.