MY SIMULATOR

Beaver Dam Close-Up

How fast a pond fills, how much a stick-and-mud dam leaks, and what mud plastering changes.

INTERACTIVE 3D

Time 0:00Depth 0 mOutflow 0 m³/sFPS 0

STORED WATER0 m³

LEAK SHARE0 %

MUD SEAL0 %

TIME☀🌙

Beaver Dam Close-Up: Leaky Weir, Seepage, Mud Sealing & Pond Fill-Up

One stick-and-mud dam, seen up close. Water fills the pond behind it, seeps through the sticks (Darcy), spills over the crest (weir) and is lost to the air and the ground. Beavers raise the crest and plaster the leaks with mud — change the numbers and watch the pond respond.

Water supply

Time speed

Preset

Stream, dam and beavers

Live numbers

Inflow (dashed) and outflow below the dam, m³/s

Pond depth at the dam, m (crest in gold)

Seepage and spill, m³/s

Missions

Independent numerical checks

Also run outside the browser: node src/check.js (mass balance, steady state vs bisection, fill time vs closed form, stage-storage vs numeric surface integral, Dupuit vs Darcy-flux integration, mud-seal exponential, weir value).

Educational model, not a dam-safety or flood tool. One lumped pond, a trapezoid valley, uniform dam body, no breach mechanics. Constants marked [assumption] are illustrative. Animals are drawn a little large.

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Hero, Pond, Section and Map buttons (keys H, P, S, T) jump the camera.
The TIME slider scrubs the whole run (precomputed, exact in both directions); Start plays it.
Sliders re-run the model at once. The crest slider raises or lowers the real 3D dam; the dam's mud darkens as the seal grows.
Keys: Space play/pause, R reset.

The science

Pond storage. The valley has a flat 5 m channel, floodplain sides 1:6 and bed slope S₀ = 0.02. A pond of depth h at the dam holds V = w₀h²/(2S₀) + z_sh³/(3S₀) and has surface area dV/dh; the pond reaches h/S₀ metres upstream. Balance: dV/dt = Q_in − Q_seep − Q_weir − (E + f)A(h) (Heun, 5 s step).

Seepage (Darcy). Water creeps through the porous sticks: flux q = −K h dh/dx. For a body of thickness T = 2 m, width W = 18 m and tailwater depth h_T = 0.2 m, integrating gives the Dupuit formula Q = K W (h² − h_T²) / 2T, reduced by the mud-seal fraction s: (1 − s). K = 0.02 m/s is a made-up round number [assumption]; real brush dams vary by orders of magnitude, and at higher speeds the flow is turbulent (not Darcy) — not modelled.

Weir. Over the crest the water behaves as a broad-crested weir, Q = C_w W e^3/2, C_w = 1.6 [textbook 1.5–1.7], e = h − crest. Seepage plus spill always settle at the level where inflow equals total outflow; the page's check solves this independently by bisection.

Beaver upkeep. Beavers are reported to work on a dam when they hear running water, so in the model crest raising (cm/day, up to 1.7 m) and mud plastering (ds/dt = r(0.92 − s), a dam never becomes fully tight) only run while the outflow exceeds 2 L/s. The rates are sliders, not measurements.

Fish passage. The page counts the hours when water spills and the pond sits no more than 0.6 m above the plunge pool; 0.6 m as a trout leap limit is an illustrative [assumption] — real leaping depends on species, pool depth and flow.

Honest limits. No sediment, no breach, no turbulence in the dam body, no ice, no groundwater feedback, a fixed 200 m valley. Evaporation and infiltration are flat rates per day. The flood is a smooth gamma-shaped pulse, not a gauged hydrograph.