Presets and playback
Presets
River
Bird
Foraging
Layers
Model checks
The science
Why a bird can walk on a river bed
A dipper's plumage traps air, so the bird is buoyant: net upward force Fb = (ρw/ρb − 1) m g. To stay on the bed it must press down and grip. Angling the wings makes the current itself push the bird down: Fw = ½ ρw CL Aw u2. The normal force is N = Fw − Fb, claws give friction μN, and the body feels drag Fd = ½ ρw Cd A u2.
Passive hold speed
Both forces grow as u2. The friction margin is X = μFb − ½ρ(μCLAw − CdA)u2. If μCLAw > CdA the current pushes the bird onto the bed hard enough above uhold = √[μFb / (½ρ(μCLAw − CdA))] and no effort is needed; below it the bird must supply thrust (and downward force) from its own muscles, which costs oxygen. With flat wings the bird is never held. The page confirms uhold by time-stepping a bird that slides along the bed.
Flow near the bed
The speed profile is the logarithmic law u(z) = (u*/κ) ln(z/z0) with roughness z0 = 4 mm and u* set so that the depth mean equals the slider value, i.e. u* = κU / (ln(D/z0) − 1). Near the bed (4 cm) the water is much slower than the mean, which is why the bird forages there.
Dive time and oxygen
Prey eaten in a dive follows a depleting patch g(t) = nτ(1 − e−t/τ). Charnov's marginal value theorem picks the dive length that maximises g(t)/(t + Ts(t)), i.e. where the slope of the gain curve equals the average rate. The dive cannot exceed the aerobic limit ADL = (oxygen store) / (metabolic rate), where the metabolic power is a base value plus the muscle work to hold position (thrust X u and any needed downward force) divided by efficiency η = 0.2, converted with 20.1 J per mL O2.
Honest simplifications
Coefficients (Cd = 0.55, lift slope, μ = 0.6, efficiency 0.2) are plausible round numbers, not measurements of a particular species; the bird is a point-like body in steady flow with no turbulence, no buoyancy change with depth and no real prey population dynamics. It illustrates the physics of the strategy, not field data.
What to try
Compare Calm pool and Fast spate: in the spate the current presses the bird to the bed (passive hold, lower oxygen cost); in the pool it must work to stay down. Choose Flat wings: with no downforce the bird is never held passively. In Rich prey patch dives get shorter, in Poor patch longer, until the oxygen limit takes over.