Wheat field in wind — 2D stalk and gust-wave lab

Switch to 3D
Controls
Live readouts
Numerical checks
What to try
  1. Press "Breezy afternoon": waves of lean roll across the field in the direction of the wind, slightly slower than the mean wind.
  2. Press "Stiff stalks": the same wind leans them much less because the lean scales as U² / f².
  3. Press "Uncoupled" and compare: neighbour contact smooths the pattern.
  4. Look at the green curve: doubling the wind speed roughly quadruples the steady lean (until the stalk is far from vertical).
The science

Each stalk is a rigid rod of height L hinged at the ground by a bending spring. The lean angle θ obeys a damped, driven oscillator with quadratic aerodynamic drag:

θ̈ + 2ζω0 θ̇ + ω0² θ = Cw Un|Un| + kc(θi−1 − 2θi + θi+1) Un = U cosθ − (L/2) θ̇,   Cw = ½ ρ Cd d L (L/2) / I ≈ 0.9 m¹,   steady lean: ω0² θ ≈ Cw U² (small angles)

The wind field is the mean U0 plus a pair of travelling sinusoidal gusts moving at cg U0; the aerodynamic term also gives the stalk extra damping through the (L/2)θ̇ part of Un. Checks: free-decay period vs the damped-oscillator formula, the relaxed lean vs the torque-balance root, and the gust travel time between two stalks.

Simplifications: rigid rod with a linear bending spring (a real stalk bends and its stiffness changes with height), constant drag coefficient, no lodging, no vertical wind shear, a 1-D row not a 2-D field; the gust pattern is prescribed, not turbulence.