Mathematics of waving wheat

Here on the Yorkshire Wolds Way, we’ve walked by many fields of wheat waving in the breeze. It’s beautiful how at any given moment, twenty patches are waving left and another twenty are waving right. Back and forth, forth and back, each plant coupled to some friends nearby but uncoupled to those ten feet away.

What makes this possible is that each stem of wheat, viewed as an oscillator, is in the underdamped regime. If the damping were stronger, we’d see much less motion, with the plants bending placidly in proportion to the local wind speed. The waving back and forth reveals that the damping is subcritical.

[25 August 2019]

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