Earth & climate · the experiment
Shake the slope
Heaps of grains that look identical, the same push every time, and slides that diverge near the critical angle. Four questions, from beginner to expert.
1 · Say what changes near the limit
Beginner
Near the critical angle, what does the same push do to slopes that look identical?
2 · Move closer to the critical angle
Critical angle: about 16.65 degrees. The average transport varies as 1 / (θc − θ). A slope at 14.65 degrees goes to 15.65 degrees: its distance to the critical angle is halved.
Intermediate
By how much is the average transport multiplied?
3 · Lengthen the slope
The standard deviation of transport decreases as (Lx / d)^(−1/2), where Lx is the length of the simulated slope and d the reference grain diameter, 1 mm. Imagine going from Lx / d = 100 to Lx / d = 400, at the same angle, assuming the law holds beyond the simulated sizes (30, 100 and 300).
Expert
What happens to the standard deviation?
4 · Explain where the classic model fails
The constant-friction energy balance gives Q = K0 / a, where Q is the transport, K0 the kinetic energy given by the push, and a = g(µ0 cos θ − sin θ) the energy lost per unit of transport (µ0: friction coefficient; θ: slope angle).
Expert
Why can this model alone not describe the results?
Slope shaken
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