Parabolic Hilltops

Why are hilltops round? More specifically, why are they parabolic?

Learning Goals

• Rounded hililtops are the rule in nature.
• Derive how this is consistent with hillslope diffusion.
• Gain intuition for how hills steepen with higher river incision rates and lower diffusivity (erodibility).
• Gain practice in separating variables to solve differential equations.

Videos

Pictoral and descriptive introduction

Parabolic hilltop derivation

Notes

PDF of the parabolic hilltop derivation from the above video

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