Can a floating log move downstream faster than the river's maximum current speed?

Settled by Standard open-channel flow theory.

Kapitza's problem #61 asks whether a floating body can exceed the river's maximum flow rate. This is a standard exercise in open-channel hydraulics: the water's velocity profile varies with depth and lateral position (fastest typically at the center of the channel near the surface), a floating body samples some average of the local velocity field depending on its size and draft, and under normal passive-floating conditions cannot exceed the true local maximum surface velocity, though real complications like wind-driven surface drift and Stokes drift from waves can push measured object speeds above the mean current. The problem is a fully solved application of classical fluid velocity-profile theory.

A question that sounds like it might hide a paradox turns out to reduce cleanly to reading a velocity profile correctly, and the 'gotcha' is entirely in careful bookkeeping of what 'the current' means.

Explanations that circulated

• A passive floating object can never move faster than the river's fastest water, since it is 'just carried along' (a purely passive point-like surface float indeed cannot exceed the local surface current, but a body with finite size/draft samples a depth-averaged velocity, and other effects such as wind or wave-induced Stokes drift can add to the surface current, so naive 'it just matches the flow' reasoning needs qualification)

References

• Open-channel flow velocity profiles (standard hydraulics), Standard fluid mechanics / hydraulics literature, Textbook treatment, 2020