Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 329 / 3 / d

Table of contents
- Solution d

Solution

The dimensionless equation is

H^{3} H^{'''} = 1 - H^{3}

. At a crest,

H ≫ 1

, so

H^{'''} \sim - 1.

The imposed far-field flux is negligible there; the dominant physical balance is between local gravity-driven drainage and the capillary-pressure gradient.

At a trough,

H ≪ 1

, so

H^{3} H^{'''} \sim 1.

Local gravity-driven flux is negligible; the capillary-pressure gradient drives the fixed flux through the trough against viscous resistance. These alternating balances generate the strongly nonlinear capillary waves.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version