Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 333 / 3 / i

Table of contents
- Solution i

Solution

At the displaced free surface, constant atmospheric pressure and the hydrostatic approximation give the dynamic condition

η = \frac{f _{0}}{g} ψ at z = 0.

The linearized kinematic condition is

w = D_{g} η / D t

. Combining these relations with

w = - \frac{D _{g}}{D t} (\frac{f _{0} ψ _{z}}{N ^{2}})

gives

\frac{D _{g} ψ _{z}}{D t} + \frac{N ^{2}}{g} \frac{D _{g} ψ}{D t} = 0 at z = 0.

 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