Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 331 / 3 / c

Table of contents
- Solution c

Solution

Let

D = \partial_{t} + z \partial_{x}

. Retaining terms linear in the primed fields gives

Ro (D u^{'} + Ro w^{'}) - v^{'} = - p_{x}^{'},

Ro D v^{'} + u^{'} = - p_{y}^{'},

Ro^{2} D w^{'} = - p_{z}^{'} + B θ^{'},

D θ^{'} + w^{'} - \frac{1}{B} v^{'} = 0, u_{x}^{'} + v_{y}^{'} + Ro w_{z}^{'} = 0 .

The terms

Ro^{2} w^{'}

and

- v^{'} / B

respectively arise from perturbation advection of the velocity and temperature gradients in the basic state.

 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