Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 1 / 16A / b

Table of contents
- Solution b

Solution

Both

sin (x - t)

and

cos (x - t)

have zero average over one period, so

⟨ u ⟩ = 0

at every fixed point.

The material derivative gives the particle acceleration

a = \frac{\partial u}{\partial t} + (u \cdot \nabla) u .

Direct differentiation yields

a_{x} = ε y sin θ + ε^{2} (1 - y^{2}) sin θ cos θ,

a_{y} = - ε cos θ + ε^{2} y cos^{2} θ .

Therefore the Eulerian time average at fixed

(x, y)

is

⟨ a ⟩ = (0, ε^{2} y /2) .

 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