course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Fluid Dynamics |
IB |
22 |
|
Paper 4, Section II, C |
2016 |
(a) Show that for an incompressible fluid,
(b) State the equation of motion for an inviscid flow of constant density in a rotating frame subject to gravity. Show that, on Earth, the local vertical component of the centrifugal force is small compared to gravity. Present a scaling argument to justify the linearisation of the Euler equations for sufficiently large rotation rates, and hence deduce the linearised version of the Euler equations in a rapidly rotating frame.
(c) Denoting the rotation rate of the frame as
(d) Assume that there exist solutions of the form