The rule: the “devoir maison” is a personal exercise aimed at helping the assimilation of the subject that you study. Each student returns his/her own manuscript copy of the work.
science
Description
The rule: the “devoir maison” is a personal exercise aimed at helping the assimilation of the subject that you study. Each student returns his/her own manuscript copy of the work. Of course you can talk to each other, read books, etc. but answers must always be personal and argued
This problem considers the stability of a fluid layer staying between two horizontal plates
that are maintained at two different temperatures: Tb for the bottom plate and Tt for the
top plate. The fluid is viscous and diffuses heat. It is bathed by a uniform gravity ~g = −g~ez.
The whole system rotates about the z-axis at an angular velocity Ω~ez. We shall study the
conditions by which rotation influences the rise of thermal convection using Boussinesq’s
approximation. Of course it is useful to study chapter 2 of the notes before.
1. Briefly recall what is the Boussinesq approximation and what are the conditions of its use.
2. In the following we shall neglect the centrifugal acceleration. Give the conditions by which this approximation is acceptable.
3. The thickness of the layer is d, the heat diffusivity of the fluid is κ and the kinematic
viscosity is ν. We use d
2/κ as the time scale and d as the length scale. We also assume
that density fluctuations δρ are related to temperature fluctuations δT by:
