Title:

The flow between two coaxial cones

This thesis provides a study of the flow between two coaxial cones, a geometry with many
interesting features and of practical importance. We consider the flow for different driving
mechanisms and start by studying the highly viscous flow when the fluid is driven by
rotation of the cones or a spherical lid. The solution is found through a low Reynolds
number e)...pansion expressed as a combination of forced modes and geometric eigenmodes.
The latter may cause an infinite sequence of counterrotating vortices at the apex of the
cones, we study the flow topology for a wide range of parameter values and specify when
an infinite sequence of eddies occurs. We also cons.ider the nonaxisymmetric Stokes flow
where each wave number m gives rise to infinitely many eigeninodes. We map the spectra
for different wave numbers and study the relative dominance between the eigenmodes. In
contrast to the axisymmetric flow and the flow in one cone, no infinite sequence of eddies
occur except in special cases. The solutions to the Stokes equations can be expressed as
a symmetric and antisymmetric part and we consider the response from a moving nonrigid
lid, where the .flow exhibits a transition from a flow with closed streamlines to what
appears to be a completely chaotic flow.
in the second part we consider the flow which results from a point sink situated at
the apex of the cones. The problem is reminiscent of the classical JefferyHamel flow.
We study the flow in the Stokes limit and find that the similarity solution experiences
a breakdown for certain cone openings. For a general Reynolds number the governing
equations do not admit separable solutions so we consider asymptotic expansions of the
flow in a narrow gap limit. In the far field the viscous forces dominate and the flow
assumes a parabolic profile, the influence of inertia increases as we move downstream and
by computing solutions of a PDE we find the resulting boundary layer flow. In the final
chapter we consider the same flow for a slightly different cone geometry where there is a
constant gap between the cones. We compare the solutions between the two geometries
and discuss their qualitative differences.
