event
Thursday 08 Dec 2011: Maths seminar - Radiative instability of a vortex in a stratified fluid
Xavier Riedinger - University of Exeter
Harrison 203 15:00-16:00
Vortices are widely present in geophysical flows at all scales. They are involved in the dynamics
of flows as well as in their statistical properties. In order to identify precisely their role in the global
properties of the flow it is important to know their individual dynamics as finely as possible.
With this purpose, we study through theoretical, numerical and experimental means,
the stability properties of models of stratified vortices : The Lamb-Oseen vortex and a family of Taylor-
Couette flows. We show, in particular, that these flows, stable in a homogeneous
fluid, can become unstable in the presence of a stable stratification along their rotation axis. The two
kinds of flows are subject to the same form of destabilisation, the radiative instability of which we describe
the mechanism. For the Lamb-Oseen vortex, a comprehensive numerical study is performed by varying
the Reynolds number and the Froude number which characterize the viscosity and the buoyancy of the
fluid. For low Reynolds numbers, we show that the most unstable mode leads to an undulation of the
vortex that we have obtained successfully in the experiments.
For the Taylor-Couette flow generated by the rotation of a cylinder, the most unstable mode is also
helical but it exhibits a more pronounced radiative structure. We also succeeded in obtaining this mode
experimentally. The frequency and wavelength of the mode have been measured using shadowgraphy and
the synthetic schlieren technique, and a very good agreement with the numerics has been demonstrated.
