Instabilities of a columnar vortex in a stratified fluid
Seminar Room 1, Newton Institute
The stability of a columnar vortex in a stratified fluid is addressed theoretically and experimentally.
In a first part, we show that the addition of a small tilt angle between the vortex axis and the density gradient direction changes drastically the structure and stability of the vortex. For Froude numbers larger than one, a strong axial flow is created around the critical radius where the angular velocity equals the Brunt-Vaisala frequency. For large Reynolds numbers, this axial flow is sufficiently localized in the critical layer to become unstable with respect to the shear instability. Theoretical predictions for the structure of the critical layer and the instability characteristics are compared with experimental results.
In a second part, we analyse the stability of a vortex aligned along with the density gradient direction. We show that the linear modes of the vortex are weakly unstable for small Froude numbers. These modes are radiative at large radii, which means that the vortex generates internal waves spontaneously. At moderate Froude numbers, these radiative modes cease to be unstable. However, a resonance between the radiative modes and the Kelvin modes of the vortex becomes possible leading to instability in narrow wavenumber bands.