Nicolas Boulanger

Tilt-induced instability of a stratified vortex

This experimental and theoretical study considers the dynamics and the instability of a Lamb-Oseen vortex in a stably stratified fluid. In a companion paper, it was shown that tilting the vortex axis with respect to the direction of stratification induces the formation of a rim of strong axial flow near a critical radius when the Froude number of the vortex is larger than one. Here, we demonstrate that this tilt-induced flow is responsible for a three-dimensional instability. We show that the instability results from a shear instability of the basic axial flow in the critical-layer region. The theoretical predictions for the wavelength and the growth rate obtained by a local stability analysis of the theoretical critical-layer profile are compared to experimental measurements and a good agreement is observed. The late stages of the instability are also analysed experimentally. In particular, we show that the tilt-induced instability does not lead to the destruction of the vortex, but to a sudden decrease of its Froude number, through the turbulent diffusion of its core size, when the initial Froude number is close to 1. A movie is available with the online version of the paper.

Structure of a stratified tilted vortex

The structure of a columnar vortex in a stably stratified fluid is studied experimentally and theoretically when the vortex axis is slightly tilted with respect to the direction of stratification. When the Froude number of the vortex is larger than 1, we show that tilting induces strong density variations and an intense axial flow in a rim around the vortex. We demonstrate that these characteristics can be associated with a critical-point singularity of the correction of azimuthal wavenumber m = 1 generated by tilting where the angular velocity of the vortex equals the Brunt–Vaisala frequency of the stratified fluid. The theoretical structure obtained by smoothing this singularity using viscous effects (in a viscous critical-layer analysis) is compared to particle image velocimetry measurements of the axial velocity field and visualizations of the density field and a good agreement is demonstrated.

Instabilities of a columnar vortex in a stratified fluid

In this paper, we show that the presence of a vertical density gradient can destabilise a Gaussian vortex in two different ways. First, when the vortex axis is slightly tilted with respect to the vertical and if its Froude number is larger than one, the vortex exhibits strong axial flows inside a critical layer, which lead to a violent three-dimensional instability. Second, when the vortex axis is vertical, the vortex is weakly unstable by emission of internal gravity waves. Theoretical predictions for both instabilities are compared with experimental evidences.