Abstracts - KTH Mechanics

Stability of a stratified tilted vortex
N.Boulanger, P.Meunier, S.Le Dizès ∗
The stability of a vortex tilted with respect to the stratification has been investigated
theoretically and experimentally.
The basic flow solution has been obtained analytically in the limit of small inclination
angles. The inviscid approximation of the solution exhibits a singularity where
N =Ω(r), with N the Brunt-Väisala frequency and Ω(r) the angular velocity profile.
This singularity can be smoothed by a viscous critical layer analysis. The solution
corresponds to strong jets and strong density variations of order O(Re 1
3 ) localized in
1 −
the critical layer of O(Re
3 )width. PIV measurements and shadowgraph visualiza-
tion have been used to validate the theory (see figure 1a).
The basic flow has been observed to be unstable. A shadowgraph picture reveals the
emergence of co-rotating structures in two distinct strips arranged symmetrically on
either side of the vortex (see figure 1b). The evolution of the azimuthal vorticity has
been obtained experimentally and show a reorganization of the vorticity from vertical
homogeneous distribution toward ponctual and regularly spaced vortices. The unstable
mode is not an helicoidal mode but instead localized on either side of the vortex
as if it was due to a Kelvin-Helmholtz instability of the shear generated in the critical
layer. This interpretation is discussed and validated by simple models.
The impact of this new and very general instability induced by tilting on mixing and
internal waves generation are also considered.
This work has been supported by the french ministry of research and is part of
the ACI ” Dynamics of cyclonic vortices ”.
∗ IRPHE, Marseille, France.
Figure 1: (a)Theoretical (solid line) and experimental (dashed line) radial profile of
axial velocity . (b)Shadowgraph visualization of the instability of a tilted vortex.
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