Iman Toghraei - LadHyX - Dynamics of a vortex in stratified-rotating fluids under the complete Coriolis force

The traditional approximation of the Coriolis force is widely used to study the effects of the planetary rotation on geophysical flows. In this approximation, only the vertical component of the planetary rotation vector at a given latitude is considered, while the horizontal component is ignored. Yet, the Coriolis force associated with the horizontal component of the planetary rotation may have notable effects under some circumstances [1]. In this context, we have studied numerically and analytically the dynamics of a single vertical vortex in a stratified-rotating fluid under the complete Coriolis force [2].

We will see that the Coriolis force due to the horizontal component of the planetary rotation generates a critical layer when the Froude number is larger than one. As a result, an intense vertical velocity field and a vertical vorticity anomaly are created in the vicinity of the critical layer. I will show that these flows can then lead to two types of instability: a two-dimensional instability triggered by the shear of the vertical vorticity anomaly and a three-dimensional instability due to the shear of the vertical velocity field. It is surprising that these instabilities can occur despite a small horizontal rotation component when the Reynolds number is large. It is therefore conceivable that the horizontal component of the planetary rotation could have a much larger impact on geophysical vortices than one might think based only on its magnitude.

References:

[1] Gerkema, T., Zimmerman, J.T.F., Maas, L.R.M. & Van Haren, H. 2008 Geophysical and astrophysical fluid dynamics beyond the traditional approximation. Rev. Geophys. 46 (2), RG2004.

[2] Toghraei, I & Billant, P 2022 Dynamics of a stratified vortex under the complete Coriolis force: two-dimensional three-components evolution. J. Fluid Mech. 950, A29.