Eye Formation in Rotating Convection

TL;DR

This paper investigates the formation of an eye in rotating convection within a cylindrical domain, revealing that an eyewall of intense vorticity forms near the axis, driven by boundary layer vorticity and high Reynolds number conditions.

Contribution

It demonstrates that eye formation results from boundary layer vorticity being advected upward, independent of buoyancy and Coriolis forces, in steady axisymmetric Boussinesq flows.

Findings

Eye forms as a passive response to eyewall development.

Vorticity in the eyewall originates from the lower boundary layer.

High Reynolds number is necessary for vorticity advection to dominate diffusion.

Abstract

We consider rotating convection in a shallow, cylindrical domain. We examine the conditions under which the resulting vortex develops an eye at its core; that is, a region where the poloidal flow reverses and the angular momentum is low. For simplicity, we restrict ourselves to steady, axisymmetric flows in a Boussinesq fluid. Our numerical experiments show that, in such systems, an eye forms as a passive response to the development of a so-called eyewall, a conical annulus of intense, negative azimuthal vorticity that can form near the axis and separates the eye from the primary vortex. We also observe that the vorticity in the eyewall comes from the lower boundary layer, and relies on the fact the poloidal flow strips negative vorticity out of the boundary layer and carries it up into the fluid above as it turns upward near the axis. This process is effective only if the Reynolds number is sufficiently high for the advection of vorticity to dominate over diffusion. Finally we observe that, in the vicinity of the eye and the eyewall, the buoyancy and Coriolis forces are negligible, and so although these forces are crucial to driving and shaping the primary vortex, they play no direct role in eye formation in a Boussinesq fluid.