Eye formation in rotating convection

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.

Formation of eyes in large-scale cyclonic vortices

“…The geometry is inspired by that of tropical cyclones and the global flow pattern consists of a shallow, swirling vortex combined with a poloidal flow in the r − z plane which is predominantly inward near the bottom boundary and outward along the upper surface. Our numerical experiments confirm that, as suggested by [1], an eye forms at the centre of the vortex which is reminiscent of that seen in a tropical cyclone and is characterised by a local reversal in the direction of the poloidal flow. We establish scaling laws for the flow and map out the conditions under which an eye will, or will not, form.…”

“…Our model problem is the same as that in [1]. It consists of the steady, laminar flow of a Boussinesq fluid in a closed, rotating cylinder of height H and radius R, with aspect ratio ε = H/R 1.…”

“…Recently, however, Oruba et al [1], (hereafter denoted ODD17) identified one mechanism of eye formation in the context of a simple model problem. Inspired by the geometry of tropical cyclones, they considered convection in a shallow, rotating, cylindrical domain of low aspect ratio.…”

On the inertial wave activity during spin-down in a rapidly rotating penny shaped cylinder: a reduced model

“…Harlow & Stein 1974;Chen et al 2015). The benefits of modelling such objects by isolated structures is well established (see Persing et al 2015;Oruba, Davidson & Dormy 2017Atkinson, Davidson & Perry 2019, and references therein). For those applications the aspect ratio ought to be large, and so our previous choice = 1 is clearly not the most appropriate.…”

Dynamics of a trapped vortex in rotating convection

“…One omission in much of the work of Harlow and Stein [12], Rotunno [13], and the model of Pearce [11] is the presence of a no-slip lower boundary. This is discussed in a recent paper by Oruba et al [18]. They present a purely hydrodynamical explanation for the formation of eyes in atmospheric vortices.…”