• Featured in Physics

Formation of eyes in large-scale cyclonic vortices

L. Oruba, P. A. Davidson, and E. Dormy
Phys. Rev. Fluids 3, 013502 – Published 12 January 2018
Physics logo See Synopsis: Eyeing the Storm

Abstract

We present numerical simulations of steady, laminar, axisymmetric convection of a Boussinesq fluid in a shallow, rotating, cylindrical domain. The flow is driven by an imposed vertical heat flux and shaped by the background rotation of the domain. 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 rz plane which is predominantly inward near the bottom boundary and outward along the upper surface. Our numerical experiments confirm that, as suggested in our recent work [L. Oruba et al., J. Fluid Mech. 812, 890 (2017)], an eye forms at the center of the vortex which is reminiscent of that seen in a tropical cyclone and is characterized 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. We show that, to leading order, the velocity scales with V=(αgβ)1/2H, where g is gravity, α is the expansion coefficient, β is the background temperature gradient, and H is the depth of the domain. We also show that the two most important parameters controlling the flow are Re=VH/ν and Ro=V/(ΩH), where Ω is the background rotation rate and ν the viscosity. The Prandtl number and aspect ratio also play an important, if secondary, role. Finally, and most importantly, we establish the criteria required for eye formation. These consist of a lower bound on Re, upper and lower bounds on Ro, and an upper bound on the Ekman number.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
7 More
  • Received 26 August 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.013502

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Synopsis

Key Image

Eyeing the Storm

Published 12 January 2018

Numerical simulations of a hurricane-like system have determined the conditions necessary for the formation of a calm “eye” in the center of the storm.

See more in Physics

Authors & Affiliations

L. Oruba*

  • Physics Department, Ecole Normale Supérieure, 24 Rue Lhomond, 75005 Paris, France

P. A. Davidson

  • Engineering Department, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom

E. Dormy

  • Department of Mathematics and Applications, CNRS UMR No. 8553, Ecole Normale Supérieure, 45 Rue d'Ulm, 75005 Paris, France

  • *Present address: LATMOS, IPSL, UPMC, CNRS, Paris, France.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 3, Iss. 1 — January 2018

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Fluids

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×