23 research outputs found
Formation of eyes in large-scale cyclonic vortices
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 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 Oruba et al 2017, 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. We show that, to leading order, the velocity
scales with V=(\alpha g \beta)^{1/2}H, where g is gravity, \alpha the expansion
coefficient, \beta 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/\nu and Ro=V/\Omega H, where \Omega is the background rotation
rate and \nu 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 Ekman number.Comment: 18 pages, 14 figures, 1 tabl
B{\'e}nard convection in a slowly rotating penny shaped cylinder subject to constant heat flux boundary conditions
We consider axisymmetric Boussinesq convection in a shallow cylinder radius,
L, and depth, H (<< L), which rotates with angular velocity about its
axis of symmetry aligned to the vertical. Constant heat flux boundary
conditions, top and bottom, are adopted, for which the onset of instability
occurs on a long horizontal length scale provided that is sufficiently
small. We investigate the nonlinear development by well-established two-scale
asymptotic expansion methods. Comparisons of the results with the direct
numerical simulations (DNS) of the primitive governing equations are good at
sufficiently large Prandtl number, . As is reduced, the finite
amplitude range of applicability of the asymptotics reduces in concert. Though
the large meridional convective cell, predicted by the DNS, is approximated
adequately by the asymptotics, the azimuthal flow fails almost
catastrophically, because of significant angular momentum transport at small
, exacerbated by the cylindrical geometry. To appraise the situation,
we propose hybrid methods that build on the meridional streamfunction
derived from the asymptotics. With given, we solve the now linear
azimuthal equation of motion for the azimuthal velocity v by DNS. Our
''hybrid'' methods enable us to explain features of the flow at large Rayleigh
number, found previously by Oruba, Davidson \& Dormy (J. Fluid Mech.,vol. 812,
2017, pp. 890-904)
Eye formation in rotating convection
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.The authors are grateful to the ENS for support. The simulations were performed using HPC resources from GENCI-IDRIS (grants 2015-100584 and 2016-100610)
Eye formation in rotating convection
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
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 r-z 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, J. Fluid Mech. 812, 890 (2017)JFLSA70022-112010.1017/jfm.2016.846], 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