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with fixed heat flux boundaries

**Shin-ichi Takehiro (Faculty of Science, Kyushu Univ.)
Masaki Ishiwatari (Graduate school of Earth Environmental Science, Hokkaido Univ.)
Kensuke Nakajima (Faculty of Science, Kyushu Univ.)
Yoshi-Yuki Hayashi (Graduate School of Mathematical Sciences, Univ. of Tokyo)**

## Abstract:

Two-dimensional thermal convection in a rotating cylindrical annulus under a fixed heat flux boundary condition is examined. The purpose of the system is to present a conceptual model for the problem of convection in rapidly rotating spherical shells. The annulus is heated from the inner boundary and cooled from the outer boundary. The gravity axis is directed radially and is perpendicular to the rotation axis. The top and the bottom boundaries in the direction of the rotation axis are inclined to the rotation axis to produce the topographic

beffect.The linear stability analysis with the truncation assumption at the vertical wave number one shows that the mode with the horizontal wave number

always appears as a local extremum point of the critical curve. However, the neutral curve has another minimum point atk=0k¹0in addition to the critical point at. The characteristics of thisk=0k¹0mode coincide with those obtained under the fixed temperature boundary condition in the limit of large rotation rates.Nonlinear numerical calculations show the existence of a state where convection cells with a small horizontal scale and cells with a large horizontal scale coexist. The cells with the small horizontal scale correspond to an unstable mode in the vicinity of the minimum point at

k¹0, while the cells with the large horizontal scale correspond to an unstable mode near.k=0

Received 26 January, 1998; in revised form 26 March, 1998 |

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©1998-2008 The Japan Society of Fluid Mechanics, ALL RIGHTS RESERVED.

©1998-2008 The Japan Society of Fluid Mechanics, ALL RIGHTS RESERVED.