Convection in rotating annular channels heated from below. Part 2. Transitions from steady flow to turbulence

Details Convection in rotating annular channels heated from below. Part 2. Transitions from steady flow to turbulence Convection in rotating annular channels heated from below. Part 2. Transitions from steady flow to turbulence

Jun 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006gapfd.100..215c&link_type=abstract

Geophysical and Astrophysical Fluid Dynamics, vol. 100, Issue 3, p.215-241

Physics

Fluid Dynamics

2

Rotation, Annular Channel, Nonlinear Convection

Scientific paper

We report the results of fully three-dimensional numerical simulations of nonlinear convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral no-slip or stress-free sidewalls, stress-free top and bottom, uniformly heated from below, a problem first studied by Davies-Jones and Gilman (1971) and Gilman (1973). A substantial range of the Rayleigh number R (Rc≤R≤O(100 Rc)), where Rc denotes the critical value at the onset of convection) is considered. It is found that the wall-localized convection mode, unaffected by the velocity boundary condition imposed on the sidewalls, is nonlinearly robust. Both directions of travelling waves, one propagating against the sense of rotation near the outer sidewall and the other propagating in the same sense as the rotation in the vicinity of the inner sidewall, are always present in the nonlinear solutions. In contrast to nonlinear convection in a rotating Bénard layer, neither convection rolls nor the Küpper Lortz instability can exist in a rotating annular channel because of the effect of the sidewalls. It is the nonlinear interaction between the wall-localized modes and the internal mode that plays an essential role in determining the nonlinear properties of convection in a rotating annular channel. Our studies reveal systematically the various nonlinear phenomena, from steady travelling waves trapped in the vicinities of the sidewalls to convective turbulence exhibiting columnar structure.

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