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• W3150592194 abstract "Two-dimensional thermal convection in the presence of a strong oblique magnetic eld is studied using an asymptotic expansion in inverse powers of the Chandrasekhar number. The linear stability problem reveals the existence of two distinct scales in the vertical structure of the critical eigenfunctions: a small length-scale whose vertical wavenumber kz is comparable with the large horizontal wavenumber k? selected at onset, and a large-scale modulation which forms an envelope on the order of the layer depth d. The small-scale structure in the vertical results from magnetic alignment that forces fluid motions to be (nearly) parallel to the eld lines. For convective transport in the vertical this constraint must be relaxed. This is achieved by molecular dissipation which allows weak upward (downward) motions of hot (cold) fluid elements across the eld lines and results in a large-scale vertical modulation of the magnetic columns. Using the scaling suggested by the linear theory, strongly nonlinear steady and overstable solutions are constructed. These are characterized by large departures of the mean temperature prole from the conduction prole. For overstable rolls two modes of convection are uncovered. The rst ‘vertical eld’ mode is characterized by thin thermal boundary layers and a Nusselt number that increases rapidly with the applied Rayleigh number; this mode is typical of steady convection as well. The second or ‘horizontal eld’ mode is present in overstable convection only and has broad thermal boundary layers and a Nusselt number that remains small and approximately independent of the Rayleigh number. At large Rayleigh numbers this regime is characterized by a piecewise linear temperature prole with a small isothermal core. The ‘horizontal eld’ mode is favoured for substantial inclinations of the eld and suciently small ohmic diusivity. The transition between the two regimes is typically hysteretic and for xed inclination and diusivity may occur with increasing Rayleigh number. Similar but highly asymmetric states are obtained for depth-dependent , where is the ratio of ohmic to thermal diusivity. These results are obtained from a nonlinear eigenvalue problem for the Nusselt number and mean temperature prole, and suggest a possible explanation for the sharp boundary between the umbra and penumbra in sunspots." @default.
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• W3150592194 date "2000-01-01" @default.
• W3150592194 modified "2023-09-27" @default.
• W3150592194 title "Nonlinear magnetoconvection in the presence of strong oblique elds" @default.
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