Undergraduate Honors Theses

Thesis Defended

Spring 2019

Document Type

Thesis

Type of Thesis

Departmental Honors

Department

Physics

First Advisor

Michael Andrew Calkins

Abstract

A numerical study of magnetoconvection with a horizontal magnetic field in a plane layer geometry is conducted. Novel dynamical regimes are observed beyond those occurring in classical (i.e non-magnetic) Rayleigh-Bénard convection. Imposed magnetic field strengths up to Chandrasekhar numbers of Q = 106 are investigated. The most unstable flow configuration is two-dimensional rolls oriented parallel to the direction of the imposed magnetic field in which the induced magnetic field is identically zero. The convective roll structure exhibits a preferential flow alignment along the direction of the imposed magnetic field thereby sustaining an anisotropic flow field. Deviations away from the convective roll structure induce a magnetic field separate from the externally-imposed magnetic field. For weak magnetic field strengths (Q = 102), we observe the Nu ∼ Ra2/7 scaling law, where Nu is the Nusselt number, though the overall heat transfer is less than that observed in non-magnetic Rayleigh-Bénard convection; we hypothesize this reduction is due to the presence of ohmic dissipation. For Q = 104 and 106 we find that the two-dimensional convective roll structure is maintained for Ra values orders of magnitude larger than the critical Rayleigh number. In this flow regime our calculations suggest a Nu ∼ Ra0.37 power law. Two-dimensional turbulence is not observed in any of the imposed magnetic field regimes, rather we observe turbulent flow behavior when the flow becomes three-dimensional. For Q = 104 we observe the development of large-scale modulations along the direction of the magnetic field when Ra ≥ 6×105. For Q = 104 and 6×105 ≤Ra ≤ 107 the Nu ∼ Ra2/7 power law is observed.

In general, for sufficiently strong magnetic fields, we find three primary regimes: (1) laminar, 2D convection with a heat transfer scaling that exceeds Nu ∼ Ra1/3; (2) a transitional region where 3D modulations begin and the heat transfer scaling law is reduced; and (3) anisotropic 3D convection with Nu ∼ Ra2/7 but with an overall heat transfer that is always less than the hydrodynamic case.

A fourth regime at very high Rayleigh numbers, in which the convection is no longer influenced by the magnetic field, is hypothesized to occur, but not observed in the simulations.

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