## 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 = 10^{6} 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 = 10^{2}), we observe the Nu ∼ Ra^{2/7} 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 = 10^{4} and 10^{6} 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 ∼ Ra^{0.37} 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 = 10^{4} we observe the development of large-scale modulations along the direction of the magnetic field when Ra ≥ 6×10^{5}. For Q = 10^{4} and 6×10^{5} ≤Ra ≤ 10^{7} the Nu ∼ Ra^{2/7} 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 ∼ Ra^{1/3}; (2) a transitional region where 3D modulations begin and the heat transfer scaling law is reduced; and (3) anisotropic 3D convection with Nu ∼ Ra^{2/7} 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.

#### Recommended Citation

Al-Refae, Talal, "Numerical Simulations of Convection with a Horizontal Magnetic Field" (2019). *Undergraduate Honors Theses*. 1879.

https://scholar.colorado.edu/honr_theses/1879

#### Included in

Astrophysics and Astronomy Commons, Fluid Dynamics Commons, Geophysics and Seismology Commons, Numerical Analysis and Computation Commons