E-mail: edward.bolton@yale.edu

Computational Spherical Shell Convection

Convection in rotating and nonrotating spherical shells is of fundamental importance to outer-core convection and mantle convection, respectively. Mantle convection creates a lower thermal boundary layer which is spatially inhomogeneous. By continuity of heat flux, less heat is extracted from the outer core near upwelling mantle plumes than from regions where the mantle isotherms are compressed by the downwelling of relatively cool material. This creates a spatially inhomogeneous thermal boundary condition for outer-core convection. I have constructed numerical and experimental models to investigate outer core convection with thermal coupling at the outer boundary. The numerical (spectral) code is similar to the one I developed in my dissertation research, except that I allow full time-dependence. I have taken considerable pains to optimize the calculation of the nonlinear terms. By pre-summing repeated factors, I believe the code is competitive with mixed spectral/finite difference codes. Although it would be most relevant to impose spatially varying heat flux conditions, this turns out to be a difficult problem. Instead, I have imposed a temperature boundary condition. Although the core/mantle boundary is generally thought to be isothermal, the overall effect on core convection should be similar, whether the variable condition is for temperature or heat flux. The temperature at the outer spherical surface (core/mantle boundary) is specified as a constant plus a factor, E, times a low order spherical harmonic. Because the temperature varies laterally, fluid motion is forced. If E is large enough, the normally drifting thermal Rossby waves can become locked onto the inhomogeneity [Bolton and Sayler 1990, abst.].

I developed a code for temperature-dependent viscosity convection in a spherical shell, at infinite Prandtl number. Nonlinear model simulation results were used to calculate the expected anisotropy using a theory developed by Neil Ribe [Bolton and Park, 1991, abst.].

I also developed a code for convection and magnetic field generation in rotating, self-gravitating, spherical shells [Bolton, Ph.D. dissertation 1985]. This study was motivated by the problem of the geodynamo, and magnetic field generation in the major planets. The velocity, magnetic, and thermal fields are expanded in terms of spherical harmonics, and radial functions which satisfy the boundary conditions. We considered only traveling wave solutions. We were successful in finding nonlinear convection solutions over a wide range of parameter space, but solutions with magnetic fields eluded us.

Ph.D. DISSERTATION: Problems in Nonlinear Convection in Planar and Spherical Geometries, University of California, Los Angeles, (Advisor: F.H. Busse) 1985

E.W. Bolton and F.H. Busse, Nonlinear thermal convection in rotating spherical shells, paper presented on 4 Aug. 87 at the Nonlinear Dynamics of Rotating Magnetic Systems Conference at University of California, Los Angeles, 1987.

E.W. Bolton and F.H. Busse, Nonlinear thermal convection in rotating spherical shells, paper GA1.3-7 presented on 19 Aug. 87 at the International Union of Geodesy and Geophysics (IUGG) at Vancouver, Canada, 1987.

E.W. Bolton and B. Sayler, The influence of lateral variations of thermal boundary conditions on core convection: Numerical and laboratory experiments, presented at Santa Fe, Studies of the Earth's Deep Interior (SEDI) symposium, August, 1990.

E.W. Bolton and J. Park, The development of anisotropy in a convecting mantle, EOS, Trans of Am. Geoph. Union, 72, p. 508 of Fall 1991 AGU Meeting Supplement, 1991.