Stochastic excitation of the solar oscillations by turbulent convection

Details Stochastic excitation of the solar oscillations by turbulent convection Stochastic excitation of the solar oscillations by turbulent convection

Jan 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phdt........24w&link_type=abstract

PhD Dissertation, California Inst. of Tech. Pasadena, CA United States

Astronomy and Astrophysics

Astrophysics

2

Solar Oscillations, Turbulence, Stochastic Processes, Mixing Length Flow Theory, Solar Observatories, Radiation Distribution, Plumes, Quadrupoles, Nonlinearity, Mathematical Models, Hamiltonian Functions, Boltzmann Distribution, Incompressible Fluids, Astrophysics

Scientific paper

The thesis topic is the stochastic excitation of the solar p-modes by turbulent convection, and the work consists of four parts: three theoretical sections and one observational. In the first section of the thesis, an explicit calculation of the acoustic radiation of a buoyant oscillating bubble is presented as a model for the excitation of the solar p-modes. The central scientific issue addressed in this work is the cancellation of monopole and dipole radiation fields in an anisotropic medium, first pointed out by Goldreich and Kumar (1990). When the bubble oscillation frequency is small compared to the acoustic cutoff, the monopole and dipole disturbances cancel to the quadrupole order in the far field. The second section deals with the role of convective structures in a wide number of problems, including the creation of acoustic disturbances, the transport of heat and magnetic fields, and the penetration of flows into stable layers of the atmosphere (overshoot). A model of plume convection is developed to discuss these issues. It is argued that the scaleheight-sized flows (the only energetically significant ones) are properly characterized as coherent, entropy-preserving plumes, in contradistinction to the picture of amorphous parcels of fluid suggested by the Mixing Length Theory, and in spite of the large Reynolds numbers typical in astrophysical convection. The third section of the thesis is an analysis of high-resolution surface velocity data taken with a magneto-optical filter on the 10 inch telescope at Big Bear Solar Observatory. Estimates are obtained for the frequencies and amplitudes of the solar oscillations of high spherical harmonic degree (l approximately less than 2000). The observed mode energies follow a Boltzmann distribution (P(E) varies as exp(-E/(bar-E)), as is predicted in the stochastic excitation model. In the final section of the thesis, a derivation of the variational principle for an incompressible fluid is presented. The Lagrange and Hamiltonian densities are calculated to third order in the displacement field, and these results are suitable to study the non-linear interactions among incompressible modes.

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