| dc.description.abstracteng | Recent observations have revealed that we lack a fundamental understanding of the large scale (with spherical harmonic degrees $l < 60$) flows in the Sun. Flows at these large scales are strongly influenced by rotation. In this thesis, we report both observational detection and identification of a number of different types of inertial modes where the restoring force is the Coriolis force. We then use numerical techniques to investigate the modes, first in the linear regime where we investigate the effect of viscosity, superadiabaticity and latitudinal entropy gradients on the modes. We further proceed by identifying some of modes in fully non-linear 3D stratified convection simulations, and in mean-field simulations. The knowledge obtained in this thesis will help us to establish a novel method of using the inertial modes to probe the interior of the Sun, i.e., inertial mode helioseismology.
In particular, in Chapter 2, we report a comprehensive observational detection of the inertial modes on the Sun. With the help of linear-eigenmode calculations, we successfully identify three classes of solar inertial modes: the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. Since these modes are sensitive to properties of the deep convection zone, they give us a new diagnostic potential to learn about the deep interior of the Sun.
In Chapter 3, we develop a 2.5D numerical code to study the linear eigenmodes of rotating compressible fluid with the solar-like stratification. We take into account the effects of turbulent diffusion, entropy gradients, and helioseismically-constrained differential rotation in the Sun. We focus on the vorticity modes of oscillation in the inertial frequency range at low azimuthal orders, and show that the equatorial Rossby modes with one radial node ($n=1$) are essentially mixed with the north-south anti-symmetric columnar convective modes. We also find that when the we include turbulent viscosity at a level of about $10^{12}$ cm$^{2}$ s$^{-1}$ the radial eigenfunction of the $n=0$ Rossby modes very different from the theoretically-expected $r^{m}$ dependence and become confined near the base of the convection zone.
In Chapter 4, we carry out a numerical simulation of rotating turbulent convection in a stratified spherical shell to examine if the linear modes persist in this highly nonlinear regime. The code has been newly developed for this purpose and uses the reduced-speed of sound technique and a Yin-Yang grid. Various types of vorticity modes are extracted from the simulation data by performing a singular-value decomposition. The simulated power spectra and the extracted eigenfunctions are compared with the results of the linear analysis. We successfully identify both columnar convective modes and the equatorial Rossby modes in our simulation. North-south symmetric columnar convective modes contain the dominant velocity power and contribute substantially to the convective energy and angular momentum transport. Furthermore, we confirm the existence of the "mixed" modes between the $n=1$ Rossby modes and the north-south anti-symmetric columnar convective modes near the surface where convection is most vigorous. These results are in a qualitative agreement with our linear calculations.
In Chapter 5, we give a physical explanation for the high amplitudes of the observed high-latitude inertial modes on the Sun. We propose that they are driven by a baroclinic instability due to the latitudinal entropy gradient in the solar convection zone.
Chapter 6 is finally devoted to a development of the first three-dimensional magnetohydrodynamic(MHD) Babcock-Leighton-type solar dynamo code. In this framework, large-scale mean flows are maintained by the parameterized convective angular momentum transport ($\Lambda$-effect) without explicitly solving the thermal convection. We include a time-dependent random contribution in the $\Lambda$-effect which mimics the stochastic turbulent convective motions and can excite large-scale inertial modes. We successfully demonstrate that several inertial modes discussed above exist in this type of simulation. Therefore, our model can be potentially used to further study the effect of torsional oscillations, subsurface magnetic fields, and active region inflows on the Rossby and baroclinic modes. | de |