  In this thesis, various studies are performed leading to better understanding
of the 11-year solar cycle and its theoretical modeling with the flux transport
dynamo model. Although this is primarily a theoretical thesis, there is a part
dealing with the analysis of observational data. The various proxies of solar
activity from various observatory including the sunspot area records of
Kodaikanal Observatory have been analyzed to study the irregular aspects of
solar cycles and an analysis has been carried out on the correlation between
the decay rate and the next cycle amplitude. Theoretical analysis starts with
explaining how the magnetic buoyancy has been treated in the flux transport
dynamo models, and advantages and disadvantages of different treatments. It is
found that some of the irregular properties of the solar cycle in the decaying
phase can only be well explained using a particular treatment of the magnetic
buoyancy. Next, the behavior of the dynamo with different spatial structures of
the meridional flow based on recent helioseismology results has been studied. A
theoretical model is constructed considering the back reaction due to the
Lorentz force on the meridional flows which explains the observed variation of
the meridional flow with the solar cycle. Finally, some results with 3D FTD
models are presented. This 3D model is developed to handle the Babcock-Leighton
mechanism and magnetic buoyancy more realistically than previous 2D models and
can capture some important effects connected with the subduction of the
magnetic field in polar regions, which are missed in 2D surface flux transport
models. This 3D model is further used to study the evolution of the magnetic
fields due to a turbulent non-axisymmetric velocity field and to compare the
results with the results obtained by using a simple turbulent diffusivity
coefficient.
