Stellar rotation plays an important role in maintaining the magnetic fields inside the stellar interior through convection, and starspots are the most visible manifestation of the interplay between stellar rotation rate and magnetic fields. It is revealed through high end observations of evolution of magnetic fields and rotation rate of the Sun and other solar type stars that they exhibit a wide range of variation among their rotation rates yet there are some common ingredients such as rotational shear, turbulent transport and various nonlinear transport mechanisms which contribute towards the evolution and maintenance of the magnetic activity displayed by them. Also, these observations provide us with valuable information about the dependence of differential rotation and magnetic activity on rotation rate of stars with different ages and different rotation rates. Thus, the main challenge in dynamo theory is to explain these observations which is in fact a very strenuous problem and is challenging to do with full MHD simulations due to the various constraints such as expensive computations in terms of time and resolution.
Therefore, it is useful to construct a simple parameterized model in order to understand the evolution of rotation rate and magnetic fields which can provide valuable insight into the various observations.
This thesis discusses the modelling of solar dynamo and spindown of solar-type stars by using ODE and the effect of shear in kinematic dynamo in full MHD. We propose a simple parameterized model to understand the effect of nonlinear transport coefficients as well as mean/fluctuating differential rotation in the generation and destruction of magnetic fields and their capability in the working of dynamo near marginal stability. This model is then utilised to discuss detailed dynamics to understand the self-regulation of magnetic fields in solar/stellar dynamo. This work is further extended to understand the spindown of solar-type stars where the angular momentum loss is dynamically prescribed via equation of evolution of rotation rate and magnetic fields. The results obtained from this model are consistent with observations.
Furthermore, regulatory behaviour of a kinematic dynamo by shear flow is investigated. Specifically, we study the induction equation by prescribing small scale velocity field to which a large scale radial/latitudinal shear is added in the direction of zonal flow. The results from numerical simulations are analysed and we conclude that the presence of large scale shear suppresses the small scale flows and results in quenching of a kinematic dynamo
