Quasi-modes and resonances in two-dimensional vortices with radial stratification
This project examines both the linear and nonlinear evolution of a two-dimensional axisymmetric vortex with a radial density stratification.
Start date1 October 2022
DurationMinimum of 3 years
Funding sourceUniversity of Surrey
Full UK tuition fees and a tax-free stipend. This project is on offer in competition with a number of other projects for funding. This opportunity may be available with partial funding for overseas fees for exceptional applicants. However, funding for overseas students is limited and applicants are encouraged to find suitable funding themselves.
This project examines both the linear and nonlinear evolution of a two-dimensional axisymmetric vortex with a radial density stratification. These vortices will be perturbed by axisymmetric vorticity perturbations, and by using linear stability analysis we can examine the existence of a critical layer within such vortices. In particular we are interested in critical layer positions which give a resonant response for the perturbation. These linear calculations will be supplemented by nonlinear simulations of the system under various forcing scenarios in order to identify when nonlinear structures persist for large times, or when the vortex returns to an axisymmetric state.
The successful candidate will receive comprehensive research training related to all aspects of the research and opportunities to participate in conferences, workshops and seminars to develop professional skills and research network.
Dixit, H. N. and Govindarajan, R. (2011) Stability of a vortex in radial density stratification: role of wave interactions. J. Fluid Mech. 679 582-615.
Applicants should have a minimum of a first class honours degree in mathematics, the physical sciences or engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, though exceptional BSc students will be considered.
English language requirements
IELTS minimum 6.5 or above (or equivalent) with 6.0 in each individual category
How to apply
Applications should be submitted via the Mathematics PhD Research programme page on the "Apply" tab. Please clearly state the studentship title and supervisor on your application.