If you are a maths undergraduate at Leeds, then take a look at this document, which describes the key modules for those interested in environmental fluid dynamics. Some of these modules (e.g., Atmosphere and Ocean Dynamics (SOEE 2210)) are taught by the School of Earth and Environment. Within the School of Mathematics, the main offerings are
There are various sources of funding for undergraduates wishing to undertake short research projects over the summer.
Within the School of Mathematics, you could contact me if you are interested in applying for such a project on some aspect of atmosphere-ocean fluid dynamics.
Unfortunately, there is no funding from the School of Maths to support students on this programme, so you need to be able to pay your own tuition fees and maintenance. Some bursaries are available from the University -- visit the scholarships website and then select "taught postgraduate" and then "applied mathematics". Those based in the UK might also look at the government advice on funding for postgraduate study, which includes information on the new government postgraduate loan scheme, and career development loans. If you are coming from overseas, there may be scholarships associated with your home country; for example, if you are French, then take a look at the Entente Cordiale scholarships.
There are opportunities for talented and motivated students to undertake PhD research in geophysical fluid dynamics. If you might be interested in this, then please send me an e-mail, perhaps to arrange an informal discussion.
Such study either falls under the general remit of (i) PhD study in Applied Mathematics, the procedures for which are described on the postgraduate study pages of the School of Mathematics; (ii) PhD study as part of the University of Leeds NERC Doctoral Training Programme; or (iii) PhD study as part of the University of Leeds EPSRC Centre for Doctoral Training in Fluid Dynamics.
I am always keen to hear from young scientists who wish to undertake postdoctoral research in geophysical fluid dynamics. Although I have no dedicated funding for such study at present, it is possible to apply for a dedicated research fellowship, which can be matched to your research interests and those of the group here in Leeds. Such opportunities include funding from the European Union (via the Marie Curie European Fellowship Scheme, with an application deadline of 12th September 2018), or from the UK research councils of EPSRC and NERC. Possible project areas include instabilities in rotating stratified shear flows, nonlinear internal waves, large-scale tidal modelling, and internal tide generation and propagation -- or perhaps you can think of something more interesting. Since these fellowship applications take months to process, it is best to be making applications up to a year before your current position finishes.