My research focus is on improving understanding of estuarine dynamics using idealised models that make smart use of advanced mathematical techniques. More specific research interests in estuarine dynamics and mathematics are given below. My modelling work is combined in the iFlow modelling framework, of which I am the main developer.
I am interested in mechanisms that cause sediment trapping in estuaries and understanding the spatio-temporal patterns of sediment trapping. I am specifically interested in nonlinear dynamics of trapping of high sediment concentrations.
I am interested in mechanistic classification of salt intrusion: using a model to identify different balances of essential salt transport processes and describing their properties. Additionally I have a specific interest in exchange flows.
I have a particular interest in describing the types of pythoplankton patterns and properties such as timescales and limiting processes for different model choices.
Perturbation methods are a class of methods to simplify the solution of PDEs with weak nonlinearity or different timescales. In many PDEs one or several terms are much smaller than the other terms. My interest is in the practical use of perturbations to give insight into solutions of PDEs, e.g. by assisting the decomposition of various timescales and forcing processes.
Numerical bifurcation analysis is the application of continuation and bifurcation analysis to large-scale systems that can only be solved numerically. My interest is in the application of such techniques in systems of nonlinear PDEs implemented in different software modules and its use to classification of the behaviour of PDEs in a parameter space and tracking of branches of solutions with similar properties.
While I would consider modelling as the art of simplification, I would say mathematical modelling is the art of simplification in a systematic, structured, and motivated way. My interest is in developing models with gradually increasing complexity motivated by scaling laws and always building from existing understanding.