Joseph Otieno Oloo, PhD in Applied Mathematics

Tell us about your research:

Understanding mixing in the uppermost part of the water column is crucial for modeling air-sea interaction. Specific mechanisms of mixing under strong wind conditions are poorly understood. Under strong winds entrainment of air bubbles into the water caused by intense surface wave breaking leads to the creation of multiphase flow of “bubbly” fluid adjacent to the surface. This makes the boundary layer in water density stratified. A stratified boundary layer supports gravity wave modes and vorticity mode.

Since there are arguments that vorticity mode dynamics is most interesting and important, we focus our attention on weakly nonlinear dynamics of the vorticity mode in a generic stratified boundary layer. Employing an asymptotic procedure utilizing smallness of the boundary layer thickness to the characteristic wavelength and smallness of the inverse Reynolds number we derive a nonlinear evolution equation with a pseudo-differential dispersion term taking into account viscosity and weak stratification effects in the boundary layer. It has been shown within the framework of the model that a wide class of initial conditions leads to blow-up, that is a (sufficiently large) initial perturbation becomes more and more localized and its amplitude becomes infinite in finite time. In practice, this means an intense mixing and even destruction of the boundary layer.

The work opens a new perspective on the laminar-turbulent transition of the boundary layers (homogeneous, stratified, 3-dimensional), provides new mechanisms of understanding the dynamics of the upper ocean under strong wind conditions, improve wave and climate modeling and also to improve the understanding of mixing and turbulence in the uppermost ocean.

In principle, I like this area of wave modeling because it provides a link on how the beauty of Mathematics could be applied to understand the challenges we face and possibly come up with justifiable models to investigate and understand physical processes underpinning water wave motion.

I chose this area due to its potential relevance to my country Kenya. Kenya’s economy heavily depends on the sea in many different ways. Sea lanes provide the main conduit for trade, tourism (the largest foreign exchange earning sector) source gravitates towards the shores, fishing provides livelihood to thousands of people, and exploitation of off-shore oil resources has the potential to provide a boost to the economy.

The Lake Victoria inland waters play a major role in the transportation of goods and people. Smaller vessels used by fishermen and for lake transport and fishing are particularly vulnerable to storms. Lives are being lost, properties destroyed due to lack of precise and timely information on waves. To minimize the loss of life and address the bottlenecks of Kenya’s economy a reliable wave forecasting is vital. Despite this necessity in Kenya wave modeling and forecasting have not been given enough attention. The aim of this research project is to improve wave modeling and forecasting and then to apply the findings in Kenya.

What do you plan to do after Keele?

First, the primary goal is to advance the knowledge on this field by engaging in research to publish articles in peer-reviewed journals, teach and initiate advanced courses more specifically asymptotic techniques/Computational methods that are specifically lacking in my country Kenya. I will also continue to work closely with my Supervisor Prof. Victor Shrira because of his international reputation and expertise in this field of nonlinear wave modeling.

What training did you find useful at Keele?

1. Course on how to conduct a systematic literature review using well-known databases that university has subscribed to.
2. Supervisor Student relationship.
3. Professional counseling support.
4. Academic writing workshops.
5. Faculty of Natural Science symposiums.
6. Financial support to attend international conferences
7. Professional international Student support.
8. Research grant writing techniques.