Mathematics of Environment Group


Locally the School collaborates with researchers in the School of Environmental Sciences and its associated Climate Research Unit. External collaborations include scientists at the Met OfficeNational Centre for Atmospheric ScienceNational Oceanography Centre and British Antarctic Survey.

Members of the School of Mathematics who conduct research in this area are: Mark Cooker, Paul Hammerton, Alexander Korobkin, Adrian Matthews, Emilian Parau, Davide Proment, Hayder Salman, and David Stevens. These researchers have a wide range of interests. Details of some of the past and present research areas are included below.


Predicting the climate is one of the grand challenges in science. The ocean is a vital component of the climate system due to the large heat capacity of sea water. The School has a long history in mathematical modelling of the oceans, with approaches ranging from idealised analytic models to large-scale numerical models. Current interests include the dynamics of the Southern Ocean, the Atlantic Meridional Overturning circulation and the numerical methods. The mathematical ideas are tested using observations and the mathematical modelling often informs sea-going observational campaigns. Modelling the oceans of recently discovered and hypothetical extra-solar planets is a new area of interest.

In meteorology the main focus is the physics and dynamics of the topical atmosphere and its teleconnections to higher latitudes. This includes the Madden-Julian Oscillation, Rossby Waves, scale interactions between the diurnal cycle and tropical weathers systems, diagonal convergence zones and ocean atmosphere coupling. Global coupled models of the ocean, atmosphere and cryosphere are used to understand natural and anthropogenic variability of the climate system and undertake experimental seasonal to decadal predictions.


Ocean waves are usually created by persistent winds blowing over the water surface. Momentum transfers from the wind into the wave motion. As they grow higher the waves become better wind catchers. But the waves can grow to a height so great that they overturn and break, even in the deep ocean. Another setting for breaking waves is when they approach the sea shore. The decrease in water depth over a submerged beach causes a general decrease in the wave speed. For a set of advancing waves, the deceleration in wave speed causes a shortening of the wavelength, and therefore an increase in wave surface slope. When the wave steepens too much, the wave breaks forwards onto the beach. Coastal structures are regularly subject to impacts from such breaking waves. There are especially violent flow conditions when a breaking wave hits a solid structure, such as a seawall or breakwater. Under the arch of a wave breaking on a beach the water can be moving at 4g (four times the acceleration due to gravity). But in the impact of a wave on a vertical wall the surface water can briefly accelerate to 4000g or more. Although a wave impact may last only a few milliseconds, very high pressures and forces can be exerted by the wave, like an impulsive hammer blow. The high water pressure is also able to penetrate cracks and gaps in the structure, because the water readily surges into openings in the form of violently accelerated jets.


Active volcanoes are a source of problems for many communities. For example, on the Caribbean Island of Monsterrat the ongoing growth of the volcanic lava dome of the Soufrière Hills Volcano has been associated with landslides. These landslides (or lahars) can be particularly severe and disruptive after heavy rainfall onto the hot ground surface. Mathematical modelling and computations have been carried out to show how the hot gases flow upwards through the porous volcanic rock. During rain, the rainwater percolates down through the rock pores, partially blocking the upward gas flow. There is a descending front of rainwater, and above it the counteracting flows of gas and water lead to a build-up of gas pressure deeper underground. The spatial gradient in the pressure can become big large enough to overcome the cohesion of the solid rock matrix - the surface of the ground could explode upwards. This kind of detailed modelling of complex flows, in space and time, can be valuable quantitative science. Measurements made at Montserrat provided evidence to support the hypotheses for the model, and data against which to check the mathematical and computational predictions.

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