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Turbidity currents are large-scale natural phenomena that consist of suspended sed- iment travelling over an impermeable underlying boundary. We employ a shallow- layer approach to model their dynamics, taking advantage of the fact that their streamwise length is much larger than their vertical height. We frequently consider flows initiated by the instantaneous release of a finite volume of stationary material, known as a 'dam break' configuration. New complete analytical solutions of dam-break flows into a layer of quiescent fluid, or 'tailwater', are found. The tailwater's presence introduces new phenomena: after sufficient time the front of the flow decelerates and an internal bore develops. A model of polydisperse turbidity current motion is developed in which we con- serve interstitial fluid, momentum and particulate. To integrate our model we con- struct a new numerical scheme that is second-order accurate, simple to apply, shock- capturing and non-oscillatory. The scheme is validated by comparison with existing analytical results and employed in three ways. First, the effect that entrainment of ambient fluid and the gradient of the un- derlying boundary have on particle-driven gravity currents is derived through new scaling relationships. These highlight the role that these processes may have in large- scale geophysical flows and indicate why laboratory investigations at much smaller scales may not have needed to include these effects. The turbidity current formed by a lava dome collapse on the Soufriere Hills volcano, Montserrat in July 2003 is modelled next using no fitting parameters. We employ field data to inform our model and validate the output. Agreement is found for the predicted deposit thickness and aspects of the grain size distribution, thus our model effectively captures the key dynamical processes. Finally, new analytical self-similar solutions to entraining gravity currents on inclined planes are presented. We demonstrate that these are attractive solutions of the governing equations after sufficient time.

We describe a generalization of the Bernoulli inverse method, which produces an estimate of Sea Surface Height (SSH) across the region of interest rather than simply at station positions. Real-time ‘float’ observations and satellite altimetry measurements are used to map a ‘sea surface elevation’ to study the large-scale ocean circulation in the North Atlantic. The inverse has been applied to simulated Argo floats and satellite altimetry tracks in the Ocean Circulation and climate model (OCCAM). The Bernoulli inverse method predicts the SSH by finding geostrophic streamlines along which the Bernoulli function is conserved. These streamlines are defined where modified potential temperature and salinity are conserved. This predicted SSH is combined with that measured by the satellite altimetry. The revised method uses linear regression to give a surface solution for the region rather than solving the function at fixed positions, hence increasing the resolution of the problem by combining the altimetry measurements for the region. We will present results of a comparison study where real-time Argo and satellite altimetry have been used in combination with OCCAM using the same method to see how robust the solutions are for the NorthAtlantic.