MPE Wednesday 11th December

Schedule: 

Prof Onno Bokhove ( School of Mathematics, University of Leeds): Maths is dangerous: on maths for flood mitigation and a new wave-energy device

Abstract: There is no connection between the two topics, (i) on the mathematics of a cost-effectiveness analysis for river-flood mitigation (a simple analysis) and (ii) on the mathematics of a new wave-energy device (an advanced analysis), except perhaps due to climate change. Under climate change more extreme rainfall is expected, which could result in more severe river flooding, as well as more intense storms, the latter which could result in increased wave action at sea leading to more wave energy and potential damage. Hence, both topics imply that protection is required to mitigate damage. (i) By analysing flood hydrographs (measured or simulated ones) and flood-mitigation plans, a team of scientists from Leeds and Grenoble has created a new and very straightforward graphical cost-effectiveness tool or diagnostic for every one, including experts, decision-makers and the general public. The diagnostic is based on Flood-Excess Volume (FEV) and Available Flood Storage Volume. In practice, the tool is now used in France and Slovenia, but not in the UK, regarding floods of the River Brague (in France) and River Sava near Ljubljana (in Slovenia), involving interactions of French and Slovenian scientists with stakeholders and the public. (ii) By deconstruction of three existing wave-energy devices and subsequent recombination, we have created a new wave-energy device ideally suited in a breakwater. It is based on the convergence of waves in a contraction, wave-activated and constrained buoy motion and a direct electromagnetic generator. In 2013, we established a working small-scale laboratory set-up and early 2019 we derived a complete wave-to-wire model, based on variational modelling augmented by the damping of the electrical circuits and the energy loss due to the power generation. The coupled hydrodynamics, fluid-body interactions and Maxwell’s equations (the latter under symmetry reduced to two ordinary-differential equations) for the electro-magnetic generator are solved together. Preliminary optimisation of the linearized system will be shown, with numerics based on compatible discretisations. References•  O.B., Mark Kelmanson, Tom Kent, Giullaume Piton, Jean-Marc Tacnet 2019: Communicating (nature-based) solutions using flood-excess volume for UK and French river floods. River Research and Applications 35, 1402-1414. https://onlinelibrary.wiley.com/doi/full/10.1002/rra.3507
•  O.B., Anna Kalogirou, Wout Zweers 2019: From bore-soliton-splash to a new wave-to-wire wave-energy model. Water Waves. Online: https://link.springer.com/article/10.1007/s42286-019-00022-9.

Joe Wallwork: Goal-Oriented Mesh Adaptation for Coastal Engineering Applications

Abstract: Coastal engineering applications, there is often a diagnostic quantity of interest (QoI) which we seek to accurately approximate, such as the power output of a tidal farm or the salinity at the intake pipe of a desalination plant. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this goal, using fewer computational resources than would be required by other methods, such as uniform refinement.
The theory of goal-oriented mesh adaptation for finite element methods is outlined, along with an implementation in the Thetis coastal ocean model. Results are presented for simulations of model tidal farms and desalination outfall scenarios. Convergence analysis indicates that the goal-oriented adaptation (in particular, anisotropic goal-oriented adaptation) strategy yields meshes which permit accurate QoI estimation using relatively few computational resources.

Adrian Leung: Impact of the mesoscale range on error growth and the limits to atmospheric predictability

Abstract: Global numerical weather prediction (NWP) models have begun to resolve the mesoscale k^(-5/3) range of the energy spectrum, which is known to impose an inherently finite range of deterministic predictability per se as errors develop more rapidly on these scales than on the larger scales.  However, the dynamics of these errors under the influence of the synoptic-scale k^(-3) range is little studied.  The present work examines the error growth behaviour under such a hybrid spectrum in Lorenz’s original model of 1969, and in a series of identical-twin perturbation experiments using an idealised two-dimensional barotropic turbulence model at a range of resolutions.  With the typical resolution of today’s global NWP ensembles, the quickening of error growth with decreasing spatial scale in the mesoscale range is found to be very modest compared to theoretical estimates for the k^(-5/3) spectrum, so that error growth remains largely uniform across scales.  The Lorenz model suggests that the strong predictability constraints pertaining to the k^(-5/3) range will not emerge until models become fully able to resolve features on a 2-kilometre scale.  Therefore, a much higher resolution than today’s best global NWP models is required to provide a realistic description of error growth and thus of the uncertainty in forecasts.