Mar 14, 2017 - Mar 14, 2017
15:00 - 18:00
This Maxwell Institute event will take place at ICMS, 15 South College Street, Edinburgh, EH8 9AA.
3:00-3:40 Bin Cheng (Surrey)
Error Estimates and 2nd Order Corrections to Approximate Fluid Models
In weather and climate studies/predictions, geophysical fluid dynamics (GFD) plays a central role across a wide range of temporal and spatial scales. Various constraints in multiscale simulation and observation make it necessary to enlist approximate fluid models which are typically “easier” to study and simulate and thus have long attracted the attention of theoretical and applied scientists alike. Notable examples include the incompressible approximation and quasi-geostrophic approximation. Part of this talk is proof-based analysis in getting sharp error estimates of some approximate models which essentially filters out the majority of fast waves. In this analysis, an important and difficult aspect is the physically relevant solid-wall boundary. Another part of this talk tries to establish connections to numerical analysis and geophysical studies. Approximate fluid models and their error estimates can make fundamental contribution to the development and refinement of next-generation weather/climate codes. These codes are essentially multiscale and ultimately aim at capturing GFD at regional scales, but such attempt is only meaningful if their performance at larger and longer scales are sufficiently close to the prediction of “easier” approximate models.
3:40–4:20 Ton S. van den Bremer (Edinburgh)
Experimental validations of various aspects of the wave-induced mean flow for surface gravity wave groups
For surface gravity wave groups, the well-known Stokes drift and transport are complemented by a set-down (or set-up) of the free surface and an Eulerian return flow first described by Longuet-Higgins & Stewart (1962). We present experimental validation the these classical second-order theoretical predictions for uni-directional wave groups in a laboratory flume at the University of Plymouth COAST-lab and for directionally spread wave groups in the University of Edinburgh FloWave facility. Firstly, we present detailed PTV (particle tracking velocimetry) measurements of the Lagrangian transport and trajectories of near-neutrally buoyant particles underneath two-dimensional surface gravity wave groups in a laboratory flume. By focussing our attention on wave groups of moderate steepness, we confirm the predictions of standard second-order multi-chromatic wave theory, in which the body of fluid satisfies the potential flow equations. Particles near the surface are transported forwards and their motion is dominated by Stokes drift. Particles at sufficient depth are transported backwards by the Eulerian return current. Secondly, we present detailed measurements of the surface elevation of the second-order long bound-waves in directionally spread groups. We demonstrate that the set-down becomes a set-up for sufficiently large degrees of directional spreading using measurements in the newly built FloWave facility.
4:30-5:10 Michael J.P. Cullen (Met Office)
The validity of approximate models for large–scale rotating stratified flows
This talk follows the theme of Bin Cheng’s talk. The analysis of models which approximate the Euler equations for rotating stratified flow in particular regimes is a valuable tool for designing useful numerical models of the full Euler equations which are used for operational weather and climate prediction. Most of the rigorous work on approximate models has considered cases where the solution of the Euler equations can be accurately decomposed into a ‘slow’ solution governed by a Lagrangian time-scale set by the fluid velocity and ‘fast’ wave solutions governed by a constant-coefficient wave equation. This decomposition, however, is not possible for many important cases such as the very large-scale flows simulated by climate models. The semi-geostrophic model is a formally valid ‘slow’ model in such regimes, and I present arguments showing how it may be possible to obtain a rigorous justification of this statement.