Thursday 11 Feb 2016: Error Estimates and 2nd Order Corrections to Approximate Fluid Models (GAFD Seminar)
Dr Bin Cheng - University of Surrey
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.