Videos

Separation of Time Scales with fast rotation and weak stratification and some ideas for exascale computing

Presenter
April 14, 2011
Keywords:
  • Artic ocean, projection operator, vortices, Taylor Proudman flows, separation of time scales
MSC:
  • 47A46
Abstract
Earth's high latitudes stand to be among the first regions affected by climate change issues due to changes induced by melting ice in the Arctic and Antarctic. Motivated by gaining fundamental understanding of ocean dynamics at high latitudes my collaborators and I have derived new equations, based on the method of multiple scales presented in Embid and Majda (1996,1998), that address the scale separation between slow- and fast-time scale dynamics in the limit of fast rotation while retaining order one affects due to stratification. The new slow equations and their conservation laws describe the {sl dynamics of Taylor-Proudman flows}. We also present numerical results that support the theory and that show the spontaneous creation of Taylor-Proudman columns. We also show recent measurements from the NSF Beaufort Gyre exploration program that show strong, deep columnar vortices with speeds as much as 30cm/s and which span the depth of the weakly stratified water column. The projection operators derived as a part of these results have mathematical and numerical implications for the development of time-stepping algorithms in next-generation exascale climate models.