**Author: Beth Wingate**

**Title: Separation of Time Scales at high latitudes in rotating and stratified Flows**

**Biography: **

Beth Wingate graduated from the University of Michigan in 1996 where she studied climate science, scientific computing, and applied mathematics. She was an Advanced Studies Postdoc at the National Center for Atmospheric Research and has spent the rest of her professional career at LANL where she is a member of the COSIM project and the Center for Nonlinear Studies. Her work focuses on theory and modeling of high latitude dynamics and the development of numerical methods for ocean models.

**Abstract: **

Boundary value problems are ubiquitous in computational science and engineering. I will discuss two classes of problems: multigrid for stencil-based non-uniform discretizations on bounded regular geometries, and integral equation solvers for exterior problems in complex geometries. I will discuss the basic algorithmic components of the proposed methodologies and give an overview of the challenges associated with scaling them to large number of cores. I will give details for a common component, an octree data structure. In particular, I will explain the construction, coarsening/refining, and balancing of octrees. I will present scalability results on up to 32,000 cores.

The dynamics of the Arctic ocean can be characterized by a close proximity to the axis of rotation and weaker stratification than in other parts of the ocean. In this talk I show that ocean dynamics in regions like this can be described by new reduced equations whose character is very different from quasi-geostrophy. The theory, based on a slow/fast decomposition for the method of multiple scales, states that:

1. The horizontal dynamics reduces to the 2D Navier Stokes equations and has two conserved quantities, the horizontal kinetic energy and the horizontal vertical vorticity. This implies that the Arctic could have numerous barotropic vortices.

2. The flow is non hydrostatic in a special way. There is a component of the vertical velocity, but its dynamics is two-dimensional (vertically integrated) and forced by the vertical integral of the buoyancy. There is a conservation law for these dynamics that is an area integral over the vertical kinetic energy and the buoyancy (potential energy).

3. A key part of this is that the ratio of the slow total energy to the total energy remains constant in the absence of dissipation but that the ratio of the slow potential enstrophy relative to the total potential enstrophy goes to 1. This suggests that the potential enstrophy is the more important quantity to 'get right' and that there may be some important consequences for the turbulence cascade in the Arctic.

4. Some of these results are supported by the observations of Woodgate et al. (2001) who observed numerous barotropic (depth about 1000 meters) vortices in the Arctic.