Research Projects

Click on the titles, below, for more details.

    Oscillations in Theoretical Fluid Dynamics
  • columns I've been interested in wave and mean flow interaction for many years, especially the relationship between order (low-frequency structures) and chaos (fully developed turbulence), and am especially interested in the case when there are oscillations from waves present in the dynamics.

  • Numerical Analysis and Scientific Computing

    Recently I'm interested in time-parallel methods, how they interact with the type of flows we expect in the atmosphere and ocean, and their numerical analysis.

  • The Arctic Ocean

    The earth’s high latitudes are undergoing rapid changes due to climate warming. For example, in September 2007, 2.5 million km2 of seawater was exposed for the first time in many years. Because of the changing nature of theArctic Ocean, understanding its unique dynamics and thermodynamics is important for understanding impacts of changing sea ice cover on the circulation.

  • Lagrangian Averaged Navier-Stokes Alpha Models

    After more than a century of eddy viscosity or diffusivity models for representing the effects of the small scales on the large, a new type of time-reversible model of nonlinear effects has emerged.

  • Optimal Interpolation and Cubature - Fekete Points

    Global spectral methods give exponential convergence rates and have high accuracy for smooth solutions, but are global and used with simple domains. The spectral element method combines the geometric flexibility of the finite element method with the accuracy and efficiency of the spectral method. The usual implementation on triangles becomes ill-conditioned for degree (maximum degree of the polynomial) greater than about seven. Mark Taylor and I did some work on optimal interpolation on simplicies, especially Fekete points.