The Turbulence Numerics Team

Progress in the understanding of turbulent flows is somewhat limited, except in the experimental and observational domains. Following Moore's law of doubling of computing power every 18 months, doubling the grid resolution in three dimensions occurs every six years, so direct numerical simulations (DNS) of turbulence advance slowly in Reynolds number (Re). This, and the fact that turbulent behavior may be dominated by intermittent structures, are the driving forces behind one of the main objectives of the team, i.e. to develop adaptive mesh refinement codes for the community. Combining such codes, in a quasi-DNS way, with different kinds of modeling, where hopefully the behavior of the flow at a given Re (in contrast to the limit of large Re) can be approached, represent our main directions of research.

In this context, the work in TNT is organized around two main themes.
In a nutshell, we develop both tools and models that enhance our capability to investigate turbulence, and we apply these tools and models to specific projects. The applications cover two broad areas: (1) we pursue our investigations of homogeneous and isotropic turbulence at the highest possible Reynolds numbers and/or incorporating new phenomena (specifically this year, rotation); and (2) we begin exploring turbulent flows with boundaries at moderate Re.
The software development pertains to the NCAR priority concerning highly scalable numerical tools for geophysical flows, in particular in the context of the Data Center project at NCAR and the Petascale Computing Initiative at NSF.

The forte of the team may be in the investigation of the dynamics of turbulent flows, in particular when coupled to magnetic fields, with applications to the generation of such fields (the dynamo problem, e.g., in the context of the Earth and the Sun), and to solar-terrestrial interactions in the Solar Wind, both issues being NCAR priorities as well. It is also in the dialectic approach of considering different flows and contrasting their properties, in the hope of learning from both what is universal and what is specific to a given configuration in a parameter space that is large. The challenge is to pursue this approach incorporating realistic conditions that pertain to the many facets of geophysical turbulence, as per the agenda of NCAR. We deal more with fundamental geophysics than applied mathematics, but one driving force of our research is indeed to give the applied mathematics community the most accurate data at the highest possible Reynolds number possible.
In so doing, it relates for example to the Clay Institute challenge for the 21st century, of the existence (or not) of a Navier-Stokes singularity, a problem that can be extended to MHD with important applications as for example the heating of the solar corona and the production of Coronal Mass Ejections, as currently observed and modeled at HAO in novel ways.

The staff in TNT is composed of

• Aimé Fournier (Project Scientist)
• Ed Lee (Graduate Student in Applied Mathematics at Columbia University)
• Pablo Mininni (Senior Post-Doc, on an NSF-CMG grant)
• Jonathan Pietarila Graham (Graduate Student in Applied Mathematics at CU; on an NSF-CMG grant)
• Annick Pouquet (Section head, 50% of the time and Senior Scientist; the other 50% is spent as Deputy Director of the Earth and Sun System Laboratory, on indirect funds)
• Duane Rosenberg (Software Engineer)
• Alex Alexakis (ASP Post-doc until August 31st (2006)
• Jai Sukhatme (ASP Post-doc until January 15th (2006).

The main focus areas of TNT, with emphasis on present developments, can be found in the white paper.