CISL Annual Report 2005 > CISL research accomplishments

Geophysical Turbulence Program and Turbulence Numerics Team accomplishments

Turbulence refers to the complex behavior of fluid flow that happens at many different scales and in many different physical systems. One practical hallmark of turbulence is that small-scale motion can organize into larger scale features, such as eddies or vortices, and affect the flow at even much larger scales.

The Geophysical Turbulence Program (GTP) is a formal but loosely organized NCAR-wide activity to promote research, education, and awareness of geophysical turbulence at NCAR and in the scientific community. Besides a regular seminar series, GTP sponsors a summer workshop on a specific topic with this year being "Coherent structures in atmosphere and ocean."

The Turbulence Numerics Team (TNT) is complementary to GTP and is focused on the accurate simulation and understanding of turbulence for fluids, such as the atmosphere and for charged flows in the presence of magnetic fields. TNT research emphasizes simplified physical systems that still reproduce the complexity and multi-scale properties associated with turbulent flow.

GASpAR, for Geophysical and Astrophysical Spectral-element Adaptive Refinement, is an object oriented (C++) code that provides a framework for the accurate simulation of turbulent systems. The adaptive mesh refinement has the potential to increase the resolution of the simulation with only modest increases in computational resources. In addition to GASpAR-related projects, TNT has completed research on the interaction of shear forces on stratified environments, non-local aspects of turbulence in magnetohydrodymanic flows, and condensation under diffusive mixing.

The Geophysical and Astrophysical Spectral-element Adaptive Refinement (GASpAR) code is being developed at NCAR* for high-accuracy high-resolution simulations of geophysical turbulence and fluid dynamics. It has been tested thoroughly in two space dimensions** and is now being used to explore fundamental two-dimensional vortex interactions. This is a snapshot of simulated 2D Navier-Stokes flow at Reynolds number 20000, initialized in a state of three localized vortices (two positive, red and one negative, blue). Note that dynamic mesh refinement adapts to vortices (strong gradients) and vortex filaments. Each "spectral element" (black outlined box) contains polynomial expansions of degree 8, much higher than most adaptive mesh refinement codes. * by the Turbulence Numerics Team ** Rosenberg, Fournier, Fischer, and Pouquet 2005: math.NA/0507402 accepted at J. Comp. Phys.

The generation of magnetic fields in the universe (or dynamo effect) often takes place in fluids for which the magnetic Prandtl number P_M (i.e., the ratio of viscosity to magnetic resistivity) is not equal to unity, even though most computations to this day assume P_M=1 because it is easier to compute, and such three-dimensional computations are expensive already. For the liquid core of the earth or in the convection zone of the sun, P_M is one part in a million or smaller, as it is for liquid metals used in the laboratory to study dynamos. To study what happens when P_M<<1 requires computer resources well beyond what is available today.

Thus, the community at large needs models of small-scale behavior of turbulent flows in the presence of magnetic fields, like the ones that already exist for turbulent neutral fluids. In that light, we have studied a new model, the Lagrangian Averaged MHD (or LAMHD), to examine the dynamical behavior of coupled velocity and magnetic fields in what is called the magnetohydrodynamic (MHD) approximation. The model has been implemented in pseudospectral codes and tested in both two and three space dimensions. This model has shown significant savings in computing time and memory requirements. It may prove very useful for example in studying the geo-dynamo (Phys. Rev. E (2005) vol. 71, 046304 ).

Critical magnetic Reynolds number RMc as a function of kinetic Reynolds number RV for three mechanical forcings: Taylor-Green (crosses), Roberts (squares), and ABC (diamonds). Solid lines connect DNS, while dashed lines connect Lagrangian Averaged MHD model (LAMHD) simulations. As RV increases, the magnetic Prandtl number RM/RV decreases, the lowest value achieved here being 0.005 for the ABC flow computed using the LAMHD model, and validated using direct numerical simulations with a grid of 10,243 points.