Magnetohydrodynamics (MHD) describes the macroscopic behavior of electrically conducting fluids. It has an important role in a variety of astrophysical systems. MHD turbulence is a state of randomly stirred conducting fluid in the limit of very small fluid viscosity and resistivity (we call this as high Reynolds number flows). Despite many years of research, the power law for the spectrum of MHD turbulence remains a subject of controversy. Sufficient resolution for studying high Reynolds number flows is still beyond the capability of even the most advanced supercomputers. Closures such as MHD-alpha turbulence model can help reduce this requirement. In this talk I will start by giving an overview of the theory of hydrodynamics of non-conducting fluids, with focus on how to derive the power laws of the energy spectra. Next, I will introduce the Navier-Stokes alpha equations, its success as a turbulence model and how it modifies the energy spectrum of the two- and three- dimensional turbulence. Finally, I will discuss how the theory is modified or extended in the case of MHD turbulence.
Wednesday, March 12, 2008
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9813