SPEARS seminar - Nonlinear dynamics of zonal flows generated by turbulent wave-wave interaction
Prof Daniel McCarthy, Dean of Science and Technology, Southeastern Louisiana University, Hammond, USA
Monday 22 November 2010, 1600-1700
Marcus Merriman Lecture Theatre
The spontaneous generation of zonal (or averaged) flows in plasmas and fluids is an area of intense interest. The generalized Charney-Hawegawa-Mima equation (CHME) is one of the simplest models that has been able to predict many features of drift wave turbulence. In this work, we examine the generation of zonal flows within the CHME. We find that there exists a modulational instability in which two waves beat together and generate a zonal flow. This growth rate is developed analytically, and the dynamics of the system are explored numerically using a fully nonlinear finite difference code. We find that the saturation of the zonal flow can be explained analytically from the equation. We also find that while the waves are growing that a secondary, nonlinear instability dominates, and ends up increasing the linear growth rate of the slowest growing (long wavelength) modes by an order of magnitude, thus explaining why the these modes, which should be the weakest growing, are actually the strongest.