Predator prey oscillations in a simple cascade model of drift wave turbulence
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex (France)
A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separation for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.
- OSTI ID:
- 22047056
- Journal Information:
- Physics of Plasmas, Vol. 18, Issue 11; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
Similar Records
Weak hysteresis in a simplified model of the L-H transition
Direct identification of predator-prey dynamics in gyrokinetic simulations