![]() In this case F is the electron distribution function in phase space, the corresponding advection equation is the Vlasov equation and the self-consistent constrain is the Poisson equation. Self-consistent chaotic transport in electron plasmas in the context of kinetic theory is also discussed. Numerical simulations show that the models capture the basic phenomenology of shear flow instability, vortex formation and relaxation typically observed in direct numerical simulations of the Navier-Stokes equation. From the dynamical systems perspective these models are useful because they provide relatively simple self-consistent Hamiltonians (streamfunctions) for the Lagrangian advection problem. ![]() The third model is an area preserving self-consistent map obtained from a space-time discretization of the single wave model. The first two models, the vorticity defect model and the single wave model, are constructed by successive simplifications of the vorticity-velocity coupling. To study this problem we consider three self-consistent more ยป models of intermediate complexity between the simple but limited kinematic chaotic advection models and the approach based on the direct numerical simulation of the Navier-Stokes equation.
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