Drift-ordered fluid vorticity equation with energy consistency
Although drift-ordered fluid models are widely applied in tokamak edge turbulence simulations, the models used are acknowledged not to conserve energy or even electrical charge. The present paper aims to remove many of the existing pitfalls in drift-fluid models, however, with the objective of finding a solution simple enough to be implemented in numerical applications. Our main result is an improved version of the drift-Braginskii equations involving a generalized vorticity function. In the new drift-Braginskii system, the quasi-neutrality condition translates into a transport equation for a generalized vorticity, expressed in conservation form, and related to the total mass-weighted circulation. It is found that kinetic energy conservation can be achieved if the polarization flow is defined recursively. In conclusion, the resulting model conserves the kinetic energy associated with EĆB and diamagnetic flows and retains the associated perpendicular kinetic energy flux.